U.S. patent application number 16/038914 was filed with the patent office on 2018-11-29 for frequency division multiplexing for wireless power providers.
The applicant listed for this patent is CPG Technologies, LLC. Invention is credited to James F. Corum, Kenneth L. Corum, Michael J. D'Aurelio, Basil F. Pinzone, JR..
Application Number | 20180342879 16/038914 |
Document ID | / |
Family ID | 55455747 |
Filed Date | 2018-11-29 |
United States Patent
Application |
20180342879 |
Kind Code |
A1 |
Corum; James F. ; et
al. |
November 29, 2018 |
FREQUENCY DIVISION MULTIPLEXING FOR WIRELESS POWER PROVIDERS
Abstract
Disclosed are various embodiments for frequency-division
multiplexing for wireless power providers using Zenneck surface
waveguide probes to transmit power. Zenneck surface waveguide
probes may transmit power on multiple frequencies with potentially
overlapping service areas. Frequency-agile Zenneck surface wave
receivers may tune to one or more frequencies. Cost, availability,
and/or other information may be provided to the Zenneck surface
wave receivers. Power usage may be reported by the Zenneck surface
wave receivers to power providers.
Inventors: |
Corum; James F.;
(Morgantown, WV) ; Corum; Kenneth L.; (Plymouth,
NH) ; Pinzone, JR.; Basil F.; (Newbury, OH) ;
D'Aurelio; Michael J.; (Marietta, GA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CPG Technologies, LLC |
Italy |
TX |
US |
|
|
Family ID: |
55455747 |
Appl. No.: |
16/038914 |
Filed: |
July 18, 2018 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
14849246 |
Sep 9, 2015 |
10033198 |
|
|
16038914 |
|
|
|
|
62049232 |
Sep 11, 2014 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01Q 1/00 20130101; H02J
5/005 20130101; H02J 7/025 20130101; H02J 50/20 20160201; H04B 3/52
20130101; H01P 3/00 20130101 |
International
Class: |
H02J 5/00 20160101
H02J005/00; H01Q 1/00 20060101 H01Q001/00; H02J 7/02 20160101
H02J007/02; H02J 50/20 20160101 H02J050/20; H01P 3/00 20060101
H01P003/00 |
Claims
1. An apparatus, comprising: a Zenneck surface wave receive
structure configured to obtain electrical energy from a Zenneck
surface wave traveling along a terrestrial medium; an electrical
load coupled to the Zenneck surface wave receive structure, the
electrical load being experienced as a load at an excitation source
coupled to a Zenneck surface waveguide probe generating the Zenneck
surface wave; and control circuitry configured to at least:
determine a frequency upon which the electrical energy is being
transmitted; and tune the electrical load to receive the electrical
energy on the frequency.
2. The apparatus of claim 1, wherein the control circuitry is
further configured to at least send a request for access to the
electrical energy at the frequency to a power provider system.
3. The apparatus of claim 1, wherein the control circuitry is
further configured to at least report a unique identifier of the
apparatus to a power provider system.
4. The apparatus of claim 1, wherein the control circuitry is
further configured to at least: determine a plurality of
frequencies upon which electrical energy is being transmitted; and
select the frequency from the plurality of frequencies.
5. The apparatus of claim 1, wherein the control circuitry is
further configured to at least: determine a second frequency upon
which electrical energy is being transmitted; and retune the
electrical load to receive the electrical energy on the second
frequency instead of or in addition to the frequency.
6. The apparatus of claim 1, wherein the control circuitry is
further configured to at least determine the frequency based at
least in part on a frequency scan performed by the apparatus.
7. The apparatus of claim 1, wherein the control circuitry is
further configured to at least: monitor the electrical energy
consumed by the electrical load; and report a power usage metric to
a power provider system.
8. The apparatus of claim 1, wherein the control circuitry is
further capable of receiving data modulated upon the Zenneck
surface wave.
9. The apparatus of claim 1, further comprising a load modulator
configured to transmit a data signal to the Zenneck surface
waveguide probe by modulating the electrical load.
10. The apparatus of claim 1, wherein the control circuitry is
further configured to transmit data to a power provider system via
a network.
11. The apparatus of claim 1, wherein the control circuitry is
further configured to at least: determine a current location of the
apparatus; and receive data indicating a location of the Zenneck
surface waveguide probe and a corresponding frequency used by the
Zenneck surface waveguide probe to transmit electrical energy; and
wherein the frequency is determined based at least in part on the
current location of the apparatus, the location of the Zenneck
surface waveguide probe, and the corresponding frequency used by
the Zenneck surface waveguide probe to transmit the electrical
energy.
12. An apparatus, comprising: a first Zenneck surface waveguide
probe configured to transmit electrical energy on a first
frequency, the first Zenneck surface waveguide probe having a first
service area; and a second Zenneck surface waveguide probe
configured to transmit electrical energy on a second frequency, the
second Zenneck surface waveguide probe having a second service
area, wherein the first service area overlaps the second service
area at an overlapping service area.
13. The apparatus of claim 12, further comprising a wireless power
receiver system located in the overlapping service area, the
wireless power receiver system being capable of selectively
receiving the electrical energy transmitted by the first Zenneck
surface waveguide probe or the electrical energy transmitted by the
second Zenneck surface waveguide probe.
14. The apparatus of claim 12, wherein the first service area
differs in size from the second service area.
15. The apparatus of claim 12, wherein each of the first Zenneck
surface waveguide probe and the Zenneck surface waveguide probe are
configured to establish an electric field having a wave tilt
corresponding to a wave illuminating a surface of a lossy
conducting medium at a complex Brewster angle.
16. The apparatus of claim 12, wherein the first Zenneck surface
waveguide probe and the second Zenneck surface waveguide probe are
co-located.
17. A method, comprising: receiving, via a computing device
comprising a processor and a memory, a request from a Zenneck
surface wave receiver to consume electrical energy; determining,
via the computing device, that a particular power provider of a
plurality of power providers has available capacity to service the
request; and directing, via the computing device, the Zenneck
surface wave receiver to tune to a corresponding power transmission
frequency upon which the particular power provider transmits
electrical energy via a Zenneck surface waveguide probe.
18. The method of claim 17, further comprising determining an
aggregate load of the particular power provider by measuring a
current at a ground stake of the Zenneck surface waveguide
probe.
19. The method of claim 17, further comprising determining a
location of the Zenneck surface wave receiver, wherein the
particular power provider is determined based at least in part on
the location of the Zenneck surface wave receiver.
20. The method of claim 17, further comprising adjusting a
generating capacity of the particular power provider to accommodate
an electrical load of the Zenneck surface wave receiver.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of, and claims priority
to, co-pending U.S. Patent Application entitled "FREQUENCY DIVISION
MULTIPLEXING FOR WIRELESS POWER PROVIDERS," filed on Sep. 9, 2015,
and assigned application Ser. No. 14/849,246, which claims the
benefit of, and priority to, U.S. Provisional Patent Application
No. 62/049,232 entitled "FREQUENCY DIVISION MULTIPLEXING FOR
WIRELESS POWER PROVIDERS" filed on Sep. 11, 2014, both of which are
incorporated herein by reference in their entireties.
[0002] This application is related to co-pending U.S.
Non-provisional Patent Application entitled "Excitation and Use of
Guided Surface Wave Modes on Lossy Media," which was filed on Mar.
7, 2013 and assigned application Ser. No. 13/789,538, and was
published on Sep. 11, 2014 as Publication Number US2014/0252886 A1,
and which is incorporated herein by reference in its entirety. This
application is also related to co-pending U.S. Non-provisional
Patent Application entitled "Excitation and Use of Guided Surface
Wave Modes on Lossy Media," which was filed on Mar. 7, 2013 and
assigned application Ser. No. 13/789,525, and was published on Sep.
11, 2014 as Publication Number US2014/0252865 A1, and which is
incorporated herein by reference in its entirety. This application
is further related to co-pending U.S. Non-provisional Patent
Application entitled "Excitation and Use of Guided Surface Wave
Modes on Lossy Media," which was filed on Sep. 10, 2014 and
assigned application Ser. No. 14/483,089, and which is incorporated
herein by reference in its entirety. This application is further
related to co-pending U.S. Non-provisional Patent Application
entitled "Excitation and Use of Guided Surface Waves," which was
filed on Jun. 2, 2015 and assigned application Ser. No. 14/728,507,
and which is incorporated herein by reference in its entirety. This
application is further related to co-pending U.S. Non-provisional
Patent Application entitled "Excitation and Use of Guided Surface
Waves," which was filed on Jun. 2, 2015 and assigned application
Ser. No. 14/728,492, and which is incorporated herein by reference
in its entirety.
BACKGROUND
[0003] For over a century, signals transmitted by radio waves
involved radiation fields launched using conventional antenna
structures. In contrast to radio science, electrical power
distribution systems in the last century involved the transmission
of energy guided along electrical conductors. This understanding of
the distinction between radio frequency (RF) and power transmission
has existed since the early 1900's.
BRIEF DESCRIPTION OF THE DRAWINGS
[0004] Many aspects of the present disclosure can be better
understood with reference to the following drawings. The components
in the drawings are not necessarily to scale, emphasis instead
being placed upon clearly illustrating the principles of the
disclosure. Moreover, in the drawings, like reference numerals
designate corresponding parts throughout the several views.
[0005] FIG. 1 is a chart that depicts field strength as a function
of distance for a guided electromagnetic field and a radiated
electromagnetic field.
[0006] FIG. 2 is a drawing that illustrates a propagation interface
with two regions employed for transmission of a guided surface wave
according to various embodiments of the present disclosure.
[0007] FIG. 3 is a drawing that illustrates a guided surface
waveguide probe disposed with respect to a propagation interface of
FIG. 2 according to various embodiments of the present
disclosure.
[0008] FIG. 4 is a plot of an example of the magnitudes of close-in
and far-out asymptotes of first order Hankel functions according to
various embodiments of the present disclosure.
[0009] FIGS. 5A and 5B are drawings that illustrate a complex angle
of incidence of an electric field synthesized by a guided surface
waveguide probe according to various embodiments of the present
disclosure.
[0010] FIG. 6 is a graphical representation illustrating the effect
of elevation of a charge terminal on the location where the
electric field of FIG. 5A intersects with the lossy conducting
medium at a Brewster angle according to various embodiments of the
present disclosure.
[0011] FIG. 7 is a graphical representation of an example of a
guided surface waveguide probe according to various embodiments of
the present disclosure.
[0012] FIGS. 8A through 8C are graphical representations
illustrating examples of equivalent image plane models of the
guided surface waveguide probe of FIGS. 3 and 7 according to
various embodiments of the present disclosure.
[0013] FIGS. 9A and 9B are graphical representations illustrating
examples of single-wire transmission line and classic transmission
line models of the equivalent image plane models of FIGS. 8B and 8C
according to various embodiments of the present disclosure.
[0014] FIG. 10 is a flow chart illustrating an example of adjusting
a guided surface waveguide probe of FIGS. 3 and 7 to launch a
guided surface wave along the surface of a lossy conducting medium
according to various embodiments of the present disclosure.
[0015] FIG. 11 is a plot illustrating an example of the
relationship between a wave tilt angle and the phase delay of a
guided surface waveguide probe of FIGS. 3 and 7 according to
various embodiments of the present disclosure.
[0016] FIG. 12 is a drawing that illustrates an example of a guided
surface waveguide probe according to various embodiments of the
present disclosure.
[0017] FIG. 13 is a graphical representation illustrating the
incidence of a synthesized electric field at a complex Brewster
angle to match the guided surface waveguide mode at the Hankel
crossover distance according to various embodiments of the present
disclosure.
[0018] FIG. 14 is a graphical representation of an example of a
guided surface waveguide probe of FIG. 12 according to various
embodiments of the present disclosure.
[0019] FIG. 15A includes plots of an example of the imaginary and
real parts of a phase delay (.PHI..sub.U) of a charge terminal
T.sub.1 of a guided surface waveguide probe according to various
embodiments of the present disclosure.
[0020] FIG. 15B is a schematic diagram of the guided surface
waveguide probe of FIG. 14 according to various embodiments of the
present disclosure.
[0021] FIG. 16 is a drawing that illustrates an example of a guided
surface waveguide probe according to various embodiments of the
present disclosure.
[0022] FIG. 17 is a graphical representation of an example of a
guided surface waveguide probe of FIG. 16 according to various
embodiments of the present disclosure.
[0023] FIGS. 18A through 18C depict examples of receiving
structures that can be employed to receive energy transmitted in
the form of a guided surface wave launched by a guided surface
waveguide probe according to the various embodiments of the present
disclosure.
[0024] FIG. 18D is a flow chart illustrating an example of
adjusting a receiving structure according to various embodiments of
the present disclosure.
[0025] FIG. 19 depicts an example of an additional receiving
structure that can be employed to receive energy transmitted in the
form of a guided surface wave launched by a guided surface
waveguide probe according to the various embodiments of the present
disclosure.
[0026] FIGS. 20A-E depict examples of various schematic symbols
that are used with reference to embodiments of the present
disclosure.
[0027] FIG. 21 depicts one example of a geographic area served by a
plurality of wireless power providers according to various
embodiments of the present disclosure.
[0028] FIG. 22 shows one example of a receiver system according to
various embodiments of the present disclosure.
[0029] FIG. 23 shows a networked environment according to various
embodiments of the present disclosure.
[0030] FIG. 24 shows one example of a receiver system according to
various embodiments of the present disclosure.
[0031] FIG. 25 shows one example of a receiver system according to
various embodiments of the present disclosure.
[0032] FIG. 26 shows a wireless power provider according to various
embodiments of the present disclosure.
[0033] FIGS. 27 and 28 are flowcharts that provide examples of the
operation of portions of a power provider system according to
various embodiments of the present disclosure.
[0034] FIG. 29 is a flowchart that provides one example of the
operation of a portion of the receiver system of FIG. 22 according
to various embodiments of the present disclosure.
[0035] FIG. 30 is a schematic block diagram of a power provider
system according to an embodiment of the present disclosure.
[0036] FIG. 31 is a schematic block diagram of a power meter
according to an embodiment of the present disclosure.
DETAILED DESCRIPTION
[0037] To begin, some terminology shall be established to provide
clarity in the discussion of concepts to follow. First, as
contemplated herein, a formal distinction is drawn between radiated
electromagnetic fields and guided electromagnetic fields.
[0038] As contemplated herein, a radiated electromagnetic field
comprises electromagnetic energy that is emitted from a source
structure in the form of waves that are not bound to a waveguide.
For example, a radiated electromagnetic field is generally a field
that leaves an electric structure such as an antenna and propagates
through the atmosphere or other medium and is not bound to any
waveguide structure. Once radiated electromagnetic waves leave an
electric structure such as an antenna, they continue to propagate
in the medium of propagation (such as air) independent of their
source until they dissipate regardless of whether the source
continues to operate. Once electromagnetic waves are radiated, they
are not recoverable unless intercepted, and, if not intercepted,
the energy inherent in the radiated electromagnetic waves is lost
forever. Electrical structures such as antennas are designed to
radiate electromagnetic fields by maximizing the ratio of the
radiation resistance to the structure loss resistance. Radiated
energy spreads out in space and is lost regardless of whether a
receiver is present. The energy density of the radiated fields is a
function of distance due to geometric spreading. Accordingly, the
term "radiate" in all its forms as used herein refers to this form
of electromagnetic propagation.
[0039] A guided electromagnetic field is a propagating
electromagnetic wave whose energy is concentrated within or near
boundaries between media having different electromagnetic
properties. In this sense, a guided electromagnetic field is one
that is bound to a waveguide and may be characterized as being
conveyed by the current flowing in the waveguide. If there is no
load to receive and/or dissipate the energy conveyed in a guided
electromagnetic wave, then no energy is lost except for that
dissipated in the conductivity of the guiding medium. Stated
another way, if there is no load for a guided electromagnetic wave,
then no energy is consumed. Thus, a generator or other source
generating a guided electromagnetic field does not deliver real
power unless a resistive load is present. To this end, such a
generator or other source essentially runs idle until a load is
presented. This is akin to running a generator to generate a 60
Hertz electromagnetic wave that is transmitted over power lines
where there is no electrical load. It should be noted that a guided
electromagnetic field or wave is the equivalent to what is termed a
"transmission line mode." This contrasts with radiated
electromagnetic waves in which real power is supplied at all times
in order to generate radiated waves. Unlike radiated
electromagnetic waves, guided electromagnetic energy does not
continue to propagate along a finite length waveguide after the
energy source is turned off. Accordingly, the term "guide" in all
its forms as used herein refers to this transmission mode of
electromagnetic propagation.
[0040] Referring now to FIG. 1, shown is a graph 100 of field
strength in decibels (dB) above an arbitrary reference in volts per
meter as a function of distance in kilometers on a log-dB plot to
further illustrate the distinction between radiated and guided
electromagnetic fields. The graph 100 of FIG. 1 depicts a guided
field strength curve 103 that shows the field strength of a guided
electromagnetic field as a function of distance. This guided field
strength curve 103 is essentially the same as a transmission line
mode. Also, the graph 100 of FIG. 1 depicts a radiated field
strength curve 106 that shows the field strength of a radiated
electromagnetic field as a function of distance.
[0041] Of interest are the shapes of the curves 103 and 106 for
guided wave and for radiation propagation, respectively. The
radiated field strength curve 106 falls off geometrically (1/d,
where d is distance), which is depicted as a straight line on the
log-log scale. The guided field strength curve 103, on the other
hand, has a characteristic exponential decay of e.sup.-.alpha.d/
{square root over (d)} exhibits a distinctive knee 109 on the
log-log scale. The guided field strength curve 103 and the radiated
field strength curve 106 intersect at point 112, which occurs at a
crossing distance. At distances less than the crossing distance at
intersection point 112, the field strength of a guided
electromagnetic field is significantly greater at most locations
than the field strength of a radiated electromagnetic field. At
distances greater than the crossing distance, the opposite is true.
Thus, the guided and radiated field strength curves 103 and 106
further illustrate the fundamental propagation difference between
guided and radiated electromagnetic fields. For an informal
discussion of the difference between guided and radiated
electromagnetic fields, reference is made to Milligan, T., Modern
Antenna Design, McGraw-Hill, 1.sup.st Edition, 1985, pp. 8-9, which
is incorporated herein by reference in its entirety.
[0042] The distinction between radiated and guided electromagnetic
waves, made above, is readily expressed formally and placed on a
rigorous basis. That two such diverse solutions could emerge from
one and the same linear partial differential equation, the wave
equation, analytically follows from the boundary conditions imposed
on the problem. The Green function for the wave equation, itself,
contains the distinction between the nature of radiation and guided
waves.
[0043] In empty space, the wave equation is a differential operator
whose eigenfunctions possess a continuous spectrum of eigenvalues
on the complex wave-number plane. This transverse electro-magnetic
(TEM) field is called the radiation field, and those propagating
fields are called "Hertzian waves." However, in the presence of a
conducting boundary, the wave equation plus boundary conditions
mathematically lead to a spectral representation of wave-numbers
composed of a continuous spectrum plus a sum of discrete spectra.
To this end, reference is made to Sommerfeld, A., "Uber die
Ausbreitung der Wellen in der Drahtlosen Telegraphie," Annalen der
Physik, Vol. 28, 1909, pp. 665-736. Also see Sommerfeld, A.,
"Problems of Radio," published as Chapter 6 in Partial Differential
Equations in Physics--Lectures on Theoretical Physics: Volume VI,
Academic Press, 1949, pp. 236-289, 295-296; Collin, R. E.,
"Hertzian Dipole Radiating Over a Lossy Earth or Sea: Some Early
and Late 20.sup.th Century Controversies," IEEE Antennas and
Propagation Magazine, Vol. 46, No. 2, April 2004, pp. 64-79; and
Reich, H. J., Ordnung, P. F, Krauss, H. L., and Skalnik, J. G.,
Microwave Theory and Techniques, Van Nostrand, 1953, pp. 291-293,
each of these references being incorporated herein by reference in
its entirety.
[0044] The terms "ground wave" and "surface wave" identify two
distinctly different physical propagation phenomena. A surface wave
arises analytically from a distinct pole yielding a discrete
component in the plane wave spectrum. See, e.g., "The Excitation of
Plane Surface Waves" by Cullen, A. L., (Proceedings of the IEE
(British), Vol. 101, Part IV, August 1954, pp. 225-235). In this
context, a surface wave is considered to be a guided surface wave.
The surface wave (in the Zenneck-Sommerfeld guided wave sense) is,
physically and mathematically, not the same as the ground wave (in
the Weyl-Norton-FCC sense) that is now so familiar from radio
broadcasting. These two propagation mechanisms arise from the
excitation of different types of eigenvalue spectra (continuum or
discrete) on the complex plane. The field strength of the guided
surface wave decays exponentially with distance as illustrated by
curve 103 of FIG. 1 (much like propagation in a lossy waveguide)
and resembles propagation in a radial transmission line, as opposed
to the classical Hertzian radiation of the ground wave, which
propagates spherically, possesses a continuum of eigenvalues, falls
off geometrically as illustrated by curve 106 of FIG. 1, and
results from branch-cut integrals. As experimentally demonstrated
by C. R. Burrows in "The Surface Wave in Radio Propagation over
Plane Earth" (Proceedings of the IRE, Vol. 25, No. 2, February,
1937, pp. 219-229) and "The Surface Wave in Radio Transmission"
(Bell Laboratories Record, Vol. 15, June 1937, pp. 321-324),
vertical antennas radiate ground waves but do not launch guided
surface waves.
[0045] To summarize the above, first, the continuous part of the
wave-number eigenvalue spectrum, corresponding to branch-cut
integrals, produces the radiation field, and second, the discrete
spectra, and corresponding residue sum arising from the poles
enclosed by the contour of integration, result in non-TEM traveling
surface waves that are exponentially damped in the direction
transverse to the propagation. Such surface waves are guided
transmission line modes. For further explanation, reference is made
to Friedman, B., Principles and Techniques of Applied Mathematics,
Wiley, 1956, pp. pp. 214, 283-286, 290, 298-300.
[0046] In free space, antennas excite the continuum eigenvalues of
the wave equation, which is a radiation field, where the outwardly
propagating RF energy with E.sub.z and H.sub..phi. in-phase is lost
forever. On the other hand, waveguide probes excite discrete
eigenvalues, which results in transmission line propagation. See
Collin, R. E., Field Theory of Guided Waves, McGraw-Hill, 1960, pp.
453, 474-477. While such theoretical analyses have held out the
hypothetical possibility of launching open surface guided waves
over planar or spherical surfaces of lossy, homogeneous media, for
more than a century no known structures in the engineering arts
have existed for accomplishing this with any practical efficiency.
Unfortunately, since it emerged in the early 1900's, the
theoretical analysis set forth above has essentially remained a
theory and there have been no known structures for practically
accomplishing the launching of open surface guided waves over
planar or spherical surfaces of lossy, homogeneous media.
[0047] According to the various embodiments of the present
disclosure, various guided surface waveguide probes are described
that are configured to excite electric fields that couple into a
guided surface waveguide mode along the surface of a lossy
conducting medium. Such guided electromagnetic fields are
substantially mode-matched in magnitude and phase to a guided
surface wave mode on the surface of the lossy conducting medium.
Such a guided surface wave mode can also be termed a Zenneck
waveguide mode. By virtue of the fact that the resultant fields
excited by the guided surface waveguide probes described herein are
substantially mode-matched to a guided surface waveguide mode on
the surface of the lossy conducting medium, a guided
electromagnetic field in the form of a guided surface wave is
launched along the surface of the lossy conducting medium.
According to one embodiment, the lossy conducting medium comprises
a terrestrial medium such as the Earth.
