U.S. patent application number 16/240563 was filed with the patent office on 2019-05-23 for subsurface sensing using guided surface wave modes on lossy media.
The applicant listed for this patent is CPG Technologies, LLC. Invention is credited to James F. Corum, Kenneth L. Corum.
Application Number | 20190154635 16/240563 |
Document ID | / |
Family ID | 55454499 |
Filed Date | 2019-05-23 |
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United States Patent
Application |
20190154635 |
Kind Code |
A1 |
Corum; James F. ; et
al. |
May 23, 2019 |
SUBSURFACE SENSING USING GUIDED SURFACE WAVE MODES ON LOSSY
MEDIA
Abstract
Disclosed are various systems and methods for remote surface
sensing using guided surface wave modes on lossy media. One system,
among others, comprises a guided surface waveguide probe configured
to launch a guided surface wave along a surface of a lossy
conducting medium, and a receiver configured to receive backscatter
reflected by a remotely located subsurface object illuminated by
the guided surface wave. One method, among others, includes
launching a guided surface wave along a surface of a lossy
conducting medium by exciting a charge terminal of a guided surface
waveguide probe, and receiving backscatter reflected by a remotely
located subsurface object illuminated by the guided surface
wave.
Inventors: |
Corum; James F.;
(Morgantown, WV) ; Corum; Kenneth L.; (Plymouth,
NH) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
CPG Technologies, LLC |
Italy |
TX |
US |
|
|
Family ID: |
55454499 |
Appl. No.: |
16/240563 |
Filed: |
January 4, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
14848892 |
Sep 9, 2015 |
10175203 |
|
|
16240563 |
|
|
|
|
62049237 |
Sep 11, 2014 |
|
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G01S 13/885 20130101;
H02J 5/005 20130101; G01V 3/12 20130101; H04B 3/52 20130101; H01Q
1/00 20130101; H01P 3/00 20130101; G01N 2291/045 20130101; G01N
29/041 20130101; G01S 13/00 20130101; G01S 13/02 20130101 |
International
Class: |
G01N 29/04 20060101
G01N029/04; H01Q 1/00 20060101 H01Q001/00; H01P 3/00 20060101
H01P003/00; G01S 13/00 20060101 G01S013/00; G01S 13/88 20060101
G01S013/88; H02J 5/00 20060101 H02J005/00; G01S 13/02 20060101
G01S013/02; G01V 3/12 20060101 G01V003/12 |
Claims
1. A method, comprising: launching a guided surface wave along a
surface of a lossy conducting medium in a Zenneck waveguide mode by
exciting one or more charge terminal of a guided surface waveguide
probe; and receiving backscatter reflected by a remotely located
subsurface object illuminated by the guided surface wave.
2. The method of claim 1, wherein excitation of the one or more
charge terminal generates a resultant field that synthesizes a wave
front incident at a complex Brewster angle of incidence
(.theta..sub.i,B) of the lossy conducting medium.
3. The method of claim 2, wherein the guided surface waveguide
probe comprises a feed network electrically coupled to the one or
more charge terminal, the feed network providing excitation to
individual charge terminals of the one or more charge terminal.
4. The method of claim 3, wherein the feed network is configured to
impose voltage magnitudes and phases on the individual charge
terminals to synthesize a resultant field that substantially
matches the Zenneck waveguide mode of the lossy conducting medium,
thereby launching the guided surface wave.
5. The method of claim 1, wherein the backscatter reflected by the
remotely located subsurface object is received by a receiver.
6. The method of claim 5, wherein the backscatter reflected by the
remotely located subsurface object is received by an array of
receivers including the receiver.
7. The method of claim 6, wherein the array of receivers comprises
the guided surface waveguide probe.
8. The method of claim 1, wherein the backscatter reflected by the
remotely located subsurface object is received by the guided
surface waveguide probe.
9. The method of claim 1, wherein the guided surface waveguide
probe is configured to launch a series of guided surface waves
having a defined pulse duration at a defined repetition rate.
10. The method of claim 1, wherein the guided surface wave is a
frequency modulated continuous wave.
11. The method of claim 1, comprising launching guided surface
waves along the surface of a lossy conducting medium in the Zenneck
waveguide mode by exciting charge terminals of an array of guided
surface waveguide probes, the array of guided surface waveguide
probes comprising the guided surface waveguide probe; and receiving
backscatter reflected by the remotely located subsurface object
illuminated by the guided surface waves.
