U.S. patent application number 14/283850 was filed with the patent office on 2014-11-20 for variable z0 antenna device design system and method.
This patent application is currently assigned to Variable Z0, Ltd.. The applicant listed for this patent is Variable Z0, Ltd.. Invention is credited to Richard A. Formato.
Application Number | 20140340278 14/283850 |
Document ID | / |
Family ID | 47363051 |
Filed Date | 2014-11-20 |
United States Patent
Application |
20140340278 |
Kind Code |
A1 |
Formato; Richard A. |
November 20, 2014 |
VARIABLE Z0 ANTENNA DEVICE DESIGN SYSTEM AND METHOD
Abstract
A variable Z.sub.0 impedance method ("Variable Z.sub.0") for
designing and/or optimizing antenna systems. The method provides
that the value of an antenna's feed system characteristic impedance
or apparatus internal impedance (Z.sub.0) changes as a true
variable quantity during the antenna system design or optimization
methodology. The value is allowed to be determined by the
methodology, because different values of Z.sub.0 result in
different antenna system performance. It is applied to any set of
performance objectives on any antenna system wherein apparatus
internal or transmission line characteristic impedance is an
explicit or implicit parameter. Variable Z.sub.0 is applied to any
design or optimization methodology. Structures include Yagi-Uda
arrays, Meander Monopoles, and transmission line Multi-Stub
Matching Networks, and can incorporate Central Force Optimization
or Biogeography Based Optimization or other optimization
algorithms.
Inventors: |
Formato; Richard A.;
(Harwich, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Variable Z0, Ltd. |
Harwich |
MA |
US |
|
|
Assignee: |
Variable Z0, Ltd.
Harwich
MA
|
Family ID: |
47363051 |
Appl. No.: |
14/283850 |
Filed: |
May 21, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13602513 |
Sep 4, 2012 |
8776002 |
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14283850 |
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61531237 |
Sep 6, 2011 |
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Current U.S.
Class: |
343/860 ;
716/110 |
Current CPC
Class: |
G06F 30/39 20200101;
G06F 30/392 20200101; H01L 35/00 20130101; H01Q 1/36 20130101; G06F
30/13 20200101; G06F 30/398 20200101; G06F 17/15 20130101; H01Q
1/00 20130101; H01Q 1/50 20130101; H03K 17/92 20130101; H04B 7/185
20130101; H01L 29/12 20130101; Y10S 439/916 20130101; G06F 17/11
20130101; H04B 7/14 20130101; H01Q 9/42 20130101 |
Class at
Publication: |
343/860 ;
716/110 |
International
Class: |
G06F 17/50 20060101
G06F017/50; H01Q 1/50 20060101 H01Q001/50 |
Claims
1. A method of designing an antenna connected to a feed system
including a radio frequency source, the method comprising: using an
iterative antenna design algorithm on a computer where one or more
antenna design parameters and a feed system characteristic
impedance value are variables to achieve one or more antenna
performance objectives; varying said one or more antenna design
parameters while varying said feed system characteristic impedance
value until said one or more antenna performance objectives are
achieved using said iterative antenna design algorithm; and
determining a feed system characteristic impedance value from the
varied feed system characteristic impedance values which results in
said one or more antenna performance objectives.
2. The method of claim 1 further including: designing the feed
system such that said feed system exhibits said determined feed
system characteristic impedance value or an approximation of the
determined feed system characteristic impedance value; determining
one or more antenna design parameters which results in said antenna
performance objectives; and designing the antenna according to said
one or more determined antenna design parameters to achieve said
one or more antenna performance objectives.
3. The method of claim 1 in which said one or more antenna design
parameters include one or more of antenna element length, diameter,
and/or spacing; and/or helix diameter, turn pitch, wire gauge,
and/or the number of turns.
4. The method of claim 1 in which varying the one or more antenna
design parameters includes varying the one or more antenna design
parameters between maximum and minimum values.
5. The method of claim 1 in which said one or more antenna
performance objectives are input into the iterative antenna design
algorithm.
6. The method of claim 1 in which said iterative antenna design
algorithm includes Central Force Optimization, Dominating Cone Line
Search, Particle Swarm Optimization, a Genetic Algorithm, Ant
Colony Optimization, and/or Differential Evolution.
7. The method of claim 2 in which the feed system further includes
a transmission line and/or a matching network and designing the
feed system includes choosing a transmission line and/or matching
network such as that the feed system exhibits said determined feed
system characteristic impedance value.
8. The method of claim 1 in which said antenna performance
objectives include voltage standing wave ratio, gain, and/or
Front-to-Back ratio.
9. A method of designing an antenna connected to a feed system
including a radio frequency source, the method comprising: choosing
minimum and maximum feed system characteristic impedance values;
using an iterative antenna design algorithm on a computer where one
or more antenna design parameters and a feed system characteristic
impedance value are variables to achieve one or more antenna
performance objectives; varying said one or more antenna design
parameters while varying feed system characteristic impedance
values between the minimum and maximum feed system characteristic
impedance values until said one or more antenna performance
objectives are achieved using said iterative antenna design
algorithm; and determining a feed system characteristic impedance
value from the varied feed system characteristic impedance values
which results in said one or more antenna performance
objectives.
10. The method of claim 9 further including: designing the feed
system such that said feed system exhibits said determined feed
system characteristic impedance value or an approximation of the
determined feed system characteristic impedance value; determining
which one or more antenna design parameters result in said one or
more antenna performance objectives; and designing the antenna
according to said one or more determined antenna design parameters
to achieve said one or more antenna performance objectives.