[0048] Referring to FIG. 2, shown is a propagation interface that
provides for an examination of the boundary value solutions to
Maxwell's equations derived in 1907 by Jonathan Zenneck as set
forth in his paper Zenneck, J., "On the Propagation of Plane
Electromagnetic Waves Along a Flat Conducting Surface and their
Relation to Wireless Telegraphy," Annalen der Physik, Serial 4,
Vol. 23, Sep. 20, 1907, pp. 846-866. FIG. 2 depicts cylindrical
coordinates for radially propagating waves along the interface
between a lossy conducting medium specified as Region 1 and an
insulator specified as Region 2. Region 1 can comprise, for
example, any lossy conducting medium. In one example, such a lossy
conducting medium can comprise a terrestrial medium such as the
Earth or other medium. Region 2 is a second medium that shares a
boundary interface with Region 1 and has different constitutive
parameters relative to Region 1. Region 2 can comprise, for
example, any insulator such as the atmosphere or other medium. The
reflection coefficient for such a boundary interface goes to zero
only for incidence at a complex Brewster angle. See Stratton, J.
A., Electromagnetic Theory, McGraw-Hill, 1941, p. 516.
[0049] According to various embodiments, the present disclosure
sets forth various guided surface waveguide probes that generate
electromagnetic fields that are substantially mode-matched to a
guided surface waveguide mode on the surface of the lossy
conducting medium comprising Region 1. According to various
embodiments, such electromagnetic fields substantially synthesize a
wave front incident at a complex Brewster angle of the lossy
conducting medium that can result in zero reflection.
[0050] To explain further, in Region 2, where an e.sup.j.omega.t
field variation is assumed and where .rho..noteq.0 and z.gtoreq.0
(with z being the vertical coordinate normal to the surface of
Region 1, and .rho. being the radial dimension in cylindrical
coordinates), Zenneck's closed-form exact solution of Maxwell's
equations satisfying the boundary conditions along the interface
are expressed by the following electric field and magnetic field
components:
H 2 .phi. = Ae - u 2 z H 1 ( 2 ) ( - j .gamma. .rho. ) , ( 1 ) E 2
.rho. = A ( u 2 j .omega. o ) e - u 2 z H 1 ( 2 ) ( - j .gamma.
.rho. ) , and ( 2 ) E 2 z = A ( - .gamma. .omega. o ) e - u 2 z H 0
( 2 ) ( - j .gamma. .rho. ) . ( 3 ) ##EQU00001##
[0051] In Region 1, where the e.sup.j.omega.t field variation is
assumed and where .rho..noteq.0 and z.ltoreq.0, Zenneck's
closed-form exact solution of Maxwell's equations satisfying the
boundary conditions along the interface is expressed by the
following electric field and magnetic field components:
H 1 .phi. = Ae u 1 z H 1 ( 2 ) ( - j .gamma. .rho. ) , ( 4 ) E 1
.rho. = A ( - u 1 .sigma. 1 + j .omega. 1 ) e u 1 z H 1 ( 2 ) ( - j
.gamma. .rho. ) , and ( 5 ) E 1 z = A ( - j .gamma. .sigma. 1 + j
.omega. 1 ) e u 1 z H 0 ( 2 ) ( - j .gamma. .rho. ) . ( 6 )
##EQU00002##
[0052] In these expressions, z is the vertical coordinate normal to
the surface of Region 1 and .rho. is the radial coordinate,
H.sub.n.sup.(2)(-j.gamma..rho.) is a complex argument Hankel
function of the second kind and order n, u.sub.1 is the propagation
constant in the positive vertical (z) direction in Region 1,
u.sub.2 is the propagation constant in the vertical (z) direction
in Region 2, .sigma..sub.1 is the conductivity of Region 1, .omega.
is equal to 2.pi.f, where f is a frequency of excitation,
.epsilon..sub.o is the permittivity of free space, .epsilon..sub.1
is the permittivity of Region 1, A is a source constant imposed by
the source, and .gamma. is a surface wave radial propagation
constant.
[0053] The propagation constants in the .+-.z directions are
determined by separating the wave equation above and below the
interface between Regions 1 and 2, and imposing the boundary
conditions. This exercise gives, in Region 2,
u 2 = - jk o 1 + ( r - jx ) ( 7 ) ##EQU00003##
and gives, in Region 1,
u.sub.1=-u.sub.2(.epsilon..sub.r-jx). (8)
The radial propagation constant .gamma. is given by
.gamma. = j k o 2 + u 2 2 = j k o n 1 + n 2 , ( 9 )
##EQU00004##
which is a complex expression where n is the complex index of
refraction given by
n= {square root over (.epsilon..sub.r-jx)}. (10)
In all of the above Equations,
x = .sigma. 1 .omega. o , and ( 11 ) k o = .omega. .mu. o o =
.lamda. o 2 .pi. , ( 12 ) ##EQU00005##
where .epsilon..sub.r comprises the relative permittivity of Region
1, .sigma..sub.1 is the conductivity of Region 1, .epsilon..sub.o
is the permittivity of free space, and .mu..sub.o comprises the
permeability of free space. Thus, the generated surface wave
propagates parallel to the interface and exponentially decays
vertical to it. This is known as evanescence.
[0054] Thus, Equations (1)-(3) can be considered to be a
cylindrically-symmetric, radially-propagating waveguide mode. See
Barlow, H. M., and Brown, J., Radio Surface Waves, Oxford
University Press, 1962, pp. 10-12, 29-33. The present disclosure
details structures that excite this "open boundary" waveguide mode.
Specifically, according to various embodiments, a guided surface
waveguide probe is provided with a charge terminal of appropriate
size that is fed with voltage and/or current and is positioned
relative to the boundary interface between Region 2 and Region 1.
This may be better understood with reference to FIG. 3, which shows
an example of a guided surface waveguide probe 200a that includes a
charge terminal T.sub.1 elevated above a lossy conducting medium
203 (e.g., the Earth) along a vertical axis z that is normal to a
plane presented by the lossy conducting medium 203. The lossy
conducting medium 203 makes up Region 1, and a second medium 206
makes up Region 2 and shares a boundary interface with the lossy
conducting medium 203.
[0055] According to one embodiment, the lossy conducting medium 203
can comprise a terrestrial medium such as the planet Earth. To this
end, such a terrestrial medium comprises all structures or
formations included thereon whether natural or man-made. For
example, such a terrestrial medium can comprise natural elements
such as rock, soil, sand, fresh water, sea water, trees,
vegetation, and all other natural elements that make up our planet.
In addition, such a terrestrial medium can comprise man-made
elements such as concrete, asphalt, building materials, and other
man-made materials. In other embodiments, the lossy conducting
medium 203 can comprise some medium other than the Earth, whether
naturally occurring or man-made. In other embodiments, the lossy
conducting medium 203 can comprise other media such as man-made
surfaces and structures such as automobiles, aircraft, man-made
materials (such as plywood, plastic sheeting, or other materials)
or other media.
[0056] In the case where the lossy conducting medium 203 comprises
a terrestrial medium or Earth, the second medium 206 can comprise
the atmosphere above the ground. As such, the atmosphere can be
termed an "atmospheric medium" that comprises air and other
elements that make up the atmosphere of the Earth. In addition, it
is possible that the second medium 206 can comprise other media
relative to the lossy conducting medium 203.
[0057] The guided surface waveguide probe 200a includes a feed
network 209 that couples an excitation source 212 to the charge
terminal T.sub.1 via, e.g., a vertical feed line conductor.
According to various embodiments, a charge Q.sub.1 is imposed on
the charge terminal T.sub.1 to synthesize an electric field based
upon the voltage applied to terminal T.sub.1 at any given instant.
Depending on the angle of incidence (.theta..sub.i) of the electric
field (E), it is possible to substantially mode-match the electric
field to a guided surface waveguide mode on the surface of the
lossy conducting medium 203 comprising Region 1.
[0058] By considering the Zenneck closed-form solutions of
Equations (1)-(6), the Leontovich impedance boundary condition
between Region 1 and Region 2 can be stated as
{circumflex over (z)}.times..sub.2(.rho.,.phi.,0)=.sub.s, (13)
where {circumflex over (z)} is a unit normal in the positive
vertical (+z) direction and .sub.2 is the magnetic field strength
in Region 2 expressed by Equation (1) above. Equation (13) implies
that the electric and magnetic fields specified in Equations
(1)-(3) may result in a radial surface current density along the
boundary interface, where the radial surface current density can be
specified by
J.sub..rho.(.rho.')=-AH.sub.1.sup.(2)(-j.gamma..rho.') (14)
where A is a constant. Further, it should be noted that close-in to
the guided surface waveguide probe 200 (for .rho.<<.lamda.),
Equation (14) above has the behavior
J close ( .rho. ' ) = - A ( j 2 ) .pi. ( - j .gamma. .rho. ' ) = -
H .phi. = - I o 2 .pi. .rho. ' . ( 15 ) ##EQU00006##
The negative sign means that when source current (I.sub.o) flows
vertically upward as illustrated in FIG. 3, the "close-in" ground
current flows radially inward. By field matching on
H.sub..phi."close-in," it can be determined that
A = - I o .gamma. 4 = - .omega. q 1 .gamma. 4 ( 16 )
##EQU00007##
where q.sub.1=C.sub.1V.sub.1, in Equations (1)-(6) and (14).
Therefore, the radial surface current density of Equation (14) can
be restated as
J .rho. ( .rho. ' ) = I o .gamma. 4 H 1 ( 2 ) ( - j .gamma. .rho. '
) . ( 17 ) ##EQU00008##
The fields expressed by Equations (1)-(6) and (17) have the nature
of a transmission line mode bound to a lossy interface, not
radiation fields that are associated with groundwave propagation.
See Barlow, H. M. and Brown, J., Radio Surface Waves, Oxford
University Press, 1962, pp. 1-5.
[0059] At this point, a review of the nature of the Hankel
functions used in Equations (1)-(6) and (17) is provided for these
solutions of the wave equation. One might observe that the Hankel
functions of the first and second kind and order n are defined as
complex combinations of the standard Bessel functions of the first
and second kinds
H.sub.n.sup.(1)(x)=J.sub.n(x)+jN.sub.n(x), and (18)
H.sub.n.sup.(2)(x)=J.sub.n(x)-jN.sub.n(x), and (19)
These functions represent cylindrical waves propagating radially
inward (H.sub.n.sup.(1)) and outward (H.sub.n.sup.(2)),
respectively. The definition is analogous to the relationship
e.sup..+-.jx=cos.times.j sin x. See, for example, Harrington, R.
F., Time-Harmonic Fields, McGraw-Hill, 1961, pp. 460-463.
[0060] That H.sub.n.sup.(2)(k.sub..rho..phi. is an outgoing wave
can be recognized from its large argument asymptotic behavior that
is obtained directly from the series definitions of J.sub.n(x) and
N.sub.n(x). Far-out from the guided surface waveguide probe:
H n ( 2 ) ( x ) .fwdarw. x .fwdarw. .infin. 2 j .pi. x j n e - jx =
2 .pi. x j n e - j ( x - .pi. 4 ) , ( 20 a ) ##EQU00009##
[0061] which, when multiplied by e.sup.j.omega.t, is an outward
propagating cylindrical wave of the form e.sup.j(.omega.t-k.rho.)
with a 1/ {square root over (.rho.)} spatial variation. The first
order (n=1) solution can be determined from Equation (20a) to
be
H 1 ( 2 ) ( x ) .fwdarw. x .fwdarw. .infin. j 2 j .pi. x e - jx = 2
.pi. x e - j ( x - x 2 - .pi. 4 ) . ( 20 b ) ##EQU00010##
Close-in to the guided surface waveguide probe (for
p<<.lamda.), the Hankel function of first order and the
second kind behaves as
H 1 ( 2 ) ( x ) .fwdarw. x .fwdarw. 0 2 j .pi. x . ( 21 )
##EQU00011##
Note that these asymptotic expressions are complex quantities. When
x is a real quantity, Equations (20b) and (21) differ in phase by
{square root over (j)} which corresponds to an extra phase advance
or "phase boost" of 45.degree. or, equivalently, .lamda./8. The
close-in and far-out asymptotes of the first order Hankel function
of the second kind have a Hankel "crossover" or transition point
where they are of equal magnitude at a distance of
.rho.=R.sub.x.
[0062] Thus, beyond the Hankel crossover point the "far out"
representation predominates over the "close-in" representation of
the Hankel function. The distance to the Hankel crossover point (or
Hankel crossover distance) can be found by equating Equations (20b)
and (21) for -j.gamma..rho., and solving for R.sub.x. With
x=.sigma./.omega..epsilon..sub.o, it can be seen that the far-out
and close-in Hankel function asymptotes are frequency dependent,
with the Hankel crossover point moving out as the frequency is
lowered. It should also be noted that the Hankel function
asymptotes may also vary as the conductivity (.sigma.) of the lossy
conducting medium changes. For example, the conductivity of the
soil can vary with changes in weather conditions.
[0063] Referring to FIG. 4, shown is an example of a plot of the
magnitudes of the first order Hankel functions of Equations (20b)
and (21) for a Region 1 conductivity of .sigma.=0.010 mhos/m and
relative permittivity .epsilon..sub.r=15, at an operating frequency
of 1850 kHz. Curve 115 is the magnitude of the far-out asymptote of
Equation (20b) and curve 118 is the magnitude of the close-in
asymptote of Equation (21), with the Hankel crossover point 121
occurring at a distance of R.sub.x=54 feet. While the magnitudes
are equal, a phase offset exists between the two asymptotes at the
Hankel crossover point 121. It can also be seen that the Hankel
crossover distance is much less than a wavelength of the operation
frequency.
[0064] Considering the electric field components given by Equations
(2) and (3) of the Zenneck closed-form solution in Region 2, it can
be seen that the ratio of E.sub.z and E.sub..rho. asymptotically
passes to
E z E .rho. = ( - j .gamma. u 2 ) H 0 ( 2 ) ( - j .gamma. .rho. ) H
1 ( 2 ) ( - j .gamma. .rho. ) .fwdarw. .rho. .fwdarw. .infin. r - j
.sigma. .omega. o = n = tan .theta. i , ( 22 ) ##EQU00012##
where n is the complex index of refraction of Equation (10) and
.theta..sub.i is the angle of incidence of the electric field. In
addition, the vertical component of the mode-matched electric field
of Equation (3) asymptotically passes to
E 2 z .fwdarw. .rho. .fwdarw. .infin. ( q free o ) .gamma. 3 8 .pi.
e - u 2 z e - j ( .gamma. .rho. - .pi. / 4 ) .rho. , ( 23 )
##EQU00013##
which is linearly proportional to free charge on the isolated
component of the elevated charge terminal's capacitance at the
terminal voltage, q.sub.free=C.sub.free.times.V.sub.T.
[0065] For example, the height H.sub.1 of the elevated charge
terminal T.sub.1 in FIG. 3 affects the amount of free charge on the
charge terminal T.sub.1. When the charge terminal T.sub.1 is near
the ground plane of Region 1, most of the charge Q.sub.1 on the
terminal is "bound." As the charge terminal T.sub.1 is elevated,
the bound charge is lessened until the charge terminal T.sub.1
reaches a height at which substantially all of the isolated charge
is free.
[0066] The advantage of an increased capacitive elevation for the
charge terminal T.sub.1 is that the charge on the elevated charge
terminal T.sub.1 is further removed from the ground plane,
resulting in an increased amount of free charge q.sub.free to
couple energy into the guided surface waveguide mode. As the charge
terminal T.sub.1 is moved away from the ground plane, the charge
distribution becomes more uniformly distributed about the surface
of the terminal. The amount of free charge is related to the
self-capacitance of the charge terminal T.sub.1.
[0067] For example, the capacitance of a spherical terminal can be
expressed as a function of physical height above the ground plane.
The capacitance of a sphere at a physical height of h above a
perfect ground is given by
C.sub.elevated
sphere=4.pi..epsilon..sub.oa(1+M+M.sup.2+M.sup.3+2M.sup.4+3M.sup.5+
. . . ), (24)
where the diameter of the sphere is 2a, and where M=a/2h with h
being the height of the spherical terminal. As can be seen, an
increase in the terminal height h reduces the capacitance C of the
charge terminal. It can be shown that for elevations of the charge
terminal T.sub.1 that are at a height of about four times the
diameter (4D=8a) or greater, the charge distribution is
approximately uniform about the spherical terminal, which can
improve the coupling into the guided surface waveguide mode.
[0068] In the case of a sufficiently isolated terminal, the
self-capacitance of a conductive sphere can be approximated by
C=4.pi..epsilon..sub.oa, where a is the radius of the sphere in
meters, and the self-capacitance of a disk can be approximated by
C=8.epsilon..sub.oa, where a is the radius of the disk in meters.
The charge terminal T.sub.1 can include any shape such as a sphere,
a disk, a cylinder, a cone, a torus, a hood, one or more rings, or
any other randomized shape or combination of shapes. An equivalent
spherical diameter can be determined and used for positioning of
the charge terminal T.sub.1.
[0069] This may be further understood with reference to the example
of FIG. 3, where the charge terminal T.sub.1 is elevated at a
physical height of h.sub.p=H.sub.1 above the lossy conducting
medium 203. To reduce the effects of the "bound" charge, the charge
terminal T.sub.1 can be positioned at a physical height that is at
least four times the spherical diameter (or equivalent spherical
diameter) of the charge terminal T.sub.1 to reduce the bounded
charge effects.
[0070] Referring next to FIG. 5A, shown is a ray optics
interpretation of the electric field produced by the elevated
charge Q.sub.1 on charge terminal T.sub.1 of FIG. 3. As in optics,
minimizing the reflection of the incident electric field can
improve and/or maximize the energy coupled into the guided surface
waveguide mode of the lossy conducting medium 203. For an electric
field (.epsilon..sub..parallel.) that is polarized parallel to the
plane of incidence (not the boundary interface), the amount of
reflection of the incident electric field may be determined using
the Fresnel reflection coefficient, which can be expressed as
.GAMMA. .parallel. ( .theta. i ) = E .parallel. , R E .parallel. ,
i = ( r - jx ) - sin 2 .theta. i - ( r - jx ) cos .theta. i ( r -
jx ) - sin 2 .theta. i + ( r - jx ) cos .theta. i , ( 25 )
##EQU00014##
where .theta..sub.i is the conventional angle of incidence measured
with respect to the surface normal.
[0071] In the example of FIG. 5A, the ray optic interpretation
shows the incident field polarized parallel to the plane of
incidence having an angle of incidence of .theta..sub.i, which is
measured with respect to the surface normal ({circumflex over
(z)}). There will be no reflection of the incident electric field
when .GAMMA..sub..parallel.(.theta..sub.i)=0 and thus the incident
electric field will be completely coupled into a guided surface
waveguide mode along the surface of the lossy conducting medium
203. It can be seen that the numerator of Equation (25) goes to
zero when the angle of incidence is
.theta..sub.i=arctan( {square root over
(.epsilon..sub.r-jx)})=.theta..sub.i,B, (26)
where x=.sigma./.omega..epsilon..sub.o. This complex angle of
incidence (.theta..sub.i,B) is referred to as the Brewster angle.
Referring back to Equation (22), it can be seen that the same
complex Brewster angle (.theta..sub.i,B) relationship is present in
both Equations (22) and (26).
[0072] As illustrated in FIG. 5A, the electric field vector E can
be depicted as an incoming non-uniform plane wave, polarized
parallel to the plane of incidence. The electric field vector E can
be created from independent horizontal and vertical components
as
(.theta..sub.i)=E.sub..rho.{circumflex over
(.rho.)}+E.sub.z{circumflex over (z)}. (27)
Geometrically, the illustration in FIG. 5A suggests that the
electric field vector E can be given by
E .rho. ( .rho. , z ) = E ( .rho. , z ) cos .theta. i , and ( 28 a
) E z ( .rho. , z ) = E ( .rho. , z ) cos ( .pi. 2 - .theta. i ) =
E ( .rho. , z ) sin .theta. i , ( 28 b ) ##EQU00015##
which means that the field ratio is
E .rho. E z = 1 tan .theta. i = tan .psi. i . ( 29 )
##EQU00016##
[0073] A generalized parameter W, called "wave tilt," is noted
herein as the ratio of the horizontal electric field component to
the vertical electric field component given by
W = E .rho. E z = W e j .PSI. , or ( 30 a ) 1 W = E z E .rho. = tan
.theta. i = 1 W e - j .PSI. , ( 30 b ) ##EQU00017##
which is complex and has both magnitude and phase. For an
electromagnetic wave in Region 2, the wave tilt angle (.psi.) is
equal to the angle between the normal of the wave-front at the
boundary interface with Region 1 and the tangent to the boundary
interface. This may be easier to see in FIG. 5B, which illustrates
equi-phase surfaces of an electromagnetic wave and their normals
for a radial cylindrical guided surface wave. At the boundary
interface (z=0) with a perfect conductor, the wave-front normal is
parallel to the tangent of the boundary interface, resulting in
W=0. However, in the case of a lossy dielectric, a wave tilt W
exists because the wave-front normal is not parallel with the
tangent of the boundary interface at z=0.
[0074] Applying Equation (30b) to a guided surface wave gives
tan .theta. i , B = E z E .rho. = u 2 .gamma. = r - jx = n = 1 W =
1 W e - j .PSI. . ( 31 ) ##EQU00018##
With the angle of incidence equal to the complex Brewster angle
(.theta..sub.i,B), the Fresnel reflection coefficient of Equation
(25) vanishes, as shown by
.GAMMA. .parallel. ( .theta. i , B ) = ( r - jx ) - sin 2 .theta. i
- ( r - jx ) cos .theta. i ( r - jx ) - sin 2 .theta. i + ( r - jx
) cos .theta. i .theta. i = .theta. i , B = 0. ( 32 )
##EQU00019##
By adjusting the complex field ratio of Equation (22), an incident
field can be synthesized to be incident at a complex angle at which
the reflection is reduced or eliminated. Establishing this ratio as
n= {square root over (.epsilon..sub.r-jx)} results in the
synthesized electric field being incident at the complex Brewster
angle, making the reflections vanish.
[0075] The concept of an electrical effective height can provide
further insight into synthesizing an electric field with a complex
angle of incidence with a guided surface waveguide probe 200. The
electrical effective height (h.sub.eff) has been defined as
h eff = 1 I 0 .intg. 0 h p I ( z ) dz ( 33 ) ##EQU00020##
for a monopole with a physical height (or length) of h.sub.p. Since
the expression depends upon the magnitude and phase of the source
distribution along the structure, the effective height (or length)
is complex in general. The integration of the distributed current
I(z) of the structure is performed over the physical height of the
structure (h.sub.p), and normalized to the ground current (I.sub.0)
flowing upward through the base (or input) of the structure. The
distributed current along the structure can be expressed by
I(z)=I.sub.C cos(.beta..sub.0z), (34)
where .beta..sub.0 is the propagation factor for current
propagating on the structure. In the example of FIG. 3, I.sub.C is
the current that is distributed along the vertical structure of the
guided surface waveguide probe 200a.
[0076] For example, consider a feed network 209 that includes a low
loss coil (e.g., a helical coil) at the bottom of the structure and
a vertical feed line conductor connected between the coil and the
charge terminal T.sub.1. The phase delay due to the coil (or
helical delay line) is .theta..sub.C=.beta..sub.pl.sub.C, with a
physical length of l.sub.C and a propagation factor of
.beta. p = 2 .pi. .lamda. p = 2 .pi. V f .lamda. 0 , ( 35 )
##EQU00021##
where V.sub.f is the velocity factor on the structure,
.lamda..sub.0 is the wavelength at the supplied frequency, and
.lamda..sub.p is the propagation wavelength resulting from the
velocity factor V.sub.f. The phase delay is measured relative to
the ground (stake) current I.sub.0.
[0077] In addition, the spatial phase delay along the length
l.sub.w of the vertical feed line conductor can be given by
.theta..sub.y=.beta..sub.wl.sub.w where .beta..sub.w is the
propagation phase constant for the vertical feed line conductor. In
some implementations, the spatial phase delay may be approximated
by .theta..sub.y=.beta..sub.wh.sub.p, since the difference between
the physical height h.sub.p of the guided surface waveguide probe
200a and the vertical feed line conductor length l.sub.w is much
less than a wavelength at the supplied frequency (.lamda..sub.0).