12. The method of claim 11, wherein the array of guided surface
waveguide probes is configured to focus the guided surface waves in
at least one direction.
13. The method of claim 11, wherein the array of guided surface
waveguide probes is configured to increase a field strength of the
guided surface waves in at least one direction.
14. The method of claim 1, wherein the remotely located subsurface
object is a subsurface feature of the lossy conducting medium.
15. The method of claim 14, wherein the lossy conducting medium is
a terrestrial medium, and the subsurface feature is a variation in
the terrestrial medium.
16. The method of claim 1, comprising determining a characteristic
of the remotely located subsurface object based at least in part
upon the backscatter.
17. A system, comprising: a guided surface waveguide probe
configured to launch a guided surface wave along a surface of a
lossy conducting medium by substantially mode-matching to a Zenneck
waveguide mode of the lossy conducting medium; and a receiver
configured to receive backscatter reflected by a remotely located
subsurface object illuminated by the guided surface wave.
18. The system of claim 17, comprising an array of guided surface
waveguide probes including the guided surface waveguide probe, the
array of guided surface waveguide probes configured to launch
guided surface waves along the surface of a lossy conducting medium
in the Zenneck waveguide mode.
19. The system of claim 17, comprising a plurality of receivers
comprising the receiver, the plurality of receivers configured to
receive backscatter reflected by the remotely located subsurface
object illuminated by the guided surface wave.
20. The system of claim 17, wherein the lossy conducting medium is
a terrestrial medium, and the remotely located subsurface object is
a subsurface feature of the terrestrial substrate.
Description
CROSS REFERENCE TO RELATED APPLICATIONS
[0001] This application is a continuation of co-pending U.S. patent
application Ser. No. 14/848,892, filed on Sep. 9, 2015, which
claims the benefit of, and priority to, U.S. Provisional Patent
Application No. 62/049,237 entitled "SUBSURFACE SENSING USING
GUIDED SURFACE WAVE MODES ON LOSSY MEDIA" 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 through 20E illustrate examples of various
schematic symbols used for discussion of guided surface wave probes
and receiving structures according to the various embodiments of
the present disclosure.
[0027] FIG. 21 is a drawing that illustrates field strength as a
function of distance for a guided electromagnetic field and a
radiated electromagnetic field according to the various embodiments
of the present disclosure.
[0028] FIGS. 22A and 22B are graphical representations of examples
of a detection system including one or more guided surface
waveguide probe(s) according to the various embodiments of the
present disclosure.
DETAILED DESCRIPTION
[0029] 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.
[0030] 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.
[0031] 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.
[0032] 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.
[0033] 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)} and 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.
[0034] 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.
[0035] 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 20th 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.
[0036] 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.
[0037] 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.
[0038] 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.
[0039] 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.
[0040] 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, September 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.
[0041] 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.
[0042] 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##
[0043] 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##
[0044] 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.0 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.
[0045] 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)}.
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.0
is the permittivity of free space, and .mu..sub.0 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.
[0046] 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.
[0047] 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.
[0048] 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.
[0049] 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.
[0050] 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.(.rho.,.phi.,0)= (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 ( j2 ) .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.
[0051] 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), (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 x.+-.j sin x. See, for example, Harrington, R. F.,
Time-Harmonic Fields, McGraw-Hill, 1961, pp. 460-463.
[0052] That H.sub.n.sup.(2)(k.sub..rho..rho.) 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##
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 - .pi. 2 - .pi. 4 ) . ( 20 b ) ##EQU00010##
Close-in to the guided surface waveguide probe (for
.rho.<<.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.
[0053] 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.
[0054] 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.
[0055] 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.
[0056] 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.
[0057] 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
[0058] 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.o.alpha.(1+M+M.sup.2+M.sup.3+2M.sup.4+3M.sup.5+
. . . ), (24)
where the diameter of the sphere is 2.alpha., and where
M=.alpha./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=8.alpha.) or greater, the charge
distribution is approximately uniform about the spherical terminal,
which can improve the coupling into the guided surface waveguide
mode.
[0059] In the case of a sufficiently isolated terminal, the
self-capacitance of a conductive sphere can be approximated by
C=4.pi..epsilon..sub.o.alpha., 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.o.alpha., 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.
[0060] 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.
[0061] 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 (E.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. || ( .theta. i ) = E || , R E || , 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.
[0062] 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).
[0063] 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.p{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##
[0064] 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 (W) 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.
[0065] 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. || ( .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.
[0066] 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
l(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.
[0067] 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.
[0068] 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.