As a result, the total phase delay through the coil and vertical
feed line conductor is .PHI.=.theta..sub.c+.theta..sub.y, and the
current fed to the top of the coil from the bottom of the physical
structure is
I.sub.C(.theta..sub.c+.theta..sub.y)=I.sub.0e.sup.j.PHI., (36)
with the total phase delay .PHI. measured relative to the ground
(stake) current I.sub.0. Consequently, the electrical effective
height of a guided surface waveguide probe 200 can be approximated
by
h eff = 1 I 0 .intg. 0 h p I 0 e j .PHI. cos ( .beta. 0 z ) dz
.apprxeq. h p e j .PHI. , ( 37 ) ##EQU00022##
for the case where the physical height
h.sub.p<<.lamda..sub.0. The complex effective height of a
monopole, h.sub.eff=h.sub.p at an angle (or phase shift) of .PHI.,
may be adjusted to cause the source fields to match a guided
surface waveguide mode and cause a guided surface wave to be
launched on the lossy conducting medium 203.
[0078] In the example of FIG. 5A, ray optics are used to illustrate
the complex angle trigonometry of the incident electric field (E)
having a complex Brewster angle of incidence (.theta..sub.i,B) at
the Hankel crossover distance (R.sub.x) 121. Recall from Equation
(26) that, for a lossy conducting medium, the Brewster angle is
complex and specified by
tan .theta. i , B = r - j .sigma. .omega. o = n . ( 38 )
##EQU00023##
Electrically, the geometric parameters are related by the
electrical effective height (h.sub.eff) of the charge terminal
T.sub.1 by
R.sub.x tan
.psi..sub.i,B=R.sub.x.times.W=h.sub.eff=h.sub.pe.sup.j.PHI.,
(39)
where .psi..sub.i,B=(.pi./2)-.theta..sub.i,B is the Brewster angle
measured from the surface of the lossy conducting medium. To couple
into the guided surface waveguide mode, the wave tilt of the
electric field at the Hankel crossover distance can be expressed as
the ratio of the electrical effective height and the Hankel
crossover distance
h eff R x = tan .psi. i , B = W Rx . ( 40 ) ##EQU00024##
Since both the physical height (h.sub.p) and the Hankel crossover
distance (R.sub.x) are real quantities, the angle (.psi.) of the
desired guided surface wave tilt at the Hankel crossover distance
(R.sub.x) is equal to the phase (.PHI.) of the complex effective
height (h.sub.eff). This implies that by varying the phase at the
supply point of the coil, and thus the phase shift in Equation
(37), the phase, .PHI., of the complex effective height can be
manipulated to match the angle of the wave tilt, .psi., of the
guided surface waveguide mode at the Hankel crossover point 121:
.PHI.=.psi..
[0079] In FIG. 5A, a right triangle is depicted having an adjacent
side of length R.sub.x along the lossy conducting medium surface
and a complex Brewster angle .psi..sub.i,B measured between a ray
124 extending between the Hankel crossover point 121 at R.sub.x and
the center of the charge terminal T.sub.1, and the lossy conducting
medium surface 127 between the Hankel crossover point 121 and the
charge terminal T.sub.1. With the charge terminal T.sub.1
positioned at physical height h.sub.p and excited with a charge
having the appropriate phase delay .PHI., the resulting electric
field is incident with the lossy conducting medium boundary
interface at the Hankel crossover distance R.sub.x, and at the
Brewster angle. Under these conditions, the guided surface
waveguide mode can be excited without reflection or substantially
negligible reflection.
[0080] If the physical height of the charge terminal T.sub.1 is
decreased without changing the phase shift .PHI. of the effective
height (h.sub.eff), the resulting electric field intersects the
lossy conducting medium 203 at the Brewster angle at a reduced
distance from the guided surface waveguide probe 200. FIG. 6
graphically illustrates the effect of decreasing the physical
height of the charge terminal T.sub.1 on the distance where the
electric field is incident at the Brewster angle. As the height is
decreased from h.sub.3 through h.sub.2 to h.sub.1, the point where
the electric field intersects with the lossy conducting medium
(e.g., the Earth) at the Brewster angle moves closer to the charge
terminal position. However, as Equation (39) indicates, the height
H.sub.1 (FIG. 3) of the charge terminal T.sub.1 should be at or
higher than the physical height (h.sub.p) in order to excite the
far-out component of the Hankel function. With the charge terminal
T.sub.1 positioned at or above the effective height (h.sub.eff),
the lossy conducting medium 203 can be illuminated at the Brewster
angle of incidence (.psi..sub.i,B=(.pi./2)-.theta..sub.i,B) at or
beyond the Hankel crossover distance (R.sub.x) 121 as illustrated
in FIG. 5A. To reduce or minimize the bound charge on the charge
terminal T.sub.1, the height should be at least four times the
spherical diameter (or equivalent spherical diameter) of the charge
terminal T.sub.1 as mentioned above.
[0081] A guided surface waveguide probe 200 can be configured to
establish an electric field having a wave tilt that corresponds to
a wave illuminating the surface of the lossy conducting medium 203
at a complex Brewster angle, thereby exciting radial surface
currents by substantially mode-matching to a guided surface wave
mode at (or beyond) the Hankel crossover point 121 at R.sub.x.
[0082] Referring to FIG. 7, shown is a graphical representation of
an example of a guided surface waveguide probe 200b that includes a
charge terminal T.sub.1. An AC source 212 acts as the excitation
source for the charge terminal T.sub.1, which is coupled to the
guided surface waveguide probe 200b through a feed network 209
(FIG. 3) comprising a coil 215 such as, e.g., a helical coil. In
other implementations, the AC source 212 can be inductively coupled
to the coil 215 through a primary coil. In some embodiments, an
impedance matching network may be included to improve and/or
maximize coupling of the AC source 212 to the coil 215.
[0083] As shown in FIG. 7, the guided surface waveguide probe 200b
can include the upper charge terminal T.sub.1 (e.g., a sphere at
height h.sub.p) that is positioned along a vertical axis z that is
substantially normal to the plane presented by the lossy conducting
medium 203. A second medium 206 is located above the lossy
conducting medium 203. The charge terminal T.sub.1 has a
self-capacitance C.sub.T. During operation, charge Q.sub.1 is
imposed on the terminal T.sub.1 depending on the voltage applied to
the terminal T.sub.1 at any given instant.
[0084] In the example of FIG. 7, the coil 215 is coupled to a
ground stake 218 at a first end and to the charge terminal T.sub.1
via a vertical feed line conductor 221. In some implementations,
the coil connection to the charge terminal T.sub.1 can be adjusted
using a tap 224 of the coil 215 as shown in FIG. 7. The coil 215
can be energized at an operating frequency by the AC source 212
through a tap 227 at a lower portion of the coil 215. In other
implementations, the AC source 212 can be inductively coupled to
the coil 215 through a primary coil.
[0085] The construction and adjustment of the guided surface
waveguide probe 200 is based upon various operating conditions,
such as the transmission frequency, conditions of the lossy
conducting medium (e.g., soil conductivity a and relative
permittivity .epsilon..sub.r), and size of the charge terminal
T.sub.1. The index of refraction can be calculated from Equations
(10) and (11) as
n= {square root over (.epsilon..sub.r-jx)}, (41)
where x=.sigma./.omega..epsilon..sub.o with .omega.=2.pi.f. The
conductivity .sigma. and relative permittivity .epsilon..sub.r can
be determined through test measurements of the lossy conducting
medium 203. The complex Brewster angle (.theta..sub.i,B) measured
from the surface normal can also be determined from Equation (26)
as
.theta..sub.i,B=arctan( {square root over (.epsilon..sub.r-jx)}),
(42)
or measured from the surface as shown in FIG. 5A as
.psi. i , B = .pi. 2 - .theta. i , B . ( 43 ) ##EQU00025##
The wave tilt at the Hankel crossover distance (W.sub.Rx) can also
be found using Equation (40).
[0086] The Hankel crossover distance can also be found by equating
the magnitudes of Equations (20b) and (21) for -j.gamma..rho., and
solving for R.sub.x as illustrated by FIG. 4. The electrical
effective height can then be determined from Equation (39) using
the Hankel crossover distance and the complex Brewster angle as
h.sub.eff=h.sub.pe.sup.j.PHI.=R.sub.x tan .psi..sub.i,B. (44)
As can be seen from Equation (44), the complex effective height
(h.sub.eff) includes a magnitude that is associated with the
physical height (h.sub.p) of the charge terminal T.sub.1 and a
phase delay (.PHI.) that is to be associated with the angle (.psi.)
of the wave tilt at the Hankel crossover distance (R.sub.x). With
these variables and the selected charge terminal T.sub.1
configuration, it is possible to determine the configuration of a
guided surface waveguide probe 200.
[0087] With the charge terminal T.sub.1 positioned at or above the
physical height (h.sub.p), the feed network 209 (FIG. 3) and/or the
vertical feed line connecting the feed network to the charge
terminal T.sub.1 can be adjusted to match the phase (.PHI.) of the
charge Q.sub.1 on the charge terminal T.sub.1 to the angle (.psi.)
of the wave tilt (W). The size of the charge terminal T.sub.1 can
be chosen to provide a sufficiently large surface for the charge
Q.sub.1 imposed on the terminals. In general, it is desirable to
make the charge terminal T.sub.1 as large as practical. The size of
the charge terminal T.sub.1 should be large enough to avoid
ionization of the surrounding air, which can result in electrical
discharge or sparking around the charge terminal.
[0088] The phase delay .theta..sub.c of a helically-wound coil can
be determined from Maxwell's equations as has been discussed by
Corum, K. L. and J. F. Corum, "RF Coils, Helical Resonators and
Voltage Magnification by Coherent Spatial Modes," Microwave Review,
Vol. 7, No. 2, September 2001, pp. 36-45., which is incorporated
herein by reference in its entirety. For a helical coil with
H/D>1, the ratio of the velocity of propagation (.nu.) of a wave
along the coil's longitudinal axis to the speed of light (c), or
the "velocity factor," is given by
V f = .upsilon. c = 1 1 + 20 ( D s ) 2.5 ( D .lamda. o ) 0.5 , ( 45
) ##EQU00026##
where H is the axial length of the solenoidal helix, D is the coil
diameter, N is the number of turns of the coil, s=H/N is the
turn-to-turn spacing (or helix pitch) of the coil, and
.lamda..sub.o is the free-space wavelength. Based upon this
relationship, the electrical length, or phase delay, of the helical
coil is given by
.theta. c = .beta. p H = 2 .pi. .lamda. p H = 2 .pi. V f .lamda. o
H . ( 46 ) ##EQU00027##
The principle is the same if the helix is wound spirally or is
short and fat, but V.sub.f and .theta..sub.c are easier to obtain
by experimental measurement. The expression for the characteristic
(wave) impedance of a helical transmission line has also been
derived as
Z c = 60 V f [ n ( V f .lamda. o D ) - 1.027 ] . ( 47 )
##EQU00028##
[0089] The spatial phase delay .theta..sub.y of the structure can
be determined using the traveling wave phase delay of the vertical
feed line conductor 221 (FIG. 7). The capacitance of a cylindrical
vertical conductor above a prefect ground plane can be expressed
as
C A = 2 .pi. o h w n ( h a ) - 1 Farads , ( 48 ) ##EQU00029##
where h.sub.w is the vertical length (or height) of the conductor
and a is the radius (in mks units). As with the helical coil, the
traveling wave phase delay of the vertical feed line conductor can
be given by
.theta. y = .beta. w h w = 2 .pi. .lamda. w h w = 2 .pi. V w
.lamda. o h w , ( 49 ) ##EQU00030##
where .beta..sub.w is the propagation phase constant for the
vertical feed line conductor, h.sub.w is the vertical length (or
height) of the vertical feed line conductor, V.sub.w is the
velocity factor on the wire, .lamda..sub.o is the wavelength at the
supplied frequency, and .lamda..sub.w is the propagation wavelength
resulting from the velocity factor V.sub.w. For a uniform
cylindrical conductor, the velocity factor is a constant with
V.sub.w.apprxeq.0.94, or in a range from about 0.93 to about 0.98.
If the mast is considered to be a uniform transmission line, its
average characteristic impedance can be approximated by
Z w = 60 V w [ n ( h w a ) - 1 ] , ( 50 ) ##EQU00031##
where V.sub.w.apprxeq.0.94 for a uniform cylindrical conductor and
a is the radius of the conductor. An alternative expression that
has been employed in amateur radio literature for the
characteristic impedance of a single-wire feed line can be given
by
Z w = 138 log ( 1.123 V w .lamda. o 2 .pi. a ) . ( 51 )
##EQU00032##
Equation (51) implies that Z.sub.w for a single-wire feeder varies
with frequency. The phase delay can be determined based upon the
capacitance and characteristic impedance.
[0090] With a charge terminal T.sub.1 positioned over the lossy
conducting medium 203 as shown in FIG. 3, the feed network 209 can
be adjusted to excite the charge terminal T.sub.1 with the phase
shift (.PHI.) of the complex effective height (h.sub.eff) equal to
the angle (.psi.) of the wave tilt at the Hankel crossover
distance, or .PHI.=.psi.. When this condition is met, the electric
field produced by the charge oscillating Q.sub.1 on the charge
terminal T.sub.1 is coupled into a guided surface waveguide mode
traveling along the surface of a lossy conducting medium 203. For
example, if the Brewster angle (.theta..sub.i,B), the phase delay
(.theta..sub.y) associated with the vertical feed line conductor
221 (FIG. 7), and the configuration of the coil 215 (FIG. 7) are
known, then the position of the tap 224 (FIG. 7) can be determined
and adjusted to impose an oscillating charge Q.sub.1 on the charge
terminal T.sub.1 with phase .PHI.=.psi.. The position of the tap
224 may be adjusted to maximize coupling the traveling surface
waves into the guided surface waveguide mode. Excess coil length
beyond the position of the tap 224 can be removed to reduce the
capacitive effects. The vertical wire height and/or the geometrical
parameters of the helical coil may also be varied.
[0091] The coupling to the guided surface waveguide mode on the
surface of the lossy conducting medium 203 can be improved and/or
optimized by tuning the guided surface waveguide probe 200 for
standing wave resonance with respect to a complex image plane
associated with the charge Q.sub.1 on the charge terminal T.sub.1.
By doing this, the performance of the guided surface waveguide
probe 200 can be adjusted for increased and/or maximum voltage (and
thus charge Q.sub.1) on the charge terminal T.sub.1. Referring back
to FIG. 3, the effect of the lossy conducting medium 203 in Region
1 can be examined using image theory analysis.
[0092] Physically, an elevated charge Q.sub.1 placed over a
perfectly conducting plane attracts the free charge on the
perfectly conducting plane, which then "piles up" in the region
under the elevated charge Q.sub.1. The resulting distribution of
"bound" electricity on the perfectly conducting plane is similar to
a bell-shaped curve. The superposition of the potential of the
elevated charge Q.sub.1, plus the potential of the induced "piled
up" charge beneath it, forces a zero equipotential surface for the
perfectly conducting plane. The boundary value problem solution
that describes the fields in the region above the perfectly
conducting plane may be obtained using the classical notion of
image charges, where the field from the elevated charge is
superimposed with the field from a corresponding "image" charge
below the perfectly conducting plane.
[0093] This analysis may also be used with respect to a lossy
conducting medium 203 by assuming the presence of an effective
image charge Q.sub.1' beneath the guided surface waveguide probe
200. The effective image charge Q.sub.1' coincides with the charge
Q.sub.1 on the charge terminal T.sub.1 about a conducting image
ground plane 130, as illustrated in FIG. 3. However, the image
charge Q.sub.1' is not merely located at some real depth and
180.degree. out of phase with the primary source charge Q.sub.1 on
the charge terminal T.sub.1, as they would be in the case of a
perfect conductor. Rather, the lossy conducting medium 203 (e.g., a
terrestrial medium) presents a phase shifted image. That is to say,
the image charge Q.sub.1' is at a complex depth below the surface
(or physical boundary) of the lossy conducting medium 203. For a
discussion of complex image depth, reference is made to Wait, J.
R., "Complex Image Theory--Revisited," IEEE Antennas and
Propagation Magazine, Vol. 33, No. 4, August 1991, pp. 27-29, which
is incorporated herein by reference in its entirety.
[0094] Instead of the image charge Q.sub.1' being at a depth that
is equal to the physical height (H.sub.1) of the charge Q.sub.1,
the conducting image ground plane 130 (representing a perfect
conductor) is located at a complex depth of z=-d/2 and the image
charge Q.sub.1' appears at a complex depth (i.e., the "depth" has
both magnitude and phase), given by
-D.sub.1=-(d/2+d/2+H.sub.1).noteq.H.sub.1. For vertically polarized
sources over the Earth,
d = 2 .gamma. e 2 + k o 2 .gamma. e 2 .apprxeq. 2 .gamma. e = d r +
jd i = d .angle..zeta. , where ( 52 ) .gamma. e 2 = j .omega..mu. 1
.sigma. 1 - .omega. 2 .mu. 1 1 , and ( 53 ) k o = .omega. .mu. o o
, ( 54 ) ##EQU00033##
as indicated in Equation (12). The complex spacing of the image
charge, in turn, implies that the external field will experience
extra phase shifts not encountered when the interface is either a
dielectric or a perfect conductor. In the lossy conducting medium,
the wave front normal is parallel to the tangent of the conducting
image ground plane 130 at z=-d/2, and not at the boundary interface
between Regions 1 and 2.
[0095] Consider the case illustrated in FIG. 8A where the lossy
conducting medium 203 is a finitely conducting Earth 133 with a
physical boundary 136. The finitely conducting Earth 133 may be
replaced by a perfectly conducting image ground plane 139 as shown
in FIG. 8B, which is located at a complex depth z.sub.1 below the
physical boundary 136. This equivalent representation exhibits the
same impedance when looking down into the interface at the physical
boundary 136. The equivalent representation of FIG. 8B can be
modeled as an equivalent transmission line, as shown in FIG. 8C.
The cross-section of the equivalent structure is represented as a
(z-directed) end-loaded transmission line, with the impedance of
the perfectly conducting image plane being a short circuit
(z.sub.s=0). The depth z.sub.1 can be determined by equating the
TEM wave impedance looking down at the Earth to an image ground
plane impedance z.sub.in seen looking into the transmission line of
FIG. 8C.
[0096] In the case of FIG. 8A, the propagation constant and wave
intrinsic impedance in the upper region (air) 142 are
.gamma. o = j .omega. .mu. o o = 0 + j .beta. o , and ( 55 ) z o =
j .omega..mu. o .gamma. o = .mu. o o . ( 56 ) ##EQU00034##
In the lossy Earth 133, the propagation constant and wave intrinsic
impedance are
.gamma. e = j .omega..mu. 1 ( .sigma. 1 + j .omega. 1 ) , and ( 57
) Z e = j .omega..mu. 1 .gamma. e . ( 58 ) ##EQU00035##
For normal incidence, the equivalent representation of FIG. 8B is
equivalent to a TEM transmission line whose characteristic
impedance is that of air (z.sub.o), with propagation constant of
.gamma..sub.o, and whose length is z.sub.1. As such, the image
ground plane impedance Z.sub.in seen at the interface for the
shorted transmission line of FIG. 8C is given by
Z.sub.in=Z.sub.o tan h(.gamma..sub.oz.sub.1). (59)
Equating the image ground plane impedance Z.sub.in associated with
the equivalent model of FIG. 8C to the normal incidence wave
impedance of FIG. 8A and solving for z.sub.1 gives the distance to
a short circuit (the perfectly conducting image ground plane 139)
as
z 1 = 1 .gamma. o tanh - 1 ( Z e Z o ) = 1 .gamma. o tanh - 1 (
.gamma. o .gamma. e ) .apprxeq. 1 .gamma. e , ( 60 )
##EQU00036##
where only the first term of the series expansion for the inverse
hyperbolic tangent is considered for this approximation. Note that
in the air region 142, the propagation constant is
.gamma..sub.o=j.beta..sub.o, so Z.sub.in=jZ.sub.o tan
.beta..sub.oz.sub.1 (which is a purely imaginary quantity for a
real z.sub.1), but z.sub.e is a complex value if .sigma..noteq.0.
Therefore, Z.sub.in=Z.sub.e only when z.sub.1 is a complex
distance.
[0097] Since the equivalent representation of FIG. 8B includes a
perfectly conducting image ground plane 139, the image depth for a
charge or current lying at the surface of the Earth (physical
boundary 136) is equal to distance z.sub.1 on the other side of the
image ground plane 139, or d=2.times.z.sub.1 beneath the Earth's
surface (which is located at z=0). Thus, the distance to the
perfectly conducting image ground plane 139 can be approximated
by
d = 2 z 1 .apprxeq. 2 .gamma. e . ( 61 ) ##EQU00037##
Additionally, the "image charge" will be "equal and opposite" to
the real charge, so the potential of the perfectly conducting image
ground plane 139 at depth z.sub.1=-d/2 will be zero.
[0098] If a charge Q.sub.1 is elevated a distance H.sub.1 above the
surface of the Earth as illustrated in FIG. 3, then the image
charge Q.sub.1' resides at a complex distance of D.sub.1=d+H.sub.1
below the surface, or a complex distance of d/2+H.sub.1 below the
image ground plane 130. The guided surface waveguide probe 200b of
FIG. 7 can be modeled as an equivalent single-wire transmission
line image plane model that can be based upon the perfectly
conducting image ground plane 139 of FIG. 8B. FIG. 9A shows an
example of the equivalent single-wire transmission line image plane
model, and FIG. 9B illustrates an example of the equivalent classic
transmission line model, including the shorted transmission line of
FIG. 8C.
[0099] In the equivalent image plane models of FIGS. 9A and 9B,
.PHI.=.theta..sub.y+.theta..sub.c is the traveling wave phase delay
of the guided surface waveguide probe 200 referenced to Earth 133
(or the lossy conducting medium 203), .theta..sub.c=.beta..sub.pH
is the electrical length of the coil 215 (FIG. 7), of physical
length H, expressed in degrees, .theta..sub.y=.beta..sub.wh.sub.w
is the electrical length of the vertical feed line conductor 221
(FIG. 7), of physical length h.sub.w, expressed in degrees, and
.theta..sub.d=.beta..sub.od/2 is the phase shift between the image
ground plane 139 and the physical boundary 136 of the Earth 133 (or
lossy conducting medium 203). In the example of FIGS. 9A and 9B,
Z.sub.w is the characteristic impedance of the elevated vertical
feed line conductor 221 in ohms, Z.sub.c is the characteristic
impedance of the coil 215 in ohms, and Z.sub.o is the
characteristic impedance of free space.
[0100] At the base of the guided surface waveguide probe 200, the
impedance seen "looking up" into the structure is
Z.sub..uparw.=Z.sub.base. With a load impedance of:
Z L = 1 j .omega. C T , ( 62 ) ##EQU00038##
where C.sub.T is the self-capacitance of the charge terminal
T.sub.1, the impedance seen "looking up" into the vertical feed
line conductor 221 (FIG. 7) is given by:
Z 2 = Z W Z L + Z w tanh ( j .beta. w h w ) Z w + Z L tanh ( j
.beta. w h w ) = Z W Z L + Z w tanh ( j .theta. y ) Z w + Z L tanh
( j .theta. y ) , ( 63 ) ##EQU00039##
and the impedance seen "looking up" into the coil 215 (FIG. 7) is
given by:
Z base = Z c Z 2 + Z c tanh ( j .beta. p H ) Z c + Z 2 tanh ( j
.beta. p H ) = Z c Z 2 + Z c tanh ( j .theta. c ) Z c + Z 2 tanh (
j .theta. c ) . ( 64 ) ##EQU00040##
At the base of the guided surface waveguide probe 200, the
impedance seen "looking down" into the lossy conducting medium 203
is Z.sub..dwnarw., =Z.sub.in, which is given by:
Z in = Z o Z s + Z o tanh [ j .beta. o ( d / 2 ) ] Z o + Z s tanh [
j .beta. o ( d / 2 ) ] = Z o tanh ( j .theta. d ) , ( 65 )
##EQU00041##
[0101] Neglecting losses, the equivalent image plane model can be
tuned to resonance when Z.sub..dwnarw.+Z.sub..uparw.=0 at the
physical boundary 136. Or, in the low loss case,
+X.sub..dwnarw.+X.sub..uparw.=0 at the physical boundary 136, where
X is the corresponding reactive component. Thus, the impedance at
the physical boundary 136 "looking up" into the guided surface
waveguide probe 200 is the conjugate of the impedance at the
physical boundary 136 "looking down" into the lossy conducting
medium 203. By adjusting the load impedance Z.sub.L of the charge
terminal T.sub.1 while maintaining the traveling wave phase delay
.PHI. equal to the angle of the media's wave tilt .psi., so that
.PHI.=.psi., which improves and/or maximizes coupling of the
probe's electric field to a guided surface waveguide mode along the
surface of the lossy conducting medium 203 (e.g., Earth), the
equivalent image plane models of FIGS. 9A and 9B can be tuned to
resonance with respect to the image ground plane 139. In this way,
the impedance of the equivalent complex image plane model is purely
resistive, which maintains a superposed standing wave on the probe
structure that maximizes the voltage and elevated charge on
terminal T.sub.1, and by equations (1)-(3) and (16) maximizes the
propagating surface wave.
[0102] It follows from the Hankel solutions, that the guided
surface wave excited by the guided surface waveguide probe 200 is
an outward propagating traveling wave. The source distribution
along the feed network 209 between the charge terminal T.sub.1 and
the ground stake 218 of the guided surface waveguide probe 200
(FIGS. 3 and 7) is actually composed of a superposition of a
traveling wave plus a standing wave on the structure. With the
charge terminal T.sub.1 positioned at or above the physical height
h.sub.p, the phase delay of the traveling wave moving through the
feed network 209 is matched to the angle of the wave tilt
associated with the lossy conducting medium 203. This mode-matching
allows the traveling wave to be launched along the lossy conducting
medium 203. Once the phase delay has been established for the
traveling wave, the load impedance Z.sub.L of the charge terminal
T.sub.1 is adjusted to bring the probe structure into standing wave
resonance with respect to the image ground plane (130 of FIG. 3 or
139 of FIG. 8), which is at a complex depth of -d/2. In that case,
the impedance seen from the image ground plane has zero reactance
and the charge on the charge terminal T.sub.1 is maximized.
[0103] The distinction between the traveling wave phenomenon and
standing wave phenomena is that (1) the phase delay of traveling
waves (.theta.=.beta.d) on a section of transmission line of length
d (sometimes called a "delay line") is due to propagation time
delays; whereas (2) the position-dependent phase of standing waves
(which are composed of forward and backward propagating waves)
depends on both the line length propagation time delay and
impedance transitions at interfaces between line sections of
different characteristic impedances. In addition to the phase delay
that arises due to the physical length of a section of transmission
line operating in sinusoidal steady-state, there is an extra
reflection coefficient phase at impedance discontinuities that is
due to the ratio of Z.sub.oa/Z.sub.ob, where Z.sub.oa and Z.sub.ob
are the characteristic impedances of two sections of a transmission
line such as, e.g., a helical coil section of characteristic
impedance Z.sub.oa=Z.sub.c (FIG. 9B) and a straight section of
vertical feed line conductor of characteristic impedance
Z.sub.ob=Z.sub.w (FIG. 9B).
[0104] As a result of this phenomenon, two relatively short
transmission line sections of widely differing characteristic
impedance may be used to provide a very large phase shift. For
example, a probe structure composed of two sections of transmission
line, one of low impedance and one of high impedance, together
totaling a physical length of, say, 0.05.lamda., may be fabricated
to provide a phase shift of 90.degree. which is equivalent to a
0.25.lamda. resonance. This is due to the large jump in
characteristic impedances. In this way, a physically short probe
structure can be electrically longer than the two physical lengths
combined. This is illustrated in FIGS. 9A and 9B, where the
discontinuities in the impedance ratios provide large jumps in
phase. The impedance discontinuity provides a substantial phase
shift where the sections are joined together.
[0105] Referring to FIG. 10, shown is a flow chart 150 illustrating
an example of adjusting a guided surface waveguide probe 200 (FIGS.
3 and 7) to substantially mode-match to a guided surface waveguide
mode on the surface of the lossy conducting medium, which launches
a guided surface traveling wave along the surface of a lossy
conducting medium 203 (FIG. 3). Beginning with 153, the charge
terminal T.sub.1 of the guided surface waveguide probe 200 is
positioned at a defined height above a lossy conducting medium 203.
Utilizing the characteristics of the lossy conducting medium 203
and the operating frequency of the guided surface waveguide probe
200, the Hankel crossover distance can also be found by equating
the magnitudes of Equations (20b) and (21) for -j.gamma..rho., and
solving for R.sub.x as illustrated by FIG. 4. The complex index of
refraction (n) can be determined using Equation (41), and the
complex Brewster angle (.theta..sub.i,B) can then be determined
from Equation (42). The physical height (h.sub.p) of the charge
terminal T.sub.1 can then be determined from Equation (44). The
charge terminal T.sub.1 should be at or higher than the physical
height (h.sub.p) in order to excite the far-out component of the
Hankel function. This height relationship is initially considered
when launching surface waves. To reduce or minimize the bound
charge on the charge terminal T.sub.1, the height should be at
least four times the spherical diameter (or equivalent spherical
diameter) of the charge terminal T.sub.1.
[0106] At 156, the electrical phase delay .PHI. of the elevated
charge Q.sub.1 on the charge terminal T.sub.1 is matched to the
complex wave tilt angle .psi.. The phase delay (.theta..sub.c) of
the helical coil and/or the phase delay (.theta..sub.y) of the
vertical feed line conductor can be adjusted to make .PHI. equal to
the angle (.psi.) of the wave tilt (W). Based on Equation (31), the
angle (.psi.) of the wave tilt can be determined from:
W = E .rho. E z = 1 tan .theta. i , B = 1 n = W e j .PSI. . ( 66 )
##EQU00042##
The electrical phase .PHI. can then be matched to the angle of the
wave tilt. This angular (or phase) relationship is next considered
when launching surface waves. For example, the electrical phase
delay .PHI.=.theta..sub.c+.theta..sub.y can be adjusted by varying
the geometrical parameters of the coil 215 (FIG. 7) and/or the
length (or height) of the vertical feed line conductor 221 (FIG.
7). By matching .PHI.=.psi., an electric field can be established
at or beyond the Hankel crossover distance (R.sub.x) with a complex
Brewster angle at the boundary interface to excite the surface
waveguide mode and launch a traveling wave along the lossy
conducting medium 203.
[0107] Next at 159, the load impedance of the charge terminal
T.sub.1 is tuned to resonate the equivalent image plane model of
the guided surface waveguide probe 200. The depth (d/2) of the
conducting image ground plane 139 of FIGS. 9A and 9B (or 130 of
FIG. 3) can be determined using Equations (52), (53) and (54) and
the values of the lossy conducting medium 203 (e.g., the Earth),
which can be measured. Using that depth, the phase shift
(.theta..sub.d) between the image ground plane 139 and the physical
boundary 136 of the lossy conducting medium 203 can be determined
using .theta..sub.d=.beta..sub.o d/2. The impedance (Z.sub.in) as
seen "looking down" into the lossy conducting medium 203 can then
be determined using Equation (65). This resonance relationship can
be considered to maximize the launched surface waves.
[0108] Based upon the adjusted parameters of the coil 215 and the
length of the vertical feed line conductor 221, the velocity
factor, phase delay, and impedance of the coil 215 and vertical
feed line conductor 221 can be determined using Equations (45)
through (51). In addition, the self-capacitance (C.sub.T) of the
charge terminal T.sub.1 can be determined using, e.g., Equation
(24). The propagation factor (.beta..sub.p) of the coil 215 can be
determined using Equation (35) and the propagation phase constant
(.beta..sub.w) for the vertical feed line conductor 221 can be
determined using Equation (49). Using the self-capacitance and the
determined values of the coil 215 and vertical feed line conductor
221, the impedance (Z.sub.base) of the guided surface waveguide
probe 200 as seen "looking up" into the coil 215 can be determined
using Equations (62), (63) and (64).
[0109] The equivalent image plane model of the guided surface
waveguide probe 200 can be tuned to resonance by adjusting the load
impedance Z.sub.L such that the reactance component X.sub.base of
Z.sub.base cancels out the reactance component X.sub.in of
Z.sub.in, or X.sub.base+X.sub.in=0. Thus, the impedance at the
physical boundary 136 "looking up" into the guided surface
waveguide probe 200 is the conjugate of the impedance at the
physical boundary 136 "looking down" into the lossy conducting
medium 203. The load impedance Z.sub.L can be adjusted by varying
the capacitance (C.sub.T) of the charge terminal T.sub.1 without
changing the electrical phase delay
.PHI.=.theta..sub.c+.theta..sub.y of the charge terminal T.sub.1.
An iterative approach may be taken to tune the load impedance
Z.sub.L for resonance of the equivalent image plane model with
respect to the conducting image ground plane 139 (or 130). In this
way, the coupling of the electric field to a guided surface
waveguide mode along the surface of the lossy conducting medium 203
(e.g., Earth) can be improved and/or maximized.
[0110] This may be better understood by illustrating the situation
with a numerical example. Consider a guided surface waveguide probe
200 comprising a top-loaded vertical stub of physical height
h.sub.p with a charge terminal T.sub.1 at the top, where the charge
terminal T.sub.1 is excited through a helical coil and vertical
feed line conductor at an operational frequency (f.sub.o) of 1.85
MHz. With a height (H.sub.1) of 16 feet and the lossy conducting
medium 203 (e.g., Earth) having a relative permittivity of
.epsilon..sub.r=15 and a conductivity of .sigma..sub.1=0.010
mhos/m, several surface wave propagation parameters can be
calculated for f.sub.o=1.850 MHz. Under these conditions, the
Hankel crossover distance can be found to be R.sub.x=54.5 feet with
a physical height of h.sub.p=5.5 feet, which is well below the
actual height of the charge terminal T.sub.1. While a charge
terminal height of H.sub.1=5.5 feet could have been used, the
taller probe structure reduced the bound capacitance, permitting a
greater percentage of free charge on the charge terminal T.sub.1
providing greater field strength and excitation of the traveling
wave.
[0111] The wave length can be determined as:
.lamda. o = c f o = 162.162 meters , ( 67 ) ##EQU00043##
where c is the speed of light. The complex index of refraction
is:
n= {square root over (.epsilon..sub.r-jx)}=7.529-j6.546, (68)
from Equation (41), where x=.sigma..sub.1/.omega..epsilon..sub.o
with .omega.=2.pi.f.sub.o, and the complex Brewster angle is:
.theta..sub.i,B=arctan( {square root over
(.epsilon..sub.r-jx)})=85.6-j3.744.degree.. (69)
from Equation (42). Using Equation (66), the wave tilt values can
be determined to be:
W = 1 tan .theta. i , B = 1 n = W e j .PSI. = 0.101 e j 4 0.614
.degree. . ( 70 ) ##EQU00044##
Thus, the helical coil can be adjusted to match
.PHI.=.psi.=40.614.degree.
[0112] The velocity factor of the vertical feed line conductor
(approximated as a uniform cylindrical conductor with a diameter of
0.27 inches) can be given as V.sub.w.apprxeq.0.93. Since
h.sub.p<<.lamda..sub.o, the propagation phase constant for
the vertical feed line conductor can be approximated as:
.beta. w = 2 .pi. .lamda. w = 2 .pi. V w .lamda. o = 0.042 m - 1 .
( 71 ) ##EQU00045##
From Equation (49) the phase delay of the vertical feed line
conductor is:
.theta..sub.y=.beta..sub.wh.sub.w.apprxeq..beta..sub.wh.sub.p=11.640.deg-
ree.. (72)
By adjusting the phase delay of the helical coil so that
.theta..sub.c=28.974.degree.=40.614.degree.-11.640.degree., .PHI.
will equal .psi. to match the guided surface waveguide mode. To
illustrate the relationship between .PHI. and .psi., FIG. 11 shows
a plot of both over a range of frequencies. As both .PHI. and .psi.
are frequency dependent, it can be seen that their respective
curves cross over each other at approximately 1.85 MHz.
[0113] For a helical coil having a conductor diameter of 0.0881
inches, a coil diameter (D) of 30 inches and a turn-to-turn spacing
(s) of 4 inches, the velocity factor for the coil can be determined
using Equation (45) as:
V f = 1 1 + 20 ( D s ) 2.5 ( D .lamda. o ) 0.5 = 0.069 , ( 73 )
##EQU00046##
and the propagation factor from Equation (35) is:
.beta. p = 2 .pi. V f .lamda. o = 0.564 m - 1 . ( 74 )
##EQU00047##
With .theta..sub.c=28.974.degree., the axial length of the
solenoidal helix (H) can be determined using Equation (46) such
that:
H = .theta. c .beta. p = 35.2732 inches . ( 75 ) ##EQU00048##
This height determines the location on the helical coil where the
vertical feed line conductor is connected, resulting in a coil with
8.818 turns (N=H/s).
[0114] With the traveling wave phase delay of the coil and vertical
feed line conductor adjusted to match the wave tilt angle
(.PHI.=.theta..sub.c+.theta..sub.y=.psi.), the load impedance
(Z.sub.L) of the charge terminal T.sub.1 can be adjusted for
standing wave resonance of the equivalent image plane model of the
guided surface wave probe 200. From the measured permittivity,
conductivity and permeability of the Earth, the radial propagation
constant can be determined using Equation (57)
.gamma.e= {square root over
(j.omega.u.sub.1(.sigma..sub.1+j.omega..epsilon..sub.1)})=0.25+j0.292m.su-
p.-1, (76)
And the complex depth of the conducting image ground plane can be
approximated from Equation (52) as:
d .apprxeq. 2 .gamma. e = 3.364 + j 3.963 meters , ( 77 )
##EQU00049##
with a corresponding phase shift between the conducting image
ground plane and the physical boundary of the Earth given by:
.theta..sub.d=.beta..sub.o(d/2)=4.015-j4.73.degree.. (78)
Using Equation (65), the impedance seen "looking down" into the
lossy conducting medium 203 (i.e., Earth) can be determined as:
Z.sub.in=Z.sub.o tan
h(j.theta..sub.d)=R.sub.in+jX.sub.in=31.191+j26.27 ohms. (79)
[0115] By matching the reactive component (X.sub.in) seen "looking
down" into the lossy conducting medium 203 with the reactive
component (X.sub.base) seen "looking up" into the guided surface
wave probe 200, the coupling into the guided surface waveguide mode
may be maximized. This can be accomplished by adjusting the
capacitance of the charge terminal T.sub.1 without changing the
traveling wave phase delays of the coil and vertical feed line
conductor. For example, by adjusting the charge terminal
capacitance (C.sub.T) to 61.8126 pF, the load impedance from
Equation (62) is:
Z L = 1 j .omega. C T = - j 1392 ohms , ( 80 ) ##EQU00050##
and the reactive components at the boundary are matched.
[0116] Using Equation (51), the impedance of the vertical feed line
conductor (having a diameter (2a) of 0.27 inches) is given as
Z w = 138 log ( 1.123 V w .lamda. o 2 .pi. a ) = 537.534 ohms , (
81 ) ##EQU00051##
and the impedance seen "looking up" into the vertical feed line
conductor is given by Equation (63) as:
Z 2 = Z W Z L + Z w tanh ( j .theta. y ) Z w + Z L tanh ( j .theta.
y ) = - j 835.438 ohms . ( 82 ) ##EQU00052##
Using Equation (47), the characteristic impedance of the helical
coil is given as
Z c = 60 V f [ ln ( V f .lamda. 0 D ) - 1.027 ] = 1446 ohms , ( 83
) ##EQU00053##
and the impedance seen "looking up" into the coil at the base is
given by Equation (64) as:
Z base = Z c Z 2 + Z c tanh ( j .theta. c ) Z c + Z 2 tanh ( j
.theta. c ) = - j 26.271 ohms . ( 84 ) ##EQU00054##
When compared to the solution of Equation (79), it can be seen that
the reactive components are opposite and approximately equal, and
thus are conjugates of each other. Thus, the impedance (Z.sub.ip)
seen "looking up" into the equivalent image plane model of FIGS. 9A
and 9B from the perfectly conducting image ground plane is only
resistive or Z.sub.ip=R+j0.
[0117] When the electric fields produced by a guided surface
waveguide probe 200 (FIG. 3) are established by matching the
traveling wave phase delay of the feed network to the wave tilt
angle and the probe structure is resonated with respect to the
perfectly conducting image ground plane at complex depth z=-d/2,
the fields are substantially mode-matched to a guided surface
waveguide mode on the surface of the lossy conducting medium, a
guided surface traveling wave is launched along the surface of the
lossy conducting medium. As illustrated in FIG. 1, the guided field
strength curve 103 of the guided electromagnetic field has a
characteristic exponential decay of e.sup.-.alpha.d/ {square root
over (d)} and exhibits a distinctive knee 109 on the log-log
scale.
[0118] In summary, both analytically and experimentally, the
traveling wave component on the structure of the guided surface
waveguide probe 200 has a phase delay (.PHI.) at its upper terminal
that matches the angle (.psi.) of the wave tilt of the surface
traveling wave (.PHI.=.psi.). Under this condition, the surface
waveguide may be considered to be "mode-matched". Furthermore, the
resonant standing wave component on the structure of the guided
surface waveguide probe 200 has a V.sub.MAX at the charge terminal
T.sub.1 and a V.sub.MIN down at the image plane 139 (FIG. 8B) where
Z.sub.ip=R.sub.ip+j 0 at a complex depth of z=-d/2, not at the
connection at the physical boundary 136 of the lossy conducting
medium 203 (FIG. 8B). Lastly, the charge terminal T.sub.1 is of
sufficient height H.sub.1 of FIG. 3 (h.gtoreq.R.sub.x tan
.psi..sub.i,B) so that electromagnetic waves incident onto the
lossy conducting medium 203 at the complex Brewster angle do so out
at a distance (.gtoreq.R.sub.x) where the 1/ {square root over (r)}
term is predominant. Receive circuits can be utilized with one or
more guided surface waveguide probes to facilitate wireless
transmission and/or power delivery systems.
[0119] Referring back to FIG. 3, operation of a guided surface
waveguide probe 200 may be controlled to adjust for variations in
operational conditions associated with the guided surface waveguide
probe 200. For example, an adaptive probe control system 230 can be
used to control the feed network 209 and/or the charge terminal
T.sub.1 to control the operation of the guided surface waveguide
probe 200. Operational conditions can include, but are not limited
to, variations in the characteristics of the lossy conducting
medium 203 (e.g., conductivity a and relative permittivity
.epsilon..sub.r), variations in field strength and/or variations in
loading of the guided surface waveguide probe 200. As can be seen
from Equations (31), (41) and (42), the index of refraction (n),
the complex Brewster angle (.theta..sub.i,B), and the wave tilt
(|W|e.sup.j.psi.) can be affected by changes in soil conductivity
and permittivity resulting from, e.g., weather conditions.
[0120] Equipment such as, e.g., conductivity measurement probes,
permittivity sensors, ground parameter meters, field meters,
current monitors and/or load receivers can be used to monitor for
changes in the operational conditions and provide information about
current operational conditions to the adaptive probe control system
230. The probe control system 230 can then make one or more
adjustments to the guided surface waveguide probe 200 to maintain
specified operational conditions for the guided surface waveguide
probe 200. For instance, as the moisture and temperature vary, the
conductivity of the soil will also vary. Conductivity measurement
probes and/or permittivity sensors may be located at multiple
locations around the guided surface waveguide probe 200. Generally,
it would be desirable to monitor the conductivity and/or
permittivity at or about the Hankel crossover distance R.sub.x for
the operational frequency. Conductivity measurement probes and/or
permittivity sensors may be located at multiple locations (e.g., in
each quadrant) around the guided surface waveguide probe 200.
[0121] The conductivity measurement probes and/or permittivity
sensors can be configured to evaluate the conductivity and/or
permittivity on a periodic basis and communicate the information to
the probe control system 230. The information may be communicated
to the probe control system 230 through a network such as, but not
limited to, a LAN, WLAN, cellular network, or other appropriate
wired or wireless communication network. Based upon the monitored
conductivity and/or permittivity, the probe control system 230 may
evaluate the variation in the index of refraction (n), the complex
Brewster angle (.theta..sub.i,B), and/or the wave tilt
(|W|e.sup.j.psi.) and adjust the guided surface waveguide probe 200
to maintain the phase delay (.PHI.) of the feed network 209 equal
to the wave tilt angle (.psi.) and/or maintain resonance of the
equivalent image plane model of the guided surface waveguide probe
200. This can be accomplished by adjusting, e.g., .theta..sub.y,
.theta..sub.c and/or C.sub.T. For instance, the probe control
system 230 can adjust the self-capacitance of the charge terminal
T.sub.1 and/or the phase delay (.theta..sub.y, .theta..sub.c)
applied to the charge terminal T.sub.1 to maintain the electrical
launching efficiency of the guided surface wave at or near its
maximum. For example, the self-capacitance of the charge terminal
T.sub.1 can be varied by changing the size of the terminal. The
charge distribution can also be improved by increasing the size of
the charge terminal T.sub.1, which can reduce the chance of an
electrical discharge from the charge terminal T.sub.1. In other
embodiments, the charge terminal T.sub.1 can include a variable
inductance that can be adjusted to change the load impedance
Z.sub.L. The phase applied to the charge terminal T.sub.1 can be
adjusted by varying the tap position on the coil 215 (FIG. 7),
and/or by including a plurality of predefined taps along the coil
215 and switching between the different predefined tap locations to
maximize the launching efficiency.
[0122] Field or field strength (FS) meters may also be distributed
about the guided surface waveguide probe 200 to measure field
strength of fields associated with the guided surface wave. The
field or FS meters can be configured to detect the field strength
and/or changes in the field strength (e.g., electric field
strength) and communicate that information to the probe control
system 230. The information may be communicated to the probe
control system 230 through a network such as, but not limited to, a
LAN, WLAN, cellular network, or other appropriate communication
network. As the load and/or environmental conditions change or vary
during operation, the guided surface waveguide probe 200 may be
adjusted to maintain specified field strength(s) at the FS meter
locations to ensure appropriate power transmission to the receivers
and the loads they supply.
[0123] For example, the phase delay
(.PHI.=.theta..sub.y+.theta..sub.c) applied to the charge terminal
T.sub.1 can be adjusted to match the wave tilt angle (.psi.). By
adjusting one or both phase delays, the guided surface waveguide
probe 200 can be adjusted to ensure the wave tilt corresponds to
the complex Brewster angle. This can be accomplished by adjusting a
tap position on the coil 215 (FIG. 7) to change the phase delay
supplied to the charge terminal T.sub.1. The voltage level supplied
to the charge terminal T.sub.1 can also be increased or decreased
to adjust the electric field strength. This may be accomplished by
adjusting the output voltage of the excitation source 212 or by
adjusting or reconfiguring the feed network 209. For instance, the
position of the tap 227 (FIG. 7) for the AC source 212 can be
adjusted to increase the voltage seen by the charge terminal
T.sub.1. Maintaining field strength levels within predefined ranges
can improve coupling by the receivers, reduce ground current
losses, and avoid interference with transmissions from other guided
surface waveguide probes 200.