[0069] 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..
[0070] 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.
[0071] 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.
[0072] 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.
[0073] 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.
[0074] 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 CT. 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.
[0075] 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.
[0076] 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).
[0077] 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.
[0078] 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 (.PSI.). 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.
[0079] 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 (.tau.) of a
wave along the coil's longitudinal axis to the speed of light (c),
or the "velocity factor," is given by
V f = v 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. 0
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 [ l n ( V f .lamda. 0 D ) - 1.027 ] . ( 47 )
##EQU00028##
[0080] 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 l n ( h a ) - 1 Farads , ( 48 ) ##EQU00029##
where h.sub.w is the vertical length (or height) of the conductor
and .alpha. 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. .lamda. w
.lamda. 0 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.0 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 [ l 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. 0 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.
[0081] 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 ( ) 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.
[0082] 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.
[0083] 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.
[0084] 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 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.
[0085] 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 = .gamma. e 2 + k 0 2 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.
[0086] 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.
[0087] 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.
[0088] 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.
[0089] 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.
[0090] 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.pHis
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.
[0091] 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.1=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##
where Z.sub.s=0.
[0092] 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.75
+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.
[0093] 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.
[0094] 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).
[0095] 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.
[0096] 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.
[0097] 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.
[0098] 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 FIG. 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.od/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.
[0099] 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).
[0100] 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
.sup.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.
[0101] 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.
[0102] 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-j 6.546, (68)
from Equation (41), where x=.sigma..sub.1/.omega..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 -j 3.744.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 40.614
.degree. . ( 70 ) ##EQU00044##
Thus, the helical coil can be adjusted to match
.PHI.=.PSI.=40.614.degree.
[0103] 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.
[0104] 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).
[0105] 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..sub.e= {square root over
(j.omega.u.sub.1(.sigma..sub.1+j.omega..epsilon..sub.1))}=0.25+j
0.292 m.sup.-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-j 4.73.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+j
26.27 ohms. (79)
[0106] 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.
[0107] 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 [ n ( V f .lamda. o 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.
[0108] 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.
[0109] 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+j0 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.
[0110] 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.
[0111] 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.
[0112] 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.
[0113] 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.
[0114] 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.
[0115] 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.
[0116] 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.
[0117] 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.
[0118] 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 TN
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.
[0119] 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.
[0120] 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.
[0121] 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.
[0122] 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.+.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.
[0123] 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##
[0124] 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.
[0125] 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.
[0126] An AC source 212 acts as the excitation source for the
charge terminal 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.a).
[0127] 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 244 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).
[0128] 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.
[0129] 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..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.
[0130] 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 244 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).
[0131] 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.
[0132] Voltage V.sub.2 from the coil 215 can be applied to the
charge terminal T.sub.1, and the position of tap 244 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 244 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.
[0133] 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.
[0134] 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 244 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 244 and/or 233 to maximize the ground current through the
ammeter 236.
[0135] 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.
[0136] 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.
[0137] 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.
[0138] 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
[0139] 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.
[0140] 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 J.sub.1 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..rho.=j.omega..mu..sub.o/.gamma..sub.e is the radial
impedance of the lossy conducting medium, where
.gamma..sub.e=(j.omega..mu..sub.1.sigma..sub.1-.omega..sup.2.mu..sub.1.ep-
silon..sub.1).sup.1/2.
[0141] 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.
[0142] 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 o .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. o ) 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.
[0143] 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.
[0144] 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.
[0145] 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.
[0146] 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.
[0147] 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.
[0148] 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.
[0149] 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.
[0150] 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.
[0151] 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.
[0152] 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.
[0153] 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).
[0154] 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.0.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.
[0155] 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.
[0156] 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.
[0157] 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.
[0158] 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.
[0159] 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.
[0160] 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.
[0161] In the embodiment shown in FIG. 18B, magnetic coupling is
employed where a coil L.sub.S is positioned as a secondary relative
to the coil L.sub.R that acts as a transformer primary. The coil
L.sub.S 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.
[0162] 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.
[0163] 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.
[0164] 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 .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).
[0165] 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.0 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.
[0166] Once the phase delay (.PSI.) 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.
[0167] 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.
[0168] 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. .gamma. ) 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 ) . ( 102 ) ##EQU00065##
[0169] 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.
[0170] 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.r) 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.
[0171] 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.
[0172] 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.
[0173] 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.od/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.
[0174] 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).
[0175] 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.
[0176] 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 d 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.
[0177] 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.
[0178] 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.
[0179] 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.
[0180] 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.
[0181] 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.
[0182] 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.
[0183] 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.
[0184] 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.
[0185] 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.
[0186] 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.
[0187] Radio detection and ranging or radar can be used to detect
objects by transmitting electromagnetic waves (e.g., radio,
microwave, etc.) that are reflected by any object in their path.
The transmitted waves are reflected or scattered when they come in
contact with (or illuminate) the object. The waves that are
reflected back (or backscattered) to the transmitter or a separate
receiver can be received and processed to determine properties of
the object (e.g., bearing, range, angle, velocity, etc.). If the
object is moving toward or away from the receiver, there is a
slight change in the frequency of the wave caused by the Doppler
Effect.
[0188] The electromagnetic waves scatter or reflect from the
boundary between two different materials (e.g., a solid object in
air) or two different densities. Waves having wavelengths that are
shorter than the object size will be reflected similar to light off
of a mirror. When the wavelengths are larger than the object size,
the object may result in poor reflection. At these longer
wavelengths, the object may be detected through Rayleigh
scattering. Radar can be used in air, marine and ground traffic
detection and control, air defense, navigation, surveillance,
exploration, and/or other applications.
[0189] Guided surface waveguide probes 200 can be used to transmit
surface guided waves which may be used for the detection of
objects. By matching the guided surface waveguide mode, a guided
surface wave can be launched on the lossy conducting medium 203
(e.g., a terrestrial medium). As has been discussed, the field
strength of the guided surface wave is proportional to the elevated
free charge of the guided surface waveguide probe 200 (or voltage
applied to the charge terminal(s) of the guided surface waveguide
probe 200). Ground waves refer to the propagation of
electromagnetic waves parallel to and adjacent to the terrestrial
surface (or conducting medium 203).
[0190] As previously discussed with respect to the field strength
curves for guided wave and for radiation propagation, the field
strength of the radiation field falls off geometrically (1/d, where
d is distance) while the field strength of the guided wave field
has a characteristic exponential decay of e.sup.-.alpha.d/ {square
root over (d)} and exhibits a distinctive knee. At distances less
than the crossing distance (point 112 of FIG. 1) where the guided
field strength curve 103 and the radiated field strength curve 106
intersect, the field strength of a guided electromagnetic field is
significantly greater at most locations than the field strength of
a radiated electromagnetic field. Because of this, the resulting
backscatter from remotely located objects will be stronger from the
guided surface wave than from a radiated radar wave.
[0191] This increased field strength can be useful for subsurface
radar detection. For example, the guided surface wave can be
launched on the terrestrial medium and can illuminate objects
located on and/or close to the surface of the terrestrial medium,
as well as object that may be located below the surface of the
terrestrial medium. As has been discussed, the Zenneck solutions of
Maxwell's equations may be expressed by the following electric
field and magnetic field components. At or above the surface of the
terrestrial medium (in air), with .rho..noteq.0 and z.gtoreq.0, the
fields are described by equations (1)-(3), which are reproduced
below.
H 2 .phi. = Ae - u 2 z H 1 ( 2 ) ( - j .gamma. .rho. ) , ( 106 ) E
2 .rho. = A ( u 2 j .omega. o ) e - u 2 z H 1 ( 2 ) ( - j .gamma.
.rho. ) , and ( 107 ) E 2 z = A ( - .gamma. .omega. o ) e - u 2 z H
0 ( 2 ) ( - j .gamma. .rho. ) . ( 108 ) ##EQU00067##
(with z being the vertical coordinate normal to the surface, and
.rho. being the radial dimension in cylindrical coordinates). At or
below the surface of the terrestrial medium, with .rho..noteq.0 and
z.ltoreq.0, the fields are described by equations (4)-(6), which
are reproduced below.
E 1 .phi. = Ae u 1 z H 1 ( 2 ) ( - j .gamma. .rho. ) , ( 109 ) E 1
.rho. = A ( - u 1 .sigma. 1 + j .omega. 1 ) e u 1 z H 1 ( 2 ) ( - j
.gamma. .rho. ) , and ( 110 ) E 1 z = A ( - .gamma. .sigma. 1 + j
.omega. 1 ) e u 1 z H 0 ( 2 ) ( - j .gamma. .rho. ) . ( 111 )
##EQU00068##
Thus, a guided surface wave that is launched on the terrestrial
medium includes fields located above and below the surface, which
can be used for remotely detecting objects and/or variations in
features of the monitored environment.