[0124] The probe control system 230 can be implemented with
hardware, firmware, software executed by hardware, or a combination
thereof. For example, the probe control system 230 can include
processing circuitry including a processor and a memory, both of
which can be coupled to a local interface such as, for example, a
data bus with an accompanying control/address bus as can be
appreciated by those with ordinary skill in the art. A probe
control application may be executed by the processor to adjust the
operation of the guided surface waveguide probe 200 based upon
monitored conditions. The probe control system 230 can also include
one or more network interfaces for communicating with the various
monitoring devices. Communications can be through a network such
as, but not limited to, a LAN, WLAN, cellular network, or other
appropriate communication network. The probe control system 230 may
comprise, for example, a computer system such as a server, desktop
computer, laptop, or other system with like capability.
[0125] Referring back to the example of FIG. 5A, the complex angle
trigonometry is shown for the ray optic interpretation of the
incident electric field (E) of the charge terminal T.sub.1 with a
complex Brewster angle (.theta..sub.i,B) at the Hankel crossover
distance (R.sub.x). Recall that, for a lossy conducting medium, the
Brewster angle is complex and specified by equation (38).
Electrically, the geometric parameters are related by the
electrical effective height (h.sub.eff) of the charge terminal
T.sub.1 by equation (39). Since both the physical height (h.sub.p)
and the Hankel crossover distance (R.sub.x) are real quantities,
the angle of the desired guided surface wave tilt at the Hankel
crossover distance (W.sub.Rx) is equal to the phase (.PHI.) of the
complex effective height (h.sub.eff). With the charge terminal
T.sub.1 positioned at the physical height h.sub.p and excited with
a charge having the appropriate phase .PHI., the resulting electric
field is incident with the lossy conducting medium boundary
interface at the Hankel crossover distance R.sub.x, and at the
Brewster angle. Under these conditions, the guided surface
waveguide mode can be excited without reflection or substantially
negligible reflection.
[0126] However, Equation (39) means that the physical height of the
guided surface waveguide probe 200 can be relatively small. While
this will excite the guided surface waveguide mode, this can result
in an unduly large bound charge with little free charge. To
compensate, the charge terminal T.sub.1 can be raised to an
appropriate elevation to increase the amount of free charge. As one
example rule of thumb, the charge terminal T.sub.1 can be
positioned at an elevation of about 4-5 times (or more) the
effective diameter of the charge terminal T.sub.1. FIG. 6
illustrates the effect of raising the charge terminal T.sub.1 above
the physical height (h.sub.p) shown in FIG. 5A. The increased
elevation causes the distance at which the wave tilt is incident
with the lossy conductive medium to move beyond the Hankel
crossover point 121 (FIG. 5A). To improve coupling in the guided
surface waveguide mode, and thus provide for a greater launching
efficiency of the guided surface wave, a lower compensation
terminal T.sub.2 can be used to adjust the total effective height
(h.sub.TE) of the charge terminal T.sub.1 such that the wave tilt
at the Hankel crossover distance is at the Brewster angle.
[0127] Referring to FIG. 12, shown is an example of a guided
surface waveguide probe 200c that includes an elevated charge
terminal T.sub.1 and a lower compensation terminal T.sub.2 that are
arranged along a vertical axis z that is normal to a plane
presented by the lossy conducting medium 203. In this respect, the
charge terminal T.sub.1 is placed directly above the compensation
terminal T.sub.2 although it is possible that some other
arrangement of two or more charge and/or compensation terminals
T.sub.N can be used. The guided surface waveguide probe 200c is
disposed above a lossy conducting medium 203 according to an
embodiment of the present disclosure. The lossy conducting medium
203 makes up Region 1 with a second medium 206 that makes up Region
2 sharing a boundary interface with the lossy conducting medium
203.
[0128] The guided surface waveguide probe 200c includes a feed
network 209 that couples an excitation source 212 to the charge
terminal T.sub.1 and the compensation terminal T.sub.2. According
to various embodiments, charges Q.sub.1 and Q.sub.2 can be imposed
on the respective charge and compensation terminals T.sub.1 and
T.sub.2, depending on the voltages applied to terminals T.sub.1 and
T.sub.2 at any given instant. I.sub.1 is the conduction current
feeding the charge Q.sub.1 on the charge terminal T.sub.1 via the
terminal lead, and I.sub.2 is the conduction current feeding the
charge Q.sub.2 on the compensation terminal T.sub.2 via the
terminal lead.
[0129] According to the embodiment of FIG. 12, the charge terminal
T.sub.1 is positioned over the lossy conducting medium 203 at a
physical height H.sub.1, and the compensation terminal T.sub.2 is
positioned directly below T.sub.1 along the vertical axis z at a
physical height H.sub.2, where H.sub.2 is less than H.sub.1. The
height h of the transmission structure may be calculated as
h=H.sub.1-H.sub.2. The charge terminal T.sub.1 has an isolated (or
self) capacitance C.sub.1, and the compensation terminal T.sub.2
has an isolated (or self) capacitance C.sub.2. A mutual capacitance
C.sub.M can also exist between the terminals T.sub.1 and T.sub.2
depending on the distance therebetween. During operation, charges
Q.sub.1 and Q.sub.2 are imposed on the charge terminal T.sub.1 and
the compensation terminal T.sub.2, respectively, depending on the
voltages applied to the charge terminal T.sub.1 and the
compensation terminal T.sub.2 at any given instant.
[0130] Referring next to FIG. 13, shown is a ray optics
interpretation of the effects produced by the elevated charge
Q.sub.1 on charge terminal T.sub.1 and compensation terminal
T.sub.2 of FIG. 12. With the charge terminal T.sub.1 elevated to a
height where the ray intersects with the lossy conductive medium at
the Brewster angle at a distance greater than the Hankel crossover
point 121 as illustrated by line 163, the compensation terminal
T.sub.2 can be used to adjust h.sub.TE by compensating for the
increased height. The effect of the compensation terminal T.sub.2
is to reduce the electrical effective height of the guided surface
waveguide probe (or effectively raise the lossy medium interface)
such that the wave tilt at the Hankel crossover distance is at the
Brewster angle as illustrated by line 166.
[0131] The total effective height can be written as the
superposition of an upper effective height (h.sub.UE) associated
with the charge terminal T.sub.1 and a lower effective height
(h.sub.LE) associated with the compensation terminal T.sub.2 such
that
h.sub.TE=h.sub.UE+h.sub.LE=h.sub.pe.sup.j(.beta.h.sup.p.sup.+.PHI..sup.U-
.sup.)+h.sub.de.sup.j(.beta.h.sup.d.sup.+.PHI..sup.L.sup.)=R.sub.x.times.W-
, (85)
where .PHI..sub.U is the phase delay applied to the upper charge
terminal T.sub.1, .PHI..sub.L is the phase delay applied to the
lower compensation terminal T.sub.2, .beta.=2.pi./.lamda..sub.p is
the propagation factor from Equation (35), h.sub.p is the physical
height of the charge terminal T.sub.1 and h.sub.d is the physical
height of the compensation terminal T.sub.2. If extra lead lengths
are taken into consideration, they can be accounted for by adding
the charge terminal lead length z to the physical height h.sub.p of
the charge terminal T.sub.1 and the compensation terminal lead
length y to the physical height h.sub.d of the compensation
terminal T.sub.2 as shown in
h.sub.TE=(h.sub.p+z)e.sup.j(.beta.(h.sup.p.sup.+z)+.PHI..sup.U.sup.)+(h.-
sub.d+y)e.sup.j(.beta.(h.sup.d.sup.+y)+.PHI..sup.L.sup.)=R.sub.x.times.W.
(86)
The lower effective height can be used to adjust the total
effective height (h.sub.TE) to equal the complex effective height
(h.sub.eff) of FIG. 5A.
[0132] Equations (85) or (86) can be used to determine the physical
height of the lower disk of the compensation terminal T.sub.2 and
the phase angles to feed the terminals in order to obtain the
desired wave tilt at the Hankel crossover distance. For example,
Equation (86) can be rewritten as the phase shift applied to the
charge terminal T.sub.1 as a function of the compensation terminal
height (h.sub.d) to give
.PHI. U ( h d ) = - .beta. ( h p + z ) - j ln ( R x .times. W - ( h
d + y ) e j ( .beta. h d + .beta. y + .PHI. L ) ( h p + z ) ) . (
87 ) ##EQU00055##
[0133] To determine the positioning of the compensation terminal
T.sub.2, the relationships discussed above can be utilized. First,
the total effective height (h.sub.TE) is the superposition of the
complex effective height (h.sub.UE) of the upper charge terminal
T.sub.1 and the complex effective height (h.sub.LE) of the lower
compensation terminal T.sub.2 as expressed in Equation (86). Next,
the tangent of the angle of incidence can be expressed
geometrically as
tan .psi. E = h TE R x , ( 88 ) ##EQU00056##
which is equal to the definition of the wave tilt, W. Finally,
given the desired Hankel crossover distance R.sub.x, the h.sub.TE
can be adjusted to make the wave tilt of the incident ray match the
complex Brewster angle at the Hankel crossover point 121. This can
be accomplished by adjusting h.sub.p, .PHI..sub.U, and/or
h.sub.d.
[0134] These concepts may be better understood when discussed in
the context of an example of a guided surface waveguide probe.
Referring to FIG. 14, shown is a graphical representation of an
example of a guided surface waveguide probe 200d including an upper
charge terminal T.sub.1 (e.g., a sphere at height h.sub.T) and a
lower compensation terminal T.sub.2 (e.g., a disk at height
h.sub.d) that are positioned along a vertical axis z that is
substantially normal to the plane presented by the lossy conducting
medium 203. During operation, charges Q.sub.1 and Q.sub.2 are
imposed on the charge and compensation terminals T.sub.1 and
T.sub.2, respectively, depending on the voltages applied to the
terminals T.sub.1 and T.sub.2 at any given instant.
[0135] An AC source 212 acts as the excitation source for the
charge terminal T.sub.1, which is coupled to the guided surface
waveguide probe 200d through a feed network 209 comprising a coil
215 such as, e.g., a helical coil. The AC source 212 can be
connected across a lower portion of the coil 215 through a tap 227,
as shown in FIG. 14, or can be inductively coupled to the coil 215
by way of a primary coil. The coil 215 can be coupled to a ground
stake 218 at a first end and the charge terminal T.sub.1 at a
second end. In some implementations, the connection to the charge
terminal T.sub.1 can be adjusted using a tap 224 at the second end
of the coil 215. The compensation terminal T.sub.2 is positioned
above and substantially parallel with the lossy conducting medium
203 (e.g., the ground or Earth), and energized through a tap 233
coupled to the coil 215. An ammeter 236 located between the coil
215 and ground stake 218 can be used to provide an indication of
the magnitude of the current flow (I.sub.0) at the base of the
guided surface waveguide probe. Alternatively, a current clamp may
be used around the conductor coupled to the ground stake 218 to
obtain an indication of the magnitude of the current flow
(I.sub.0).
[0136] In the example of FIG. 14, the coil 215 is coupled to a
ground stake 218 at a first end and the charge terminal T.sub.1 at
a second end via a vertical feed line conductor 221. In some
implementations, the connection to the charge terminal T.sub.1 can
be adjusted using a tap 224 at the second end of the coil 215 as
shown in FIG. 14. The coil 215 can be energized at an operating
frequency by the AC source 212 through a tap 227 at a lower portion
of the coil 215. In other implementations, the AC source 212 can be
inductively coupled to the coil 215 through a primary coil. The
compensation terminal T.sub.2 is energized through a tap 233
coupled to the coil 215. An ammeter 236 located between the coil
215 and ground stake 218 can be used to provide an indication of
the magnitude of the current flow at the base of the guided surface
waveguide probe 200d. Alternatively, a current clamp may be used
around the conductor coupled to the ground stake 218 to obtain an
indication of the magnitude of the current flow. The compensation
terminal T.sub.2 is positioned above and substantially parallel
with the lossy conducting medium 203 (e.g., the ground).
[0137] In the example of FIG. 14, the connection to the charge
terminal T.sub.1 located on the coil 215 above the connection point
of tap 233 for the compensation terminal T.sub.2. Such an
adjustment allows an increased voltage (and thus a higher charge
Q.sub.1) to be applied to the upper charge terminal T.sub.1. In
other embodiments, the connection points for the charge terminal
T.sub.1 and the compensation terminal T.sub.2 can be reversed. It
is possible to adjust the total effective height (h.sub.TE) of the
guided surface waveguide probe 200d to excite an electric field
having a guided surface wave tilt at the Hankel crossover distance
R.sub.x. The Hankel crossover distance can also be found by
equating the magnitudes of equations (20b) and (21) for
-j.gamma..rho., and solving for R.sub.x as illustrated by FIG. 4.
The index of refraction (n), the complex Brewster angle
(.theta..sub.i,B and .psi..sub.i,B), the wave tilt
(|W|e.sup.j.psi.) and the complex effective height
(h.sub.eff=h.sub.pe.sup.j.PHI.) can be determined as described with
respect to Equations (41)-(44) above.
[0138] With the selected charge terminal T.sub.1 configuration, a
spherical diameter (or the effective spherical diameter) can be
determined. For example, if the charge terminal T.sub.1 is not
configured as a sphere, then the terminal configuration may be
modeled as a spherical capacitance having an effective spherical
diameter. The size of the charge terminal T.sub.1 can be chosen to
provide a sufficiently large surface for the charge Q.sub.1 imposed
on the terminals. In general, it is desirable to make the charge
terminal T.sub.1 as large as practical. The size of the charge
terminal T.sub.1 should be large enough to avoid ionization of the
surrounding air, which can result in electrical discharge or
sparking around the charge terminal. To reduce the amount of bound
charge on the charge terminal T.sub.1, the desired elevation to
provide free charge on the charge terminal T.sub.1 for launching a
guided surface wave should be at least 4-5 times the effective
spherical diameter above the lossy conductive medium (e.g., the
Earth). The compensation terminal T.sub.2 can be used to adjust the
total effective height (h.sub.TE) of the guided surface waveguide
probe 200d to excite an electric field having a guided surface wave
tilt at R.sub.x. The compensation terminal T.sub.2 can be
positioned below the charge terminal T.sub.1 at
h.sub.d=h.sub.T-h.sub.p, where h.sub.T is the total physical height
of the charge terminal T.sub.1. With the position of the
compensation terminal T.sub.2 fixed and the phase delay
.PHI.D.sub.U applied to the upper charge terminal T.sub.1, the
phase delay .PHI..sub.L applied to the lower compensation terminal
T.sub.2 can be determined using the relationships of Equation (86),
such that:
.PHI. U ( h d ) = - .beta. ( h d + y ) - j ln ( R x .times. W - ( h
p + z ) e j ( .beta. h p + .beta. z + .PHI. L ) ( h d + y ) ) . (
89 ) ##EQU00057##
In alternative embodiments, the compensation terminal T.sub.2 can
be positioned at a height h.sub.d where Im{.PHI..sub.L}=0. This is
graphically illustrated in FIG. 15A, which shows plots 172 and 175
of the imaginary and real parts of .PHI..sub.U, respectively. The
compensation terminal T.sub.2 is positioned at a height h.sub.d
where Im{.PHI..sub.U}=0, as graphically illustrated in plot 172. At
this fixed height, the coil phase .PHI..sub.U can be determined
from Re{.PHI..sub.U}, as graphically illustrated in plot 175.
[0139] With the AC source 212 coupled to the coil 215 (e.g., at the
50.OMEGA. point to maximize coupling), the position of tap 233 may
be adjusted for parallel resonance of the compensation terminal
T.sub.2 with at least a portion of the coil at the frequency of
operation. FIG. 15B shows a schematic diagram of the general
electrical hookup of FIG. 14 in which V.sub.1 is the voltage
applied to the lower portion of the coil 215 from the AC source 212
through tap 227, V.sub.2 is the voltage at tap 224 that is supplied
to the upper charge terminal T.sub.1, and V.sub.3 is the voltage
applied to the lower compensation terminal T.sub.2 through tap 233.
The resistances R.sub.p and R.sub.d represent the ground return
resistances of the charge terminal T.sub.1 and compensation
terminal T.sub.2, respectively. The charge and compensation
terminals T.sub.1 and T.sub.2 may be configured as spheres,
cylinders, toroids, rings, hoods, or any other combination of
capacitive structures. The size of the charge and compensation
terminals T.sub.1 and T.sub.2 can be chosen to provide a
sufficiently large surface for the charges Q.sub.1 and Q.sub.2
imposed on the terminals. In general, it is desirable to make the
charge terminal T.sub.1 as large as practical. The size of the
charge terminal T.sub.1 should be large enough to avoid ionization
of the surrounding air, which can result in electrical discharge or
sparking around the charge terminal. The self-capacitance C.sub.p
and C.sub.d of the charge and compensation terminals T.sub.1 and
T.sub.2 respectively, can be determined using, for example,
equation (24).
[0140] As can be seen in FIG. 15B, a resonant circuit is formed by
at least a portion of the inductance of the coil 215, the
self-capacitance C.sub.d of the compensation terminal T.sub.2, and
the ground return resistance R.sub.d associated with the
compensation terminal T.sub.2. The parallel resonance can be
established by adjusting the voltage V.sub.3 applied to the
compensation terminal T.sub.2 (e.g., by adjusting a tap 233
position on the coil 215) or by adjusting the height and/or size of
the compensation terminal T.sub.2 to adjust C.sub.d. The position
of the coil tap 233 can be adjusted for parallel resonance, which
will result in the ground current through the ground stake 218 and
through the ammeter 236 reaching a maximum point. After parallel
resonance of the compensation terminal T.sub.2 has been
established, the position of the tap 227 for the AC source 212 can
be adjusted to the 50.OMEGA. point on the coil 215.
[0141] Voltage V.sub.2 from the coil 215 can be applied to the
charge terminal T.sub.1, and the position of tap 224 can be
adjusted such that the phase (.PHI.) of the total effective height
(h.sub.TE) approximately equals the angle of the guided surface
wave tilt (W.sub.Rx) at the Hankel crossover distance (R.sub.x).
The position of the coil tap 224 can be adjusted until this
operating point is reached, which results in the ground current
through the ammeter 236 increasing to a maximum. At this point, the
resultant fields excited by the guided surface waveguide probe 200d
are substantially mode-matched to a guided surface waveguide mode
on the surface of the lossy conducting medium 203, resulting in the
launching of a guided surface wave along the surface of the lossy
conducting medium 203. This can be verified by measuring field
strength along a radial extending from the guided surface waveguide
probe 200.
[0142] Resonance of the circuit including the compensation terminal
T.sub.2 may change with the attachment of the charge terminal
T.sub.1 and/or with adjustment of the voltage applied to the charge
terminal T.sub.1 through tap 224. While adjusting the compensation
terminal circuit for resonance aids the subsequent adjustment of
the charge terminal connection, it is not necessary to establish
the guided surface wave tilt (W.sub.Rx) at the Hankel crossover
distance (R.sub.x). The system may be further adjusted to improve
coupling by iteratively adjusting the position of the tap 227 for
the AC source 212 to be at the 50.OMEGA. point on the coil 215 and
adjusting the position of tap 233 to maximize the ground current
through the ammeter 236. Resonance of the circuit including the
compensation terminal T.sub.2 may drift as the positions of taps
227 and 233 are adjusted, or when other components are attached to
the coil 215.
[0143] In other implementations, the voltage V.sub.2 from the coil
215 can be applied to the charge terminal T.sub.1, and the position
of tap 233 can be adjusted such that the phase (.PHI.) of the total
effective height (h.sub.TE) approximately equals the angle (.psi.)
of the guided surface wave tilt at R.sub.x. The position of the
coil tap 224 can be adjusted until the operating point is reached,
resulting in the ground current through the ammeter 236
substantially reaching a maximum. The resultant fields are
substantially mode-matched to a guided surface waveguide mode on
the surface of the lossy conducting medium 203, and a guided
surface wave is launched along the surface of the lossy conducting
medium 203. This can be verified by measuring field strength along
a radial extending from the guided surface waveguide probe 200. The
system may be further adjusted to improve coupling by iteratively
adjusting the position of the tap 227 for the AC source 212 to be
at the 50.OMEGA. point on the coil 215 and adjusting the position
of tap 224 and/or 233 to maximize the ground current through the
ammeter 236.
[0144] Referring back to FIG. 12, operation of a guided surface
waveguide probe 200 may be controlled to adjust for variations in
operational conditions associated with the guided surface waveguide
probe 200. For example, a probe control system 230 can be used to
control the feed network 209 and/or positioning of the charge
terminal T.sub.1 and/or compensation terminal T.sub.2 to control
the operation of the guided surface waveguide probe 200.
Operational conditions can include, but are not limited to,
variations in the characteristics of the lossy conducting medium
203 (e.g., conductivity a and relative permittivity
.epsilon..sub.r), variations in field strength and/or variations in
loading of the guided surface waveguide probe 200. As can be seen
from Equations (41)-(44), the index of refraction (n), the complex
Brewster angle (.theta..sub.i,B and .psi..sub.i,B), the wave tilt
(|W|e.sup.j.psi.) and the complex effective height
(h.sub.eff=h.sub.pe.sup.j.PHI.) can be affected by changes in soil
conductivity and permittivity resulting from, e.g., weather
conditions.
[0145] Equipment such as, e.g., conductivity measurement probes,
permittivity sensors, ground parameter meters, field meters,
current monitors and/or load receivers can be used to monitor for
changes in the operational conditions and provide information about
current operational conditions to the probe control system 230. The
probe control system 230 can then make one or more adjustments to
the guided surface waveguide probe 200 to maintain specified
operational conditions for the guided surface waveguide probe 200.
For instance, as the moisture and temperature vary, the
conductivity of the soil will also vary. Conductivity measurement
probes and/or permittivity sensors may be located at multiple
locations around the guided surface waveguide probe 200. Generally,
it would be desirable to monitor the conductivity and/or
permittivity at or about the Hankel crossover distance R.sub.x for
the operational frequency. Conductivity measurement probes and/or
permittivity sensors may be located at multiple locations (e.g., in
each quadrant) around the guided surface waveguide probe 200.
[0146] With reference then to FIG. 16, shown is an example of a
guided surface waveguide probe 200e that includes a charge terminal
T.sub.1 and a charge terminal T.sub.2 that are arranged along a
vertical axis z. The guided surface waveguide probe 200e is
disposed above a lossy conducting medium 203, which makes up Region
1. In addition, a second medium 206 shares a boundary interface
with the lossy conducting medium 203 and makes up Region 2. The
charge terminals T.sub.1 and T.sub.2 are positioned over the lossy
conducting medium 203. The charge terminal T.sub.1 is positioned at
height H.sub.1, and the charge terminal T.sub.2 is positioned
directly below T.sub.1 along the vertical axis z at height H.sub.2,
where H.sub.2 is less than H.sub.1. The height h of the
transmission structure presented by the guided surface waveguide
probe 200e is h=H.sub.1-H.sub.2. The guided surface waveguide probe
200e includes a feed network 209 that couples an excitation source
212 to the charge terminals T.sub.1 and T.sub.2.
[0147] The charge terminals T.sub.1 and/or T.sub.2 include a
conductive mass that can hold an electrical charge, which may be
sized to hold as much charge as practically possible. The charge
terminal T.sub.1 has a self-capacitance C.sub.1, and the charge
terminal T.sub.2 has a self-capacitance C.sub.2, which can be
determined using, for example, equation (24). By virtue of the
placement of the charge terminal T.sub.1 directly above the charge
terminal T.sub.2, a mutual capacitance C.sub.M is created between
the charge terminals T.sub.1 and T.sub.2. Note that the charge
terminals T.sub.1 and T.sub.2 need not be identical, but each can
have a separate size and shape, and can include different
conducting materials. Ultimately, the field strength of a guided
surface wave launched by a guided surface waveguide probe 200e is
directly proportional to the quantity of charge on the terminal
T.sub.1. The charge Q.sub.1 is, in turn, proportional to the
self-capacitance C.sub.1 associated with the charge terminal
T.sub.1 since Q.sub.1=C.sub.1V, where V is the voltage imposed on
the charge terminal T.sub.1.
[0148] When properly adjusted to operate at a predefined operating
frequency, the guided surface waveguide probe 200e generates a
guided surface wave along the surface of the lossy conducting
medium 203. The excitation source 212 can generate electrical
energy at the predefined frequency that is applied to the guided
surface waveguide probe 200e to excite the structure. When the
electromagnetic fields generated by the guided surface waveguide
probe 200e are substantially mode-matched with the lossy conducting
medium 203, the electromagnetic fields substantially synthesize a
wave front incident at a complex Brewster angle that results in
little or no reflection. Thus, the surface waveguide probe 200e
does not produce a radiated wave, but launches a guided surface
traveling wave along the surface of a lossy conducting medium 203.
The energy from the excitation source 212 can be transmitted as
Zenneck surface currents to one or more receivers that are located
within an effective transmission range of the guided surface
waveguide probe 200e.
[0149] One can determine asymptotes of the radial Zenneck surface
current J.sub..rho.(.rho.) on the surface of the lossy conducting
medium 203 to be J.sub.1(.rho.) close-in and J.sub.2 (.rho.)
far-out, where
Close - in ( .rho. < .lamda. / 8 ) : J .rho. ( .rho. ) .about. J
1 = I 1 + I 2 2 .pi. .rho. + E .rho. QS ( Q 1 ) + E .rho. QS ( Q 2
) Z .rho. , and ( 90 ) Far - out ( .rho. >> .lamda./8 ) : J
.rho. ( .rho. ) .about. J 2 = j .gamma. .omega. Q 1 4 .times. 2
.gamma. .pi. .times. e - ( .alpha. + j .beta. ) .rho. .rho. . ( 91
) ##EQU00058##
where I.sub.1 is the conduction current feeding the charge Q.sub.1
on the first charge terminal T.sub.1, and I.sub.2 is the conduction
current feeding the charge Q.sub.2 on the second charge terminal
T.sub.2. The charge Q.sub.1 on the upper charge terminal T.sub.1 is
determined by Q.sub.1=C.sub.1V.sub.1, where C.sub.1 is the isolated
capacitance of the charge terminal T.sub.1. Note that there is a
third component to A set forth above given by
(E.sub..rho..sup.Q.sup.1)/Z.sub..rho., which follows from the
Leontovich boundary condition and is the radial current
contribution in the lossy conducting medium 203 pumped by the
quasi-static field of the elevated oscillating charge on the first
charge terminal Q.sub.1. The quantity
Z.sub.p=j.omega..mu..sub.o/.gamma..sub.e is the radial impedance of
the lossy conducting medium, where
.gamma..sub.e=(j.omega..sub.1.sigma..sub.1-.omega..sup.2.mu..sub.1.epsilo-
n..sub.1).sup.1/2.
[0150] The asymptotes representing the radial current close-in and
far-out as set forth by equations (90) and (91) are complex
quantities. According to various embodiments, a physical surface
current J(.rho.), is synthesized to match as close as possible the
current asymptotes in magnitude and phase. That is to say close-in,
|J(.rho.)| is to be tangent to |J.sub.1|, and far-out |J(.rho.)| is
to be tangent to |J.sub.2|. Also, according to the various
embodiments, the phase of J(.rho.) should transition from the phase
of J.sub.1 close-in to the phase of J.sub.2 far-out.
[0151] In order to match the guided surface wave mode at the site
of transmission to launch a guided surface wave, the phase of the
surface current |J.sub.2| far-out should differ from the phase of
the surface current |J.sub.1| close-in by the propagation phase
corresponding to e.sup.-j.beta.(.rho..sup.2.sup.-.rho..sup.1.sup.)
plus a constant of approximately 45 degrees or 225 degrees. This is
because there are two roots for {square root over (.gamma.)}, one
near .pi./4 and one near 5.pi./4. The properly adjusted synthetic
radial surface current is
J .rho. ( .rho. , .phi. , 0 ) = I 0 .gamma. 4 H 1 ( 2 ) ( - j
.gamma. .rho. ) . ( 92 ) ##EQU00059##
Note that this is consistent with equation (17). By Maxwell's
equations, such a J(.rho.) surface current automatically creates
fields that conform to
H .phi. = = .gamma. I o 4 e - u 2 z H 1 ( 2 ) ( - j .gamma. .rho. )
, ( 93 ) E .rho. = - .gamma. I o 4 ( u 2 j .omega. 0 ) e - u 2 z H
1 ( 2 ) ( - j .gamma. .rho. ) , and ( 94 ) E z = - .gamma. I o 4 (
- .gamma. .omega. o ) e - u 2 z H 0 ( 2 ) ( - j .gamma. .rho. ) . (
95 ) ##EQU00060##
Thus, the difference in phase between the surface current |J.sub.2|
far-out and the surface current |J.sub.1| close-in for the guided
surface wave mode that is to be matched is due to the
characteristics of the Hankel functions in equations (93)-(95),
which are consistent with equations (1)-(3). It is of significance
to recognize that the fields expressed by equations (1)-(6) and
(17) and equations (92)-(95) have the nature of a transmission line
mode bound to a lossy interface, not radiation fields that are
associated with groundwave propagation.
[0152] In order to obtain the appropriate voltage magnitudes and
phases for a given design of a guided surface waveguide probe 200e
at a given location, an iterative approach may be used.
Specifically, analysis may be performed of a given excitation and
configuration of a guided surface waveguide probe 200e taking into
account the feed currents to the terminals T.sub.1 and T.sub.2, the
charges on the charge terminals T.sub.1 and T.sub.2, and their
images in the lossy conducting medium 203 in order to determine the
radial surface current density generated. This process may be
performed iteratively until an optimal configuration and excitation
for a given guided surface waveguide probe 200e is determined based
on desired parameters. To aid in determining whether a given guided
surface waveguide probe 200e is operating at an optimal level, a
guided field strength curve 103 (FIG. 1) may be generated using
equations (1)-(12) based on values for the conductivity of Region 1
(.sigma..sub.1) and the permittivity of Region 1 (.epsilon..sub.1)
at the location of the guided surface waveguide probe 200e. Such a
guided field strength curve 103 can provide a benchmark for
operation such that measured field strengths can be compared with
the magnitudes indicated by the guided field strength curve 103 to
determine if optimal transmission has been achieved.
[0153] In order to arrive at an optimized condition, various
parameters associated with the guided surface waveguide probe 200e
may be adjusted. One parameter that may be varied to adjust the
guided surface waveguide probe 200e is the height of one or both of
the charge terminals T.sub.1 and/or T.sub.2 relative to the surface
of the lossy conducting medium 203. In addition, the distance or
spacing between the charge terminals T.sub.1 and T.sub.2 may also
be adjusted. In doing so, one may minimize or otherwise alter the
mutual capacitance C.sub.M or any bound capacitances between the
charge terminals T.sub.1 and T.sub.2 and the lossy conducting
medium 203 as can be appreciated. The size of the respective charge
terminals T.sub.1 and/or T.sub.2 can also be adjusted. By changing
the size of the charge terminals T.sub.1 and/or T.sub.2, one will
alter the respective self-capacitances C.sub.1 and/or C.sub.2, and
the mutual capacitance C.sub.M as can be appreciated.
[0154] Still further, another parameter that can be adjusted is the
feed network 209 associated with the guided surface waveguide probe
200e. This may be accomplished by adjusting the size of the
inductive and/or capacitive reactances that make up the feed
network 209. For example, where such inductive reactances comprise
coils, the number of turns on such coils may be adjusted.
Ultimately, the adjustments to the feed network 209 can be made to
alter the electrical length of the feed network 209, thereby
affecting the voltage magnitudes and phases on the charge terminals
T.sub.1 and T.sub.2.
[0155] Note that the iterations of transmission performed by making
the various adjustments may be implemented by using computer models
or by adjusting physical structures as can be appreciated. By
making the above adjustments, one can create corresponding
"close-in" surface current J.sub.1 and "far-out" surface current
J.sub.2 that approximate the same currents J(.rho.) of the guided
surface wave mode specified in Equations (90) and (91) set forth
above. In doing so, the resulting electromagnetic fields would be
substantially or approximately mode-matched to a guided surface
wave mode on the surface of the lossy conducting medium 203.
[0156] While not shown in the example of FIG. 16, operation of the
guided surface waveguide probe 200e may be controlled to adjust for
variations in operational conditions associated with the guided
surface waveguide probe 200. For example, a probe control system
230 shown in FIG. 12 can be used to control the feed network 209
and/or positioning and/or size of the charge terminals T.sub.1
and/or T.sub.2 to control the operation of the guided surface
waveguide probe 200e. Operational conditions can include, but are
not limited to, variations in the characteristics of the lossy
conducting medium 203 (e.g., conductivity a and relative
permittivity .epsilon..sub.r), variations in field strength and/or
variations in loading of the guided surface waveguide probe
200e.
[0157] Referring now to FIG. 17, shown is an example of the guided
surface waveguide probe 200e of FIG. 16, denoted herein as guided
surface waveguide probe 200f. The guided surface waveguide probe
200f includes the charge terminals T.sub.1 and T.sub.2 that are
positioned along a vertical axis z that is substantially normal to
the plane presented by the lossy conducting medium 203 (e.g., the
Earth). The second medium 206 is above the lossy conducting medium
203. The charge terminal T.sub.1 has a self-capacitance C.sub.1,
and the charge terminal T.sub.2 has a self-capacitance C.sub.2.
During operation, charges Q.sub.1 and Q.sub.2 are imposed on the
charge terminals T.sub.1 and T.sub.2, respectively, depending on
the voltages applied to the charge terminals T.sub.1 and T.sub.2 at
any given instant. A mutual capacitance C.sub.M may exist between
the charge terminals T.sub.1 and T.sub.2 depending on the distance
there between. In addition, bound capacitances may exist between
the respective charge terminals T.sub.1 and T.sub.2 and the lossy
conducting medium 203 depending on the heights of the respective
charge terminals T.sub.1 and T.sub.2 with respect to the lossy
conducting medium 203.
[0158] The guided surface waveguide probe 200f includes a feed
network 209 that comprises an inductive impedance comprising a coil
L.sub.1a having a pair of leads that are coupled to respective ones
of the charge terminals T.sub.1 and T.sub.2. In one embodiment, the
coil L.sub.1a is specified to have an electrical length that is
one-half (1/2) of the wavelength at the operating frequency of the
guided surface waveguide probe 200f.
[0159] While the electrical length of the coil L.sub.1a is
specified as approximately one-half (1/2) the wavelength at the
operating frequency, it is understood that the coil L.sub.1a may be
specified with an electrical length at other values. According to
one embodiment, the fact that the coil L.sub.1a has an electrical
length of approximately one-half the wavelength at the operating
frequency provides for an advantage in that a maximum voltage
differential is created on the charge terminals T.sub.1 and
T.sub.2. Nonetheless, the length or diameter of the coil L.sub.1a
may be increased or decreased when adjusting the guided surface
waveguide probe 200f to obtain optimal excitation of a guided
surface wave mode. Adjustment of the coil length may be provided by
taps located at one or both ends of the coil. In other embodiments,
it may be the case that the inductive impedance is specified to
have an electrical length that is significantly less than or
greater than 1/2 the wavelength at the operating frequency of the
guided surface waveguide probe 200f.
[0160] The excitation source 212 can be coupled to the feed network
209 by way of magnetic coupling. Specifically, the excitation
source 212 is coupled to a coil L.sub.P that is inductively coupled
to the coil L.sub.1a. This may be done by link coupling, a tapped
coil, a variable reactance, or other coupling approach as can be
appreciated. To this end, the coil L.sub.P acts as a primary, and
the coil L.sub.1a acts as a secondary as can be appreciated.
[0161] In order to adjust the guided surface waveguide probe 200f
for the transmission of a desired guided surface wave, the heights
of the respective charge terminals T.sub.1 and T.sub.2 may be
altered with respect to the lossy conducting medium 203 and with
respect to each other. Also, the sizes of the charge terminals
T.sub.1 and T.sub.2 may be altered. In addition, the size of the
coil L.sub.1a may be altered by adding or eliminating turns or by
changing some other dimension of the coil L.sub.1a. The coil
L.sub.1a can also include one or more taps for adjusting the
electrical length as shown in FIG. 17. The position of a tap
connected to either charge terminal T.sub.1 or T.sub.2 can also be
adjusted.
[0162] Referring next to FIGS. 18A, 18B, 18C and 19, shown are
examples of generalized receive circuits for using the
surface-guided waves in wireless power delivery systems. FIGS. 18A
and 18B-18C include a linear probe 303 and a tuned resonator 306,
respectively. FIG. 19 is a magnetic coil 309 according to various
embodiments of the present disclosure. According to various
embodiments, each one of the linear probe 303, the tuned resonator
306, and the magnetic coil 309 may be employed to receive power
transmitted in the form of a guided surface wave on the surface of
a lossy conducting medium 203 according to various embodiments. As
mentioned above, in one embodiment the lossy conducting medium 203
comprises a terrestrial medium (or Earth).
[0163] With specific reference to FIG. 18A, the open-circuit
terminal voltage at the output terminals 312 of the linear probe
303 depends upon the effective height of the linear probe 303. To
this end, the terminal point voltage may be calculated as
V.sub.T=.intg..sub.o.sup.h.sup.eE.sub.incdl, (96)
where E.sub.inc is the strength of the incident electric field
induced on the linear probe 303 in Volts per meter, dl is an
element of integration along the direction of the linear probe 303,
and h.sub.e is the effective height of the linear probe 303. An
electrical load 315 is coupled to the output terminals 312 through
an impedance matching network 318.
[0164] When the linear probe 303 is subjected to a guided surface
wave as described above, a voltage is developed across the output
terminals 312 that may be applied to the electrical load 315
through a conjugate impedance matching network 318 as the case may
be. In order to facilitate the flow of power to the electrical load
315, the electrical load 315 should be substantially impedance
matched to the linear probe 303 as will be described below.
[0165] Referring to FIG. 18B, a ground current excited coil 306a
possessing a phase shift equal to the wave tilt of the guided
surface wave includes a charge terminal T.sub.R that is elevated
(or suspended) above the lossy conducting medium 203. The charge
terminal T.sub.R has a self-capacitance C.sub.R. In addition, there
may also be a bound capacitance (not shown) between the charge
terminal T.sub.R and the lossy conducting medium 203 depending on
the height of the charge terminal T.sub.R above the lossy
conducting medium 203. The bound capacitance should preferably be
minimized as much as is practicable, although this may not be
entirely necessary in every instance.
[0166] The tuned resonator 306a also includes a receiver network
comprising a coil L.sub.R having a phase shift .PHI.. One end of
the coil L.sub.R is coupled to the charge terminal T.sub.R, and the
other end of the coil L.sub.R is coupled to the lossy conducting
medium 203. The receiver network can include a vertical supply line
conductor that couples the coil L.sub.R to the charge terminal
T.sub.R. To this end, the coil L.sub.R (which may also be referred
to as tuned resonator L.sub.R-C.sub.R) comprises a series-adjusted
resonator as the charge terminal C.sub.R and the coil L.sub.R are
situated in series. The phase delay of the coil L.sub.R can be
adjusted by changing the size and/or height of the charge terminal
T.sub.R, and/or adjusting the size of the coil L.sub.R so that the
phase .PHI. of the structure is made substantially equal to the
angle of the wave tilt .psi.. The phase delay of the vertical
supply line can also be adjusted by, e.g., changing length of the
conductor.
[0167] For example, the reactance presented by the self-capacitance
C.sub.R is calculated as 1/j.omega.C.sub.R. Note that the total
capacitance of the structure 306a may also include capacitance
between the charge terminal T.sub.R and the lossy conducting medium
203, where the total capacitance of the structure 306a may be
calculated from both the self-capacitance C.sub.R and any bound
capacitance as can be appreciated. According to one embodiment, the
charge terminal T.sub.R may be raised to a height so as to
substantially reduce or eliminate any bound capacitance. The
existence of a bound capacitance may be determined from capacitance
measurements between the charge terminal T.sub.R and the lossy
conducting medium 203 as previously discussed.
[0168] The inductive reactance presented by a discrete-element coil
L.sub.R may be calculated as j.omega.L, where L is the
lumped-element inductance of the coil L.sub.R. If the coil L.sub.R
is a distributed element, its equivalent terminal-point inductive
reactance may be determined by conventional approaches. To tune the
structure 306a, one would make adjustments so that the phase delay
is equal to the wave tilt for the purpose of mode-matching to the
surface waveguide at the frequency of operation. Under this
condition, the receiving structure may be considered to be
"mode-matched" with the surface waveguide. A transformer link
around the structure and/or an impedance matching network 324 may
be inserted between the probe and the electrical load 327 in order
to couple power to the load. Inserting the impedance matching
network 324 between the probe terminals 321 and the electrical load
327 can effect a conjugate-match condition for maximum power
transfer to the electrical load 327.
[0169] When placed in the presence of surface currents at the
operating frequencies power will be delivered from the surface
guided wave to the electrical load 327. To this end, an electrical
load 327 may be coupled to the structure 306a by way of magnetic
coupling, capacitive coupling, or conductive (direct tap) coupling.
The elements of the coupling network may be lumped components or
distributed elements as can be appreciated.
[0170] In the embodiment shown in FIG. 18B, magnetic coupling is
employed where a coil Ls is positioned as a secondary relative to
the coil L.sub.R that acts as a transformer primary. The coil Ls
may be link-coupled to the coil L.sub.R by geometrically winding it
around the same core structure and adjusting the coupled magnetic
flux as can be appreciated. In addition, while the receiving
structure 306a comprises a series-tuned resonator, a parallel-tuned
resonator or even a distributed-element resonator of the
appropriate phase delay may also be used.
[0171] While a receiving structure immersed in an electromagnetic
field may couple energy from the field, it can be appreciated that
polarization-matched structures work best by maximizing the
coupling, and conventional rules for probe-coupling to waveguide
modes should be observed. For example, a TE.sub.20 (transverse
electric mode) waveguide probe may be optimal for extracting energy
from a conventional waveguide excited in the TE.sub.20 mode.
Similarly, in these cases, a mode-matched and phase-matched
receiving structure can be optimized for coupling power from a
surface-guided wave. The guided surface wave excited by a guided
surface waveguide probe 200 on the surface of the lossy conducting
medium 203 can be considered a waveguide mode of an open waveguide.
Excluding waveguide losses, the source energy can be completely
recovered. Useful receiving structures may be E-field coupled,
H-field coupled, or surface-current excited.
[0172] The receiving structure can be adjusted to increase or
maximize coupling with the guided surface wave based upon the local
characteristics of the lossy conducting medium 203 in the vicinity
of the receiving structure. To accomplish this, the phase delay
(.PHI.) of the receiving structure can be adjusted to match the
angle (.psi.) of the wave tilt of the surface traveling wave at the
receiving structure. If configured appropriately, the receiving
structure may then be tuned for resonance with respect to the
perfectly conducting image ground plane at complex depth
z=-d/2.
[0173] For example, consider a receiving structure comprising the
tuned resonator 306a of FIG. 18B, including a coil L.sub.R and a
vertical supply line connected between the coil L.sub.R and a
charge terminal T.sub.R. With the charge terminal T.sub.R
positioned at a defined height above the lossy conducting medium
203, the total phase shift .PHI. of the coil L.sub.R and vertical
supply line can be matched with the angle (.psi.) of the wave tilt
at the location of the tuned resonator 306a. From Equation (22), it
can be seen that the wave tilt asymptotically passes to
W = W e j .PSI. = E .rho. E z .fwdarw. .rho. .fwdarw. .infin. 1 r -
j .sigma. 1 .omega. o , ( 97 ) ##EQU00061##
where .epsilon..sub.r comprises the relative permittivity and
.sigma..sub.1 is the conductivity of the lossy conducting medium
203 at the location of the receiving structure, .epsilon..sub.o is
the permittivity of free space, and .omega.=2.pi.f, where f is the
frequency of excitation. Thus, the wave tilt angle (.psi.) can be
determined from Equation (97).
[0174] The total phase shift (.PHI.=.theta..sub.c+.theta..sub.y) of
the tuned resonator 306a includes both the phase delay
(.theta..sub.c) through the coil L.sub.R and the phase delay of the
vertical supply line (.theta..sub.y). The spatial phase delay along
the conductor length l.sub.w of the vertical supply line can be
given by .theta..sub.y=.beta..sub.wl.sub.w, where .beta..sub.w is
the propagation phase constant for the vertical supply line
conductor. The phase delay due to the coil (or helical delay line)
is .theta..sub.c=.beta..sub.pl.sub.c, with a physical length of
l.sub.c and a propagation factor of
.beta. p = 2 .pi. .lamda. p = 2 .pi. V f .lamda. 0 , ( 98 )
##EQU00062##
where V.sub.f is the velocity factor on the structure,
.lamda..sub.o is the wavelength at the supplied frequency, and
.lamda..sub.p is the propagation wavelength resulting from the
velocity factor V.sub.f. One or both of the phase delays
(.theta..sub.c+.theta..sub.y) can be adjusted to match the phase
shift .PHI. to the angle (.psi.) of the wave tilt. For example, a
tap position may be adjusted on the coil L.sub.R of FIG. 18B to
adjust the coil phase delay (.theta..sub.c) to match the total
phase shift to the wave tilt angle (.PHI.=.psi.). For example, a
portion of the coil can be bypassed by the tap connection as
illustrated in FIG. 18B. The vertical supply line conductor can
also be connected to the coil L.sub.R via a tap, whose position on
the coil may be adjusted to match the total phase shift to the
angle of the wave tilt.
[0175] Once the phase delay (.PHI.) of the tuned resonator 306a has
been adjusted, the impedance of the charge terminal T.sub.R can
then be adjusted to tune to resonance with respect to the perfectly
conducting image ground plane at complex depth z=-d/2. This can be
accomplished by adjusting the capacitance of the charge terminal
T.sub.1 without changing the traveling wave phase delays of the
coil L.sub.R and vertical supply line. The adjustments are similar
to those described with respect to FIGS. 9A and 9B.
[0176] The impedance seen "looking down" into the lossy conducting
medium 203 to the complex image plane is given by:
Z.sub.in=R.sub.in+jX.sub.in=Z.sub.o tan h(j.beta..sub.o(d/2)),
(99)
where .beta..sub.o=.omega. {square root over
(.mu..sub.o.epsilon..sub.o)}. For vertically polarized sources over
the Earth, the depth of the complex image plane can be given
by:
d/2.apprxeq.1 {square root over
(j.omega..mu..sub.1.sigma..sub.1-.omega..sup.2.mu..sub.1.epsilon..sub.1)}-
, (100)
where .mu..sub.1 is the permeability of the lossy conducting medium
203 and .epsilon..sub.1=.epsilon..sub.r.epsilon..sub.o.
[0177] At the base of the tuned resonator 306a, the impedance seen
"looking up" into the receiving structure is
Z.sub..uparw.=Z.sub.base as illustrated in FIG. 9A. With a terminal
impedance of:
Z R = 1 j .omega. C R , ( 101 ) ##EQU00063##
where C.sub.R is the self-capacitance of the charge terminal
T.sub.R, the impedance seen "looking up" into the vertical supply
line conductor of the tuned resonator 306a is given by:
Z 2 = Z W Z R + Z w tanh ( j .beta. w h w ) Z w + Z R tanh ( j
.beta. w h w ) = Z W Z R + Z w tanh ( j .theta. y ) Z w + Z R tanh
( j .theta. y ) , ( 102 ) ##EQU00064##
and the impedance seen "looking up" into the coil L.sub.R of the
tuned resonator 306a is given by:
Z base = R base + jX base = Z R Z 2 + Z R tanh ( j .beta. p H ) Z R
+ Z 2 tanh ( j .beta. p H ) = Z c Z 2 + Z R tanh ( j .theta. c ) Z
R + Z 2 tanh ( j .theta. c ) . ( 103 ) ##EQU00065##
By matching the reactive component (X.sub.in) seen "looking down"
into the lossy conducting medium 203 with the reactive component
(X.sub.base) seen "looking up" into the tuned resonator 306a, the
coupling into the guided surface waveguide mode may be
maximized.