[0192] Referring to FIG. 21, shown is an example of the ground and
subsurface radiation fields of a monopole antenna and a guided
surface waveguide probe 200. In both cases, the ground radiation is
omnidirectional about the antenna or probe. The transmitted
radiation can be reflected and/or scattered by an object located
below the surface of the lossy conducting medium 203.
[0193] For the monopole antenna, the ground radiation 403 increases
sinusoidally from the antenna to a maximum point before returning
to a minimum. This is also true for the radiation below the surface
of the lossy conducting medium, except that attenuation of the
field is more pronounced below the surface. In contrast, the
surface guided wave launched by a guided surface waveguide probe
200 produces a radiation field 409 at and below the surface of the
lossy conducting medium 203. This can provide illumination of
objects located underground. The characteristics of the ground (or
lossy conducting medium 203), transmission frequency, and/or
generated field strength nay limit the effective depth for
detecting objects. The type of soil (e.g., rocky) can also affect
sensing due to signal scattering by heterogeneous conditions.
[0194] For example, radar using a surface guided wave launched by a
guided surface waveguide probe 200 can be used for the detection
of, e.g., shelters, tunnels, or other buried objects below the
surface of the earth. This system may also be used to detect
variations in the terrestrial substrate such as, but not limited
to, underground voids or sink holes, underground deposits of
minerals or liquids, fault lines, etc. These variations can be
naturally occurring or manmade discontinuities in the soil. For
instance, buried infrastructure (e.g., electrical water, gas,
and/or electrical lines), landfills, remediation sites, and/or
mines or other buried ordinance can be detected.
[0195] As illustrated in FIG. 21, radiated fields from an antenna
can penetrate the surface of the lossy conducting medium 203.
However, the attenuation of the radiated field is attenuated
significantly more that the field from the guided surface wave.
While the field of the guided surface wave may be attenuated by 1-2
dB, a radiated field may be attenuated by about 30 dB under the
same conditions. Because the electric field strength remains large
out the knee of the curve, and does not drop off in the same way as
radiated waves, the range of detection along the terrestrial
surface can be extended by launching a guided surface wave in a
guided surface waveguide mode using one or more guided surface
waveguide probe(s) 200.
[0196] In some cases, the guided surface wave may be used to detect
objects located up to 200 m below the surface in dry sand. As the
composition, density, stratification and/or moisture of the soil
changes, the depth of detection changes. For example, objects may
be located up to 30 m below the surface of other soils that have
higher moisture content and are richer in nutrients. In contrast,
typical ground penetrating radar is limited to about 18 meters in
clean dry sand and 6 meters in dense wet clay. The depth of
penetration can be increased by operating at lower frequencies.
[0197] The guided surface waveguide probe(s) 200 can be used for
radar detection using pulsed carrier and/or frequency modulation
continuous wave (FMCW) methods. For pulsed carrier radar, a guided
surface waveguide probe 200 launches a series of guided surface
waves at a defined repetition period. Each of the guided surface
waves are transmitted for a predefined duration (or pulse width).
The pulse width of the transmitted signal is chosen to ensure that
the radar emits sufficient energy to allow detection of the
backscatter from an object by a receiver. The amount of energy
delivered to a distant object can be affected by the duration of
the transmission and/or the field strength of the guided surface
wave. The range discrimination can also be affected by the pulse
duration. To improve the ability to sense the object, the pulses
can be launched at a defined repetition rate. The detected
backscatter from the object may then be integrated within a signal
processor every time a new pulse is transmitted, thereby
reinforcing the detection.
[0198] For FMCW radar, the guided surface wave is varied up and
down in frequency over a fixed period of time by a modulating
signal. The frequency difference between the backscatter from the
object and the guided surface wave increases with delay, and hence
with distance. The backscatter signal from the object can be mixed
with the transmitted guided surface wave signal to produce a beat
signal, which can provide the distance of the target after
demodulation. Other types of signals may also be launched by a
guided surface waveguide probe 200 for radar detection of objects.
For instance, synthetic pulse radar may be used to construct a
pulse shape by launching a series of pulsed guided surface waves at
different frequencies such that the superposition of the
transmitted signals produces the pulse shape. Since the pulse shape
is the superposition of the launched guided surface waves, the
guided surface waves can be transmitted at lower levels which can
reduce the profile of the probe. Using superposition to combine the
backscatter signals from the object, the response to the pulse
shape can be reconstructed for evaluation.