[0178] Referring next to FIG. 18C, shown is an example of a tuned
resonator 306b that does not include a charge terminal T.sub.R at
the top of the receiving structure. In this embodiment, the tuned
resonator 306b does not include a vertical supply line coupled
between the coil L.sub.R and the charge terminal T.sub.R. Thus, the
total phase shift (.PHI.) of the tuned resonator 306b includes only
the phase delay (.theta..sub.c) through the coil L.sub.R. As with
the tuned resonator 306a of FIG. 18B, the coil phase delay
.theta..sub.c can be adjusted to match the angle (.psi.) of the
wave tilt determined from Equation (97), which results in
.PHI.=.psi.. While power extraction is possible with the receiving
structure coupled into the surface waveguide mode, it is difficult
to adjust the receiving structure to maximize coupling with the
guided surface wave without the variable reactive load provided by
the charge terminal T.sub.R.
[0179] Referring to FIG. 18D, shown is a flow chart 180
illustrating an example of adjusting a receiving structure to
substantially mode-match to a guided surface waveguide mode on the
surface of the lossy conducting medium 203. Beginning with 181, if
the receiving structure includes a charge terminal T.sub.R (e.g.,
of the tuned resonator 306a of FIG. 18B), then the charge terminal
T.sub.R is positioned at a defined height above a lossy conducting
medium 203 at 184. As the surface guided wave has been established
by a guided surface waveguide probe 200, the physical height
(h.sub.p) of the charge terminal T.sub.R may be below that of the
effective height. The physical height may be selected to reduce or
minimize the bound charge on the charge terminal T.sub.R (e.g.,
four times the spherical diameter of the charge terminal). If the
receiving structure does not include a charge terminal T.sub.R
(e.g., of the tuned resonator 306b of FIG. 18C), then the flow
proceeds to 187.
[0180] At 187, the electrical phase delay .PHI. of the receiving
structure is matched to the complex wave tilt angle .psi. defined
by the local characteristics of the lossy conducting medium 203.
The phase delay (.theta..sub.c) of the helical coil and/or the
phase delay (.theta..sub.y) of the vertical supply line can be
adjusted to make .PHI. equal to the angle (.psi.) of the wave tilt
(W). The angle (.psi.) of the wave tilt can be determined from
Equation (86). The electrical phase .PHI. can then be matched to
the angle of the wave tilt. For example, the electrical phase delay
.PHI.=.theta..sub.c+.theta..sub.y can be adjusted by varying the
geometrical parameters of the coil L.sub.R and/or the length (or
height) of the vertical supply line conductor.
[0181] Next at 190, the load impedance of the charge terminal
T.sub.R can be tuned to resonate the equivalent image plane model
of the tuned resonator 306a. The depth (d/2) of the conducting
image ground plane 139 (FIG. 9A) below the receiving structure can
be determined using Equation (100) and the values of the lossy
conducting medium 203 (e.g., the Earth) at the receiving structure,
which can be locally measured. Using that complex depth, the phase
shift (.theta..sub.d) between the image ground plane 139 and the
physical boundary 136 (FIG. 9A) of the lossy conducting medium 203
can be determined using .theta..sub.d=.beta..sub.o d/2. The
impedance (Z.sub.in) as seen "looking down" into the lossy
conducting medium 203 can then be determined using Equation (99).
This resonance relationship can be considered to maximize coupling
with the guided surface waves.
[0182] Based upon the adjusted parameters of the coil L.sub.R and
the length of the vertical supply line conductor, the velocity
factor, phase delay, and impedance of the coil L.sub.R and vertical
supply line can be determined. In addition, the self-capacitance
(C.sub.R) of the charge terminal T.sub.R can be determined using,
e.g., Equation (24). The propagation factor (.beta..sub.p) of the
coil L.sub.R can be determined using Equation (98), and the
propagation phase constant (.beta..sub.w) for the vertical supply
line can be determined using Equation (49). Using the
self-capacitance and the determined values of the coil L.sub.R and
vertical supply line, the impedance (Z.sub.base) of the tuned
resonator 306a as seen "looking up" into the coil L.sub.R can be
determined using Equations (101), (102), and (103).
[0183] The equivalent image plane model of FIG. 9A also applies to
the tuned resonator 306a of FIG. 18B. The tuned resonator 306a can
be tuned to resonance with respect to the complex image plane by
adjusting the load impedance Z.sub.R of the charge terminal T.sub.R
such that the reactance component X.sub.base of Z.sub.base cancels
out the reactance component of X.sub.in of Z.sub.in, or
X.sub.base+X.sub.in=0. Thus, the impedance at the physical boundary
136 (FIG. 9A) "looking up" into the coil of the tuned resonator
306a is the conjugate of the impedance at the physical boundary 136
"looking down" into the lossy conducting medium 203. The load
impedance Z.sub.R can be adjusted by varying the capacitance
(C.sub.R) of the charge terminal T.sub.R without changing the
electrical phase delay .PHI.=.theta..sub.c+.theta..sub.y seen by
the charge terminal T.sub.R. An iterative approach may be taken to
tune the load impedance Z.sub.R for resonance of the equivalent
image plane model with respect to the conducting image ground plane
139. In this way, the coupling of the electric field to a guided
surface waveguide mode along the surface of the lossy conducting
medium 203 (e.g., Earth) can be improved and/or maximized.
[0184] Referring to FIG. 19, the magnetic coil 309 comprises a
receive circuit that is coupled through an impedance matching
network 333 to an electrical load 336. In order to facilitate
reception and/or extraction of electrical power from a guided
surface wave, the magnetic coil 309 may be positioned so that the
magnetic flux of the guided surface wave, H.sub..PHI. passes
through the magnetic coil 309, thereby inducing a current in the
magnetic coil 309 and producing a terminal point voltage at its
output terminals 330. The magnetic flux of the guided surface wave
coupled to a single turn coil is expressed by
=.intg..intg..sub.A.sub.CS.mu..sub.r.mu..sub.o{circumflex over
(n)}dA (104)
where is the coupled magnetic flux, .mu..sub.r is the effective
relative permeability of the core of the magnetic coil 309,
.mu..sub.o is the permeability of free space, is the incident
magnetic field strength vector, {circumflex over (n)} is a unit
vector normal to the cross-sectional area of the turns, and
A.sub.CS is the area enclosed by each loop. For an N-turn magnetic
coil 309 oriented for maximum coupling to an incident magnetic
field that is uniform over the cross-sectional area of the magnetic
coil 309, the open-circuit induced voltage appearing at the output
terminals 330 of the magnetic coil 309 is
V = - N dF dt .apprxeq. - j .omega. .mu. r .mu. 0 NHA CS , ( 105 )
##EQU00066##
where the variables are defined above. The magnetic coil 309 may be
tuned to the guided surface wave frequency either as a distributed
resonator or with an external capacitor across its output terminals
330, as the case may be, and then impedance-matched to an external
electrical load 336 through a conjugate impedance matching network
333.
[0185] Assuming that the resulting circuit presented by the
magnetic coil 309 and the electrical load 336 are properly adjusted
and conjugate impedance matched, via impedance matching network
333, then the current induced in the magnetic coil 309 may be
employed to optimally power the electrical load 336. The receive
circuit presented by the magnetic coil 309 provides an advantage in
that it does not have to be physically connected to the ground.
[0186] With reference to FIGS. 18A, 18B, 18C and 19, the receive
circuits presented by the linear probe 303, the mode-matched
structure 306, and the magnetic coil 309 each facilitate receiving
electrical power transmitted from any one of the embodiments of
guided surface waveguide probes 200 described above. To this end,
the energy received may be used to supply power to an electrical
load 315/327/336 via a conjugate matching network as can be
appreciated. This contrasts with the signals that may be received
in a receiver that were transmitted in the form of a radiated
electromagnetic field. Such signals have very low available power,
and receivers of such signals do not load the transmitters.
[0187] It is also characteristic of the present guided surface
waves generated using the guided surface waveguide probes 200
described above that the receive circuits presented by the linear
probe 303, the mode-matched structure 306, and the magnetic coil
309 will load the excitation source 212 (e.g., FIGS. 3, 12 and 16)
that is applied to the guided surface waveguide probe 200, thereby
generating the guided surface wave to which such receive circuits
are subjected. This reflects the fact that the guided surface wave
generated by a given guided surface waveguide probe 200 described
above comprises a transmission line mode. By way of contrast, a
power source that drives a radiating antenna that generates a
radiated electromagnetic wave is not loaded by the receivers,
regardless of the number of receivers employed.
[0188] Thus, together one or more guided surface waveguide probes
200 and one or more receive circuits in the form of the linear
probe 303, the tuned mode-matched structure 306, and/or the
magnetic coil 309 can make up a wireless distribution system. Given
that the distance of transmission of a guided surface wave using a
guided surface waveguide probe 200 as set forth above depends upon
the frequency, it is possible that wireless power distribution can
be achieved across wide areas and even globally.
[0189] The conventional wireless-power transmission/distribution
systems extensively investigated today include "energy harvesting"
from radiation fields and also sensor coupling to inductive or
reactive near-fields. In contrast, the present wireless-power
system does not waste power in the form of radiation which, if not
intercepted, is lost forever. Nor is the presently disclosed
wireless-power system limited to extremely short ranges as with
conventional mutual-reactance coupled near-field systems. The
wireless-power system disclosed herein probe-couples to the novel
surface-guided transmission line mode, which is equivalent to
delivering power to a load by a wave-guide or a load directly wired
to the distant power generator. Not counting the power required to
maintain transmission field strength plus that dissipated in the
surface waveguide, which at extremely low frequencies is
insignificant relative to the transmission losses in conventional
high-tension power lines at 60 Hz, all of the generator power goes
only to the desired electrical load. When the electrical load
demand is terminated, the source power generation is relatively
idle.
[0190] Referring next to FIGS. 20A-E, shown are examples of various
schematic symbols that are used with reference to the discussion
that follows. With specific reference to FIG. 20A, shown is a
symbol that represents any one of the guided surface waveguide
probes 200a, 200b, 200c, 200e, 200d, or 200f; or any variations
thereof. In the following drawings and discussion, a depiction of
this symbol will be referred to as a guided surface waveguide probe
P. For the sake of simplicity in the following discussion, any
reference to the guided surface waveguide probe P is a reference to
any one of the guided surface waveguide probes 200a, 200b, 200c,
200e, 200d, or 200f; or variations thereof.
[0191] Similarly, with reference to FIG. 20B, shown is a symbol
that represents a guided surface wave receive structure that may
comprise any one of the linear probe 303 (FIG. 18A), the tuned
resonator 306 (FIGS. 18B-18C), or the magnetic coil 309 (FIG. 19).
In the following drawings and discussion, a depiction of this
symbol will be referred to as a guided surface wave receive
structure R. For the sake of simplicity in the following
discussion, any reference to the guided surface wave receive
structure R is a reference to any one of the linear probe 303, the
tuned resonator 306, or the magnetic coil 309; or variations
thereof.
[0192] Further, with reference to FIG. 20C, shown is a symbol that
specifically represents the linear probe 303 (FIG. 18A). In the
following drawings and discussion, a depiction of this symbol will
be referred to as a guided surface wave receive structure R.sub.P.
For the sake of simplicity in the following discussion, any
reference to the guided surface wave receive structure R.sub.P is a
reference to the linear probe 303 or variations thereof.
[0193] Further, with reference to FIG. 20D, shown is a symbol that
specifically represents the tuned resonator 306 (FIGS. 18B-18C). In
the following drawings and discussion, a depiction of this symbol
will be referred to as a guided surface wave receive structure
R.sub.R. For the sake of simplicity in the following discussion,
any reference to the guided surface wave receive structure R.sub.R
is a reference to the tuned resonator 306 or variations
thereof.
[0194] Further, with reference to FIG. 20E, shown is a symbol that
specifically represents the magnetic coil 309 (FIG. 19). In the
following drawings and discussion, a depiction of this symbol will
be referred to as a guided surface wave receive structure R.sub.M.
For the sake of simplicity in the following discussion, any
reference to the guided surface wave receive structure R.sub.M is a
reference to the magnetic coil 309 or variations thereof.
[0195] FIG. 21 depicts one example of a geographic area 2100 served
by a plurality of wireless power providers that operate guided
surface waveguide probes P1, P2, and P3 according to various
embodiments. Each of the wireless power providers transmits power
to a respective service area 2106 using a guided surface waveguide
probe power transmission system as previously described. For
example, the wireless power provider that operates the guided
surface waveguide probe P1 transmits to service area 2106a, the
wireless power provider that operates the guided surface waveguide
probe P2 transmits to service area 2106b, and the wireless power
provider that operates the guided surface waveguide probe P3
transmits to service area 2106c.
[0196] Receivers within a service area 2106 are able to receive
power from the respective guided surface waveguide probe P that
transmits guided surface wave that comprises a transmission line
mode as previously described. The size of the service area 2106
may, for example, be a function of the frequency at which power is
transmitted by the corresponding guided surface waveguide probe P
by the wireless power provider. Lower frequencies are associated
with greater service areas 2106. Although the service areas 2106
are shown in FIG. 21 as circles, it is understood that the actual
shape of the service area 2106 may be affected, for example, by
ground conductivity, terrain, loads imposed by receivers, and other
factors.
[0197] The wireless power providers depicted in FIG. 21 may employ
frequency division multiplexing to transmit on non-overlapping
frequencies. Many different frequencies may be employed in various
examples, depending on the distances required. As a non-limiting
example, the wireless power provider that operates the guided
surface waveguide probe P1 may use 900 kHz, the wireless power
provider that operates the guided surface waveguide probe P2 may
use 925 kHz, and the wireless power provider that operates the
guided surface waveguide probe P3 may use 930 kHz or other
frequencies. The frequencies may be selected such that the signals
driven by the guided surface waveguide probes P are not
interfering. In one embodiment, the transmission systems of
wireless power providers may be arranged in a honeycomb arrangement
similar to that of conventional cellular telephone systems. Such an
arrangement may maximize reuse of frequencies. In some embodiments,
a single wireless power provider may transmit on multiple
frequencies using the same or co-located transmission
apparatus.
[0198] However, the arrangement depicted in FIG. 21 may arise out
of a desire to best serve a population within the geographic area
2100. A larger service area 2106 (such as service area 2106b) may
be used to serve a rural geography, while a smaller service area
(such as service area 2106c) may be used to serve a more densely
populated geography. The service areas 2106 may overlap in order to
supply increased loads to receivers that can utilize power
transmitted on multiple frequencies. In one embodiment, the
receiver may be configured to draw power from multiple wireless
power providers based at least in part on the size of an electric
load at the receiver. Additionally, the wireless power providers
may correspond to competing providers that offer power at varying
cost. Frequency-agile receivers may be configured to use power from
a lowest-cost wireless power provider, where multiple wireless
power providers are available.
[0199] For example, a receiver at a location 2109a may draw power
from any combination of the guided surface waveguide probes P1, P2,
or P3. However, a receiver at a location 2109b may draw power from
any combination of the guided surface waveguide probes P1 or P2.
Location 2109b is not within the service area 2106c of the guided
surface waveguide probe P3.
[0200] The ability of a wireless power provider to supply power may
vary based upon aggregate load. Suppose that between 2 pm and 7 pm
corresponds to a peak power period for a wireless power provider,
as air conditioners and other appliances in the afternoon may
generate a peak demand. The wireless power provider may bring
additional peak generating capacity online to meet the demand. Such
peak generating capacity may be higher cost, e.g., oil-fired
generators or natural gas turbines rather than hydropower.
Accordingly, the power cost passed onto the consumer by the
wireless power provider may increase during the peak period. In
some cases, the aggregate load may saturate the ability of the
wireless power provider to provide power reliably, and the wireless
power provider may limit or deny access to power.
[0201] In view of potential denial of service and/or higher costs,
receivers within the service areas 2106 of multiple wireless power
providers may seek alternative sources of power, which may be of
lower costs and/or better availability. In locations 2109a and
2109b, switching to an alternative wireless power provider may be
as simple as switching the frequency to which the receiver is
tuned.
[0202] Also, it is noted that the guided surface waveguide probes P
of FIG. 21 may include mobile guided surface waveguide probes P as
well as static guided surface waveguide probes P. Mobile guided
surface waveguide probes P may be moved to and brought online in a
given area to satisfy increased demand if necessary. For example, a
mobile guided surface waveguide probe P may be brought online in a
given area due to increased demand anticipated for a sporting
event, large gathering, etc.
[0203] As will be described, various aspects of the present
disclosure include discovering availability of different signals
from wireless power providers at a location; receiving cost and/or
availability data from a given wireless power provider; selecting
one or more wireless power providers in a frequency-agile receiver;
metering power usage for each wireless power provider; reporting
power usage back to the wireless power provider; and adjusting
generation of power at the wireless power provider based at least
in part on reported usage.
[0204] Various embodiments of a multiple frequency power receiver
are discussed in Appendix A, which is incorporated herein by
reference in its entirety.
[0205] Various embodiments of a frequency-agile power receiver are
discussed in Appendix B, which is incorporated herein by reference
in its entirety.
[0206] Moving on to FIG. 22, shown is one example of a receiver
system 2400a according to various embodiments. The receiver system
2400a may include a guided surface wave receive structure R, an
impedance matching network 2404, an electrical load 2406, a power
meter 2409, and/or other components. The guided surface wave
receive structure R comprises a multi-frequency and/or a
frequency-agile structure capable of receiving power via a guided
surface wave. The receiver system 2400a may be capable of receiving
power via multiple frequencies simultaneously. The receiver system
2400a may be capable of switching from one frequency to another via
the impedance matching circuitry 2404.
[0207] The guided surface wave receive structure R, via the
impedance matching circuitry 2404, provides power to an electrical
load 2406, which may correspond to any type of load. In various
embodiments, the power is provided via direct current (DC) or
alternating current (AC). That is to say, the load may include the
capability to convert power from a frequency at which it was
transmitted into DC power. Also, one may employ an AC-to-AC
conversion to convert the power from the frequency at which it was
transmitted to a desired frequency for the load. If alternating
current is desired, the power may be provided at 60 Hz, 50 Hz, or
another frequency, which need not be the same as the frequency of
the guided surface wave that carries the power. A sensor 2412
coupled to the power meter 2409 may be positioned on the power
supply line between the guided surface wave receive structure R and
the electrical load 2406. The sensor 2412 detects the power usage
by the electrical load 2406. In this regard, the sensor 2412 may
detect the power, current, and/or voltage used via the power supply
line.
[0208] The power meter 2409 may comprise provider control circuitry
2415, usage reporting circuitry 2418, and/or other components. The
provider control circuitry 2415 may control the impedance matching
circuitry via a frequency control line 2419 in order to select one
or more wireless power providers. In this regard, the provider
control circuitry 2415 may specify one or more power frequencies to
be received by the guided surface wave receive structure R to
receive power. The frequency control line 2419 may cause adjustment
of a variable capacitor, adjustment of a variable inductor, and/or
other similar actions, such that the impedance matching circuitry
2040 is tuned to a particular frequency.
[0209] The provider control circuitry 2415 may select a power
provider based at least in part upon any of a variety of factors. A
current location of the receiver system 2400a may determine which
wireless power providers are available. To this end, location
information (e.g., obtained via global positioning system (GPS) or
a manually entered address) may be used by the provider control
circuitry 2415 to look up the available wireless power providers at
a given location. The ability of a wireless power provider to serve
a location may change over time. For example, power provider A and
power provider B may serve a location Q at a given time T.
[0210] Current cost information associated with one or more
wireless power providers may inform a selection based at least in
part on minimizing cost. For example, during non-peak periods,
power provider A may charge $0.10 per kWh, while power provider B
may charge $0.04 per kWh. During peak periods, the power provider A
may charge $0.10 per kWh (unchanged from non-peak), while power
provider B may charge $0.20 per kWh (greatly increased from
non-peak). In some embodiments, the cost may be assessed based at
least in part on receiver location. For example, receivers that are
nearer to the transmitting probe may be given a lower price, while
receivers that are far away from the transmitting probe may be
given a higher price.
[0211] Current power usage by the electrical load 2406 may also
inform the provider selection. If the electrical load 2406 is using
relatively little power, cost of the power may be a lesser factor
than power quality. By contrast, if the electrical load 2406 is
using a large amount of power, cost of the power may be a
significant factor.
[0212] A service-level requirement of the electrical load 2406 may
also factor in the provider selection. Different power providers
may be associated with different levels of power quality and/or
availability. Quality issues may arise due to location of the
receiver, load upon the power provider, and/or other factors. As to
availability, a power provider utilizing solar arrays may be
incapable of transmitting power at night, for example. In some
cases, a wireless power provider may jettison receivers of lesser
importance from the system to maintain system quality and/or
availability. Moreover, in some cases, wireless power providers may
operate closed systems in which only certain approved customers are
authorized to use receivers.
[0213] If loss of power for the electrical load 2406 will result in
a potential loss of life or injury, power quality rather than cost
may be a dominating factor. However, some power uses may be
rescheduled to other times that have lower cost of power. In some
cases, receiver systems 2400a may be capable of switching between
wirelessly transmitted power and power transmitted by the
conventional wire-based grid.
[0214] The usage reporting circuitry 2418 is used to transmit the
power usage back to the wireless power provider. In some
embodiments, the usage reporting circuitry 2418 may store power
usage history in a local memory of the power meter 2409. The usage
reporting circuitry 2418 may transmit the power usage back in
real-time, at periodic intervals, in response to predefined events,
and/or at other times. The usage reporting circuitry 2418 may be
configured to report the usage data according to a variety of
approaches as will be described. Further, the usage data reported
by receiver systems 2400a may be employed by the wireless power
provider to adjust power generation and/or transmission
parameters.
[0215] In some embodiments, the electrical load 2406 may comprise
an aggregate load of potentially many uses. For example, the
electrical load 2406 may correspond to load imposed by the
customers of a power company via a conventional wired power grid.
In such a case, the receiver system 2400 may be operated by a power
provider in order to obtain wholesale power from a lowest-cost
provider.
[0216] With reference to FIG. 23, shown is a networked environment
2500 according to various embodiments. The networked environment
100 includes a plurality of power provider systems 2503a . . .
2503N and a plurality of power meters 2409a . . . 2409N, which are
in data communication with each other via a network 2506. The
network 2506 includes, for example, the Internet, intranets,
extranets, wide area networks (WANs), local area networks (LANs),
wired networks, wireless networks, cable networks, satellite
networks, cellular networks, or other suitable networks, etc., or
any combination of two or more such networks.
[0217] Each power provider system 2503 may comprise, for example, a
server computer or any other system providing computing capability.
Alternatively, the power provider system 2503 may employ a
plurality of computing devices that may be arranged, for example,
in one or more server banks or computer banks or other
arrangements. Such computing devices may be located in a single
installation or may be distributed among many different
geographical locations. For example, the power provider system 2503
may include a plurality of computing devices that together may
comprise a hosted computing resource, a grid computing resource,
and/or any other distributed computing arrangement. In some cases,
the power provider system 2503 may correspond to an elastic
computing resource where the allotted capacity of processing,
network, storage, or other computing-related resources may vary
over time.
[0218] Next, a general description of the operation of the various
components of the networked environment 2500 is provided. The power
provider systems 2503 are configured to transmit cost data 2509 and
availability data 2512 to the power meters 2409 via the network
2506. The cost data 2509 may indicate a rate schedule applicable
for a particular wireless power provider. The cost data 2509 may
include current rates, previous rates, and future rates. The rates
may be tiered such that a first level of usage is assessed one rate
and a second level of usage is assessed a different rate. The cost
data 2509 may be specific to a given customer or usage type or may
include rates that are generally applicable. The cost data 2509 may
include location-specific rates. For example, rates with a city or
other jurisdiction may be higher due to franchise fees, taxes,
and/or other charges.
[0219] The availability data 2512 may indicate whether one or more
wireless power providers have power capacities available, and if
so, at what frequencies. The availability data 2512 may indicate a
reference location for the transmitting probe and, potentially, one
or more metrics indicating signal quality and/or power transfer
capacity at various distances. For example, the availability data
2512 may indicate that a wireless power provider has 2.5 MW of
power capacity available at 100 kHz at a given reference location.
The availability data 2512 may indicate specific customers and/or
classes of customers that are allowed to consume power from a given
wireless power provider.
[0220] The power meters 2409 are configured to transmit power usage
data 2515 to the respective power provider systems 2503. In various
embodiments, the usage data 2515 may include power currently
consumed, power consumed over a period of time, unique customer
identification, identification of the corresponding receiver system
2400a (FIG. 22), identification of the location of the
corresponding receiver system 2400a, identification of the
frequency or frequencies via which the power was consumed,
identification of a specific transmitting station from which the
power was consumed, types of electrical loads 2406, and/or other
information.
[0221] In some cases, a power meter 2409 may communicate with a
power provider system 2503 in order to reserve power capacity
and/or gain permission to receive power. Some embodiments may rely
upon the receiver system 2400a being configured specifically not to
obtain power unless authorized. In other embodiments, a form of
scrambling and/or encryption may be used. For example, the wireless
power provider may be configured to switch frequencies randomly
and/or to enable or disable power transmission. An understanding of
the pattern driving the frequency shift may be necessary in order
to receive power successfully or at least without interruption.
Thus, a key encoding the pattern may be provided to the authorized
receiver systems 2400a. The key may be provided via encrypted
communications.
[0222] Turning now to FIG. 24, shown is one example of a receiver
system 2400b according to various embodiments. In contrast to the
receiver system 2400a (FIG. 22), the receiver system 2400b includes
a load modulator 2530 as part of the electrical load 2406. The load
modulator 2530 may be in parallel or in series with the electrical
load 2406. The load modulator 2530 is configured to modulate the
amplitude of the electrical load 2406 to convey information to the
wireless power provider from whom power is being drawn.
[0223] In one embodiment, the wireless power provider is able to
detect an aggregate electrical load seen by a guided surface
waveguide probe P. Using this feature, the aggregate electrical
load may be modulated to convey information such as the power usage
data 2515 being reported by the power meter 2409. The modulation of
the load would be configured so as not to interfere with or
interrupt the power being supplied to the electrical load 2406. In
addition, the nature of the modulation may be selected so as to be
distinct from natural fluctuations in power consumed by the
electrical loads 2406. Further, the load modulator 2530 may be
configured to avoid collisions with load modulators 2530 of other
receiver systems 2400b. Approaches similar to carrier sensing,
collision detection, collision avoidance, and so on may be
utilized. Frequency-division and/or time-division multiplexing
techniques may also be applied to enable the coexistence of
numerous load modulators 2530 for a given wireless power
provider.
[0224] Continuing now to FIG. 25, shown is one example of a
receiver system 2400c according to various embodiments. In contrast
to the receiver system 2400b (FIG. 24), the receiver system 2400c
may be configured to receive data in-band from the wireless power
provider. That is to say, a data demodulator 2533 capable of
receiving data transmissions embedded in the guided surface wave
that conveys power may intercept the received signal from the
impedance matching circuitry 2404 or from the guide surface wave
receive structure R itself. For example, the guided surface wave
may vary in frequency, phase, and/or amplitude to convey a data
signal. The data demodulator 2533 may demodulate these data
transmissions to supply provider data 2536 to the power meter 2409,
and specifically, to the provider control circuitry 2415. The
provider data 2536 may include cost data 2509 (FIG. 23),
availability or capacity data 2512 (FIG. 23), and/or other
data.
[0225] With the additions of the load modulator 2530 and the data
demodulator 2533, forward and return path communications may be
facilitated in-band for the wireless power transmission system.
Thus, the operations described in conjunction with the networked
environment 2500 (FIG. 23) may be performed in-band without a
separate network 2506 (FIG. 23). It is understood, however, that
various embodiments may employ a mixture of in-band and out-of-band
communication for the cost data 2509, the availability data 2512,
and/or the power usage data 2515.
[0226] Additional details regarding embodiments using a load
modulator 2530 are discussed in Appendix C, which is incorporated
herein by reference in its entirety.
[0227] Moving on to FIG. 26, shown is a wireless power provider
2700 according to various embodiments. The wireless power provider
2700 may include, for example, a power provider system 2503, a
generator control 2703, and a guided surface waveguide probe P. The
power provider system 2503 may be operable to receive the power
usage data 2515 from the power meters 2409 (FIG. 23). The power
provider system 2503 may process the power usage data 2515 to
determine an aggregate load for the guided surface waveguide probe
P.
[0228] Using the aggregate load information, the power provider
system 2503 may command the generator control 2703 to adjust
various parameters associated with power generation via the
generator associated with the guided surface waveguide probe P. For
example, the generator control 2703 may bring on board additional
power generating capacity to meet the demand and/or may operate the
generator so as to meet the increased load. Conversely, if the
aggregate load has decreased, the generator control 2703 may remove
or disable generating capacity and/or may operate the generator so
as to meet the reduced load. In various embodiments, various
parameters of the guided surface waveguide probe P may be adjusted
in response to the power usage data 2515 in order to meet the
present load in an efficient manner. In the end, the generator or
other power source is driven to maintain a constant voltage or
charge on the charge terminal of the respective guided surface
waveguide probe P given the nature of the load at any specific
time.
[0229] Referring next to FIG. 27, shown is a flowchart that
provides one example of the operation of a portion of the power
provider system 2503 according to various embodiments. It is
understood that the flowchart of FIG. 27 provides merely an example
of the many different types of functional arrangements that may be
employed to implement the operation of the portion of the power
provider system 2503 as described herein. As an alternative, the
flowchart of FIG. 27 may be viewed as depicting an example of
elements of a method implemented in the power provider system 2503
according to one or more embodiments.
[0230] Beginning with box 3003, the power provider system 2503 may
receive a request from a receiver system 2400 (FIG. 22) for power
capacity. In box 3006, the power provider system 2503 may determine
the location of the receiver system 2400. In some cases, the
request and/or subsequent communications may specify the location
of the receiver system 2400, e.g., in GPS coordinates.
Alternatively, the receiver system 2400 may be associated with a
fixed location, and the power provider system 2503 may look up the
fixed location in a data store.
[0231] In box 3009, the power provider system 2503 may determine an
electrical load 2406 (FIG. 22) associated with the receiver system
2400. The electrical load 2406 may be of a fixed nature and stored
in a data stored in association with an identification of the
receiver system 2400. Alternatively, the electrical load 2406 may
be specified by the request and/or subsequent communications from
the receiver system 2400.
[0232] In box 3012, the power provider system 2503 may determine an
assignment of the receiver system 2400 to one or more power
frequencies. The power provider system 2503 may determine the
guided surface waveguide probe systems that could service the
customer based on customer location, type of customer, etc.
Further, the power provider system 2503 may determine the present
available capacity for such systems. In box 3015, the power
provider system 2503 may inform the receiver system 2400 of the
proposed assignment, including cost, availability, and/or other
parameters.
[0233] In box 3018, the power provider system 2503 may obtain a
confirmation from the receiver system 2400 that it wishes to
proceed with the power connection. In box 3021, the power provider
system 2503 may determine whether generation capacity needs to be
adjusted in order to accommodate the receiver system 2400. If so,
the power provider system 2503 moves to box 3024 and may adjust the
generation capacity to accommodate the predicted electrical load
2406 associated with the receiver system 2400. The power provider
system 2503 continues to box 3027. If generation capacity does not
need to be adjusted, the power provider system 2503 moves from box
3021 to box 3027.
[0234] In box 3027, the power provider system 2503 may notify the
receiver system 2400 that the power capacity is available and
ready. In such a notification, the power provider system 2503 may
transmit information necessary to receive the power, including
frequency change patterns (e.g., frequency hopping) and/or other
data to overcome power theft deterrent measures. In box 3030, the
power provider system 2503 initiates wireless power transmission to
the receiver system 2400 when the receiver system 2400 creates a
load. Thereafter, the operation of the portion of the power
provider system 2503 ends.
[0235] Although the flowchart of FIG. 27 describes one example of a
handshake communication procedure in order to initiate wireless
power transmission, it is understood that various tasks of such a
procedure may be optional. For example, a receiver system 2400 may
be capable of discovering power frequencies automatically, and the
receiver system 2400 may be configured to report power usage on an
"honor" system. In other words, prior approval by the power
provider system 2503 may not be employed in some embodiments. The
receiver system 2400 may be hardened using various techniques to
ensure they are not tampered with, so that they properly report the
power usage to the respective power provider system 2503.
[0236] Turning now to FIG. 28, shown is a flowchart that provides
one example of the operation of another portion of the power
provider system 2503 according to various embodiments. It is
understood that the flowchart of FIG. 28 provides merely an example
of the many different types of functional arrangements that may be
employed to implement the operation of the portion of the power
provider system 2503 as described herein. As an alternative, the
flowchart of FIG. 28 may be viewed as depicting an example of
elements of a method implemented in the power provider system 2503
according to one or more embodiments.
[0237] Beginning with box 3103, the power provider system 2503 may
receive a plurality of reports of power usage data 2515 (FIG. 23)
from a plurality of receiver systems 2400 (FIG. 22). From these
reports, the power provider system 2503 may determine an aggregate
load upon a guided surface waveguide probe in box 3106. In some
embodiments, the power provider system 2503 may be able to
determine the aggregate load by measuring the current at a ground
stake of the guided surface waveguide probe P, by determining the
current and voltage supplied to the guided surface waveguide probe
P from a power source such as a generator or solar farm, etc., or
by obtaining other readings relative to components of a respective
guided surface waveguide probe P.
[0238] In box 3109, the power provider system 2503 may determine
whether to increase power capacity based at least in part on the
aggregate load and/or other operating parameters of the system such
as the voltage or charge on the upper terminal of a given guided
surface waveguide probe P. If capacity is to be increased, the
power provider system 2503 moves to box 3112 and may adjust
operating parameters of a power generator or other power source to
increase power capacity. That is to say, the power provider system
2503 may communicate with a generator control 2703 (FIG. 26) to
being more power generating capacity online. The power provider
system 2503 proceeds to box 3115.
[0239] If, instead, the power provider system 2503 determines not
to increase the power capacity in box 3109, the power provider
system 2503 transitions from box 3109 to box 3118. In box 3118, the
power provider system 2503 may determine whether to decrease the
power capacity based at least in part on the aggregate load. If
capacity is to be decreased, the power provider system 2503 moves
to box 3121 and may adjust operating parameters of generators or
other power sources to decrease power capacity. This may be done by
communicating with a generator control 2703 to take power
generating capacity offline. The power provider system 2503
proceeds to box 3115.
[0240] In box 3115, the power provider system 2503 determines
whether to transfer one or more receiver systems 2400 to other
guided surface waveguide probes. For example, the load imposed on
the guided surface waveguide probe may be maximized, and one or
more receiver systems 2400 may need to be transferred to systems
operating on other frequencies to prevent overloading. In some
embodiments, the receiver systems 2400 that are transferred may
continue to operate on the existing frequency but may also operate
upon the transferred frequency as well to obtain at least some
power. In one scenario, the aggregate load may have dropped to an
extent that the guided surface waveguide probe at the present
frequency is to be turned off, and the existing receiver systems
2400 are to be transitioned to another frequency.
[0241] If one or more receiver systems 2400 are to be transferred,
the power provider system 2503 may generate new receiver
assignments in box 3124. The power provider system 2503 then may
send notifications to the affected receiver systems 2400 in box
3127. Thereafter, the operation of the portion of the power
provider system 2503 ends.
[0242] Referring next to FIG. 29, shown is a flowchart that
provides one example of the operation of a portion of the receiver
system 2400 (FIG. 22) according to various embodiments. It is
understood that the flowchart of FIG. 29 provides merely an example
of the many different types of functional arrangements that may be
employed to implement the operation of the portion of the receiver
system 2400 as described herein. As an alternative, the flowchart
of FIG. 29 may be viewed as depicting an example of elements of a
method implemented in the receiver system 2400 according to one or
more embodiments.
[0243] Beginning with box 3203, the receiver system 2400 may
discover available wireless power providers. This discovery may
involve a scan of the frequency transmission spectrum,
communication with one or more power provider systems 2503 (FIG.
23) via the Internet, or another approach. The discovery may
involve obtaining information about cost, availability, and/or
other factors. In box 3206, the receiver system 2400 may determine
a predicted electrical load 2406 (FIG. 22). In box 3209, the
receiver system 2400 may select one or more wireless power
providers from whom to obtain power. Factors driving the selection
may include, for example, cost, availability, reliability, and so
on.
[0244] In box 3212, the receiver system 2400 may request power from
the selected wireless power provider(s). In box 3215, the receiver
system 2400 may begin receiving power from the selected wireless
power provider(s). In box 3218, the receiver system 2400 may
determine a present power usage by the electrical load 2406. In box
3221, the receiver system 2400 may report the power usage to the
corresponding wireless power providers.
[0245] In box 3224, the receiver system 2400 may receive power
provider data from one or more wireless power providers. This power
provider data may include updated availability, cost, frequencies,
and/or other information. In box 3227, the receiver system 2400
determines whether to adjust its operation. If not, the receiver
system 2400 returns to box 3215 and continues receiving power from
the wireless power provider(s).
[0246] If the operation is to be adjusted, the receiver system 2400
transitions to box 3230 and adjusts the selected wireless power
provider and/or other operating parameters. For example, the
receiver system 2400 may switch to a lower cost provider, or the
receiver system 2400 may add another provider to handle an
increased electrical load 2406. Thereafter, the receiver system
2400 returns to box 3215 and continues receiving power using the
adjusted parameters.
[0247] With reference to FIG. 30, shown is a schematic block
diagram of the power provider system 2503 according to an
embodiment of the present disclosure. The power provider system
2503 may include one or more computing devices 4000. Each computing
device 4000 includes at least one processor circuit, for example,
having a processor 4003 and a memory 4006, both of which are
coupled to a local interface 4009. To this end, each computing
device 4000 may comprise, for example, at least one server computer
or like device. The local interface 4009 may comprise, for example,
a data bus with an accompanying address/control bus or other bus
structure as can be appreciated.
[0248] Stored in the memory 4006 are both data and several
components that are executable by the processor 4003. In
particular, stored in the memory 4006 and executable by the
processor 4003 are power provider logic 4012 and potentially other
applications. Also stored in the memory 4006 may be a data store
4015 and other data. In addition, an operating system may be stored
in the memory 4006 and executable by the processor 4003.
[0249] With reference to FIG. 31, shown is a schematic block
diagram of the power meter 2409 according to an embodiment of the
present disclosure. The power meter 2409 may include at least one
processor circuit, for example, having a processor 4103 and a
memory 4106, both of which are coupled to a local interface 4109.
To this end, the power meter 2409 may comprise, for example, at
least one computer or like device. The local interface 4109 may
comprise, for example, a data bus with an accompanying
address/control bus or other bus structure as can be
appreciated.
[0250] Stored in the memory 4106 are both data and several
components that are executable by the processor 4103. In
particular, stored in the memory 4106 and executable by the
processor 4103 are provider control logic 4118 that transforms the
processor 4103 into provider control circuitry 2415 (FIG. 22),
usage reporting logic 4121 that transforms the processor 4103 into
usage reporting circuitry 2418 (FIG. 22), and potentially other
applications. Also stored in the memory 4106 may be a data store
4115 and other data. In addition, an operating system may be stored
in the memory 4106 and executable by the processor 4103.
[0251] Referring to both FIG. 30 and FIG. 31, it is understood that
there may be other applications that are stored in the memory 4006,
4106 and are executable by the processor 4003, 4103 as can be
appreciated. Where any component discussed herein is implemented in
the form of software, any one of a number of programming languages
may be employed such as, for example, C, C++, C#, Objective C,
Java.RTM., JavaScript.RTM., Perl, PHP, Visual Basic.RTM.,
Python.RTM., Ruby, Flash.RTM., or other programming languages.
[0252] A number of software components are stored in the memory
4006, 4106 and are executable by the processor 4003, 4103. In this
respect, the term "executable" means a program file that is in a
form that can ultimately be run by the processor 4003, 4103.
Examples of executable programs may be, for example, a compiled
program that can be translated into machine code in a format that
can be loaded into a random access portion of the memory 4006, 4106
and run by the processor 4003, 4103, source code that may be
expressed in proper format such as object code that is capable of
being loaded into a random access portion of the memory 4006, 4106
and executed by the processor 4003, 4103, or source code that may
be interpreted by another executable program to generate
instructions in a random access portion of the memory 4006, 4106 to
be executed by the processor 4003, 4103, etc. An executable program
may be stored in any portion or component of the memory 4006, 4106
including, for example, random access memory (RAM), read-only
memory (ROM), hard drive, solid-state drive, USB flash drive,
memory card, optical disc such as compact disc (CD) or digital
versatile disc (DVD), floppy disk, magnetic tape, or other memory
components.
[0253] The memory 4006, 4106 is defined herein as including both
volatile and nonvolatile memory and data storage components.
Volatile components are those that do not retain data values upon
loss of power. Nonvolatile components are those that retain data
upon a loss of power. Thus, the memory 4006, 4106 may comprise, for
example, random access memory (RAM), read-only memory (ROM), hard
disk drives, solid-state drives, USB flash drives, memory cards
accessed via a memory card reader, floppy disks accessed via an
associated floppy disk drive, optical discs accessed via an optical
disc drive, magnetic tapes accessed via an appropriate tape drive,
and/or other memory components, or a combination of any two or more
of these memory components. In addition, the RAM may comprise, for
example, static random access memory (SRAM), dynamic random access
memory (DRAM), or magnetic random access memory (MRAM) and other
such devices. The ROM may comprise, for example, a programmable
read-only memory (PROM), an erasable programmable read-only memory
(EPROM), an electrically erasable programmable read-only memory
(EEPROM), or other like memory device.
[0254] Also, the processor 4003, 4103 may represent multiple
processors 4003, 4103 and/or multiple processor cores and the
memory 4006, 4106 may represent multiple memories 4006, 4106 that
operate in parallel processing circuits, respectively. In such a
case, the local interface 4009, 4109 may be an appropriate network
that facilitates communication between any two of the multiple
processors 4003, 4103, between any processor 4003, 4103 and any of
the memories 4006, 4106, or between any two of the memories 4006,
4106, etc. The local interface 4009, 4109 may comprise additional
systems designed to coordinate this communication, including, for
example, performing load balancing. The processor 4003, 4103 may be
of electrical or of some other available construction.
[0255] Although the power provider logic 4012, the provider control
logic 4118, the usage reporting logic 4121, and other various
systems described herein may be embodied in software or code
executed by general purpose hardware as discussed above, as an
alternative the same may also be embodied in dedicated hardware or
a combination of software/general purpose hardware and dedicated
hardware. If embodied in dedicated hardware, each can be
implemented as a circuit or state machine that employs any one of
or a combination of a number of technologies. These technologies
may include, but are not limited to, discrete logic circuits having
logic gates for implementing various logic functions upon an
application of one or more data signals, application specific
integrated circuits (ASICs) having appropriate logic gates,
field-programmable gate arrays (FPGAs), or other components, etc.
Such technologies are generally well known by those skilled in the
art and, consequently, are not described in detail herein.
[0256] The flowcharts of FIG. 27, FIG. 28, and FIG. 29 show the
functionality and operation of an implementation of portions of the
power provider system 2503 and the receiver system 2400. If
embodied in software, each block may represent a module, segment,
or portion of code that comprises program instructions to implement
the specified logical function(s). The program instructions may be
embodied in the form of source code that comprises human-readable
statements written in a programming language or machine code that
comprises numerical instructions recognizable by a suitable
execution system such as a processor 4003, 4103 in a computer
system or other system. The machine code may be converted from the
source code, etc. If embodied in hardware, each block may represent
a circuit or a number of interconnected circuits to implement the
specified logical function(s).
[0257] Although the flowcharts of FIG. 27, FIG. 28, and FIG. 29
show a specific order of execution, it is understood that the order
of execution may differ from that which is depicted. For example,
the order of execution of two or more blocks may be scrambled
relative to the order shown. Also, two or more blocks shown in
succession in FIG. 27, FIG. 28, and FIG. 29 may be executed
concurrently or with partial concurrence. Further, in some
embodiments, one or more of the blocks shown in FIG. 27, FIG. 28,
and FIG. 29 may be skipped or omitted. In addition, any number of
counters, state variables, warning semaphores, or messages might be
added to the logical flow described herein, for purposes of
enhanced utility, accounting, performance measurement, or providing
troubleshooting aids, etc. It is understood that all such
variations are within the scope of the present disclosure.
[0258] Also, any logic or application described herein, including
the power provider logic 4012, the provider control logic 4118, and
the usage reporting logic 4121, that comprises software or code can
be embodied in any non-transitory computer-readable medium for use
by or in connection with an instruction execution system such as,
for example, a processor 4003, 4103 in a computer system or other
system. In this sense, the logic may comprise, for example,
statements including instructions and declarations that can be
fetched from the computer-readable medium and executed by the
instruction execution system. In the context of the present
disclosure, a "computer-readable medium" can be any medium that can
contain, store, or maintain the logic or application described
herein for use by or in connection with the instruction execution
system.
[0259] The computer-readable medium can comprise any one of many
physical media such as, for example, magnetic, optical, or
semiconductor media. More specific examples of a suitable
computer-readable medium would include, but are not limited to,
magnetic tapes, magnetic floppy diskettes, magnetic hard drives,
memory cards, solid-state drives, USB flash drives, or optical
discs. Also, the computer-readable medium may be a random access
memory (RAM) including, for example, static random access memory
(SRAM) and dynamic random access memory (DRAM), or magnetic random
access memory (MRAM). In addition, the computer-readable medium may
be a read-only memory (ROM), a programmable read-only memory
(PROM), an erasable programmable read-only memory (EPROM), an
electrically erasable programmable read-only memory (EEPROM), or
other type of memory device.
[0260] Further, any logic or application described herein,
including the power provider logic 4012, the provider control logic
4118, and the usage reporting logic 4121, may be implemented and
structured in a variety of ways. For example, one or more
applications described may be implemented as modules or components
of a single application. Further, one or more applications
described herein may be executed in shared or separate computing
devices or a combination thereof. For example, a plurality of the
applications described herein may execute in the same computing
device or in multiple computing devices. Additionally, it is
understood that terms such as "application," "service," "system,"
"engine," "module," and so on may be interchangeable and are not
intended to be limiting.
[0261] Disjunctive language such as the phrase "at least one of X,
Y, or Z," unless specifically stated otherwise, is otherwise
understood with the context as used in general to present that an
item, term, etc., may be either X, Y, or Z, or any combination
thereof (e.g., X, Y, and/or Z). Thus, such disjunctive language is
not generally intended to, and should not, imply that certain
embodiments require at least one of X, at least one of Y, and at
least one of Z to each be present.
[0262] It should be emphasized that the above-described embodiments
of the present disclosure are merely possible examples of
implementations set forth for a clear understanding of the
principles of the disclosure. Many variations and modifications may
be made to the above-described embodiment(s) without departing
substantially from the spirit and principles of the disclosure. All
such modifications and variations are intended to be included
herein within the scope of this disclosure and protected by the
following claims. In addition, all optional and preferred features
and modifications of the described embodiments and dependent claims
are usable in all aspects of the disclosure taught herein.
Furthermore, the individual features of the dependent claims, as
well as all optional and preferred features and modifications of
the described embodiments are combinable and interchangeable with
one another.
* * * * *