[0199] Referring now to FIG. 22A, shown is an example of a radar
system 500 including one or more guided surface waveguide probe(s)
200. A guided surface waveguide probe 200 can launch guided surface
waves 503 along the surface of the terrestrial medium as has been
previously discussed. The guided surface waveguide probe 200 can
include a transmitter as the excitation source 212 (e.g., FIGS. 3,
12 and 16) that supplies one or more charge terminals. The
transmitter can include an oscillator (e.g., a klystron or
magnetron) to generate the excitation signal and a modulator to
control the duration of the excitation signal. When excited by the
transmitter, a guided surface wave can be launched by the probe. As
the guided surface wave 503 passes by a remotely located subsurface
object 506 (e.g., a buried item and/or other subsurface feature), a
portion of the field is reflected by the object as backscatter
509.
[0200] When the transmitted signal is reflected as backscatter 509,
it can propagate back along the ground interface and be detected
using one or more receiver(s) 512. The receiver 512 can include one
or more receiving elements configured to couple with the
backscatter 509 reflected from the object 506. The receiving
elements can include, but are not limited to, the linear probe 303
(FIG. 18A), the tuned resonator 306 (FIGS. 18B and 18C), and/or the
magnetic coil 309 (FIG. 19) previously discussed, or other
receiving elements such as those used for ground penetrating radar
applications. A portion of the guided surface wave field may be
reflected above the surface. While this backscatter may be detected
using conventional receivers, the attenuation may hinder or prevent
detection above the surface.
[0201] While FIG. 22A shows a separate receiver 512, in some
implementations the guided surface waveguide probe 200 that is used
to launch the guided surface wave may also be used as a receiver to
detect the backscatter 509. In some cases, a receiver 512 may be
located on a mobile vehicle (e.g., a truck or other vehicle) that
can be positioned or moved closer to the object 506. This can aid
in detection of the backscatter 509 by reducing the return distance
that the reflection travels. In various implementations, an array
of receivers 512 can be used as illustrated in FIG. 22B. The array
of receivers 512 can allow for directional sensing of the
backscatter 509.
[0202] An individual guided surface waveguide probe 200 launches an
omnidirectional guided surface wave that propagates along the
surface of the lossy conducting medium 203 in all directions. The
backscatter 509 from an object can then be processed to determine
the location of the object 506. By evaluating the backscatter
received by the receiver 512, the distance to the object 506 (as
well as other features or characteristics) can be determined. The
processing can be carried out locally at the receiver 512, or the
backscatter information can be communicated to a remote location
for determination of the information. By using a plurality of
receivers 512 as shown in FIG. 22B, the location of the object 506
can be determined using triangulation. When multiple objects 506
are present, the backscatter 509 from each object 506 can be
detected by one or more receivers 512 and used to determine the
distance, location and/or other characteristics of the object
506.
[0203] In addition, an array of guided surface waveguide probes 200
can be used to focus and/or direct a guided surface wave and/or
increase the field strength in a desired direction. The guided
surface waves can constructively and/or destructively interfere to
produce a desired transmission pattern. For example, a plurality of
guided surface waveguide probes 200 may be positioned at predefined
distances (e.g., .lamda..sub.0/4, .lamda..sub.0/2, etc.) from each
other and/or in a defined pattern (e.g., a line, a triangle, a
square, etc.) and controlled to produce transmission nodes in one
or more directions. In some cases, the guided surface waveguide
probes 200 can be controlled so that guided surface waves may be
launched in different directions using the same probes. In some
embodiments, the transmission delays may be controlled to steer the
guided surface wave in a desired direction or to adjust the
direction that the surface waves are being launched.
[0204] With respect to the examples of FIGS. 22A and 22B, consider
a single guided surface waveguide probe 200 configured to launch a
series of pulsed guided surface waves having defined pulse duration
at a defined repetition rate. As a guided surface wave pulse 503
travels along the surface of the ground, a portion of the field is
reflected by any object 506 beneath the surface. The backscatter
509 from the object 506 can then be received by the receiver 512
and processed to determine various characteristics of the object
506. For example, position and distance to the object 506 can be
determined. Longer pulse durations can deliver more energy, and
increase the level of backscatter 509 from the object 506. In
addition, the pulsed guided surface waves can be sufficiently
spaced to allow for the launched guided surface wave to reach the
knee 109 of the guided field strength curve 103 (FIG. 1) and
backscatter to return to the receiver 512. This will avoid
interference of the backscatter by the guided surface wave.
[0205] 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.
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