11. The method of claim 9 in which said one or more antenna design
parameters include antenna element length, diameter, and/or
spacing; and/or helix diameter, turn pitch, wire gauge, and/or the
number of turns.
12. The method of claim 9 in which varying the one or more antenna
design parameters include varying the antenna design parameters
between maximum and minimum values.
13. The method of claim 9 in which said one or more antenna
performance objectives are input into the iterative antenna design
algorithm.
14. The method of claim 9 in which said iterative antenna design
algorithm includes Central Force Optimization, Dominating Cone Line
Search, Particle Swarm Optimization, a Genetic Algorithm, Ant
Colony Optimization, and/or Differential Evolution.
15. The method of claim 10 in which the feed system further
includes a transmission line and/or a matching network and
designing the feed system includes choosing a transmission line
and/or matching network such as that the feed system exhibits said
determined feed system characteristic impedance value.
16. The method of claim 9 in which said antenna performance
objectives include voltage standing wave ratio, gain, and/or
Front-to-Back ratio.
17. The method of claim 9 in which the determined feed system
characteristic impedance value is within a factor of three of a
standard fixed antenna feed system characteristic impedance
value.
18. A computer program for designing an antenna connected to a feed
system including a radio frequency source, the computer program
comprising: an iterative antenna design algorithm configured so one
or more antenna design parameters and a feed system characteristic
impedance value are variables to achieve one or more antenna
performance objectives; said antenna design parameters are varied
in said design algorithm while varying the feed system
characteristic impedance value until said one or more antenna
performance objectives are achieved; and a feed system
characteristic impedance value determined by said algorithm which
results in said one or more antenna performance objectives.
19. The computer program of claim 18 in which said antenna design
parameters include antenna element length, diameter, and/or
spacing; and/or helix diameter, turn pitch, wire gauge, and/or the
number of turns.
20. The computer program of claim 18 in which the interactive
design algorithm is configured to accept as inputs minimum and
maximum feed system characteristic impedance values and to vary the
feed system characteristic impedance value between said minimum and
maximum values.
21. The computer program of claim 18 in which said iterative
antenna design algorithm includes Central Force Optimization,
Dominating Cone Line Search, Particle Swarm Optimization, a Genetic
Algorithm, Ant Colony Optimization, and/or Differential
Evolution.
22. The computer program of claim 18 in which said antenna
performance objectives include voltage standing wave ratio, gain,
and/or Front-to-Back ratio.
23. An antenna connected to a feed system designed by a method
comprising: choosing minimum and maximum feed system characteristic
impedance values; using an iterative antenna design algorithm on a
computer where antenna design parameters and a feed system
characteristic impedance value are variables to achieve one or more
antenna performance objectives; varying said antenna design
parameters while varying feed system characteristic impedance
values between the minimum and maximum feed system characteristic
impedance values until said one or more antenna performance
objectives are achieved using said iterative antenna design
algorithm; determining a feed system characteristic impedance value
from the varied feed system characteristic impedance values which
results in said one or more antenna performance objectives;
designing the feed system such that said feed system exhibits said
determined feed system characteristic impedance value or an
approximation of the determined feed system characteristic
impedance value; determining which antenna design parameters result
in said antenna performance objectives; and designing the antenna
according to said determined antenna design parameters to achieve
said one or more antenna performance objectives.
Description
RELATED APPLICATION
[0001] This application is a continuation of U.S. patent
application Ser. No. 13/602,513 filed Sep. 4, 2012 which claims the
benefit of U.S. Provisional Application No. 61/531,237 filed Sep.
6, 2011, which hereby claims the benefit of and priority thereto
under 35 U.S.C. .sctn..sctn.119, 120, 363, 365, and 37 C.F.R.
.sctn.1.55 and .sctn.1.78, and each of which is incorporated herein
by reference.
COPYRIGHT NOTICE
[0002] A portion of the disclosure of this patent document contains
material that is subject to copyright protection. The copyright
owner has no objection to the facsimile reproduction by anyone of
the patent document or the patent disclosure, as it appears in a
published Patent and Trademark Office patent file or record, but
otherwise reserves all copyrights whatsoever.
FIELD OF THE INVENTION
[0003] The invention relates to a system and method for creating
antenna devices by providing parameters of their fabrication.
BACKGROUND OF THE INVENTION
[0004] Antennas, the devices that emit (radiate) and receive
electromagnetic radiation, have become progressively more important
in the modern world. Even though many, if not most, antennas today
are "invisible," literally out-of-sight because they are imbedded
in other devices, their numbers are ever increasing in all manner
of wireless machines ranging from cell phones, to laptop computers,
to M2M (machine-to-machine) devices as representative examples, not
an exhaustive list. In many cases antenna performance limits how
well its associated device works. Oftentimes the limitation is
bandwidth-related, which may constrain data rates or throughput,
thereby limiting, for example, how quickly an image might display
or a web page takes to load. The limitation also may relate to some
other antenna performance measure, or combination thereof, such as,
for example, radiation pattern or efficiency, sidelobe level, and
so on, as representative not exhaustive. Industry experts point out
that progressively better antennas are required to meet modern
communication requirements. As an example, demand for bandwidth is
projected to more than triple year over year, and there is
consensus that better antennas are a key element in meeting it.
(See "Mobile bandwidth crunch causing concern for innovation, extra
pay" by Jim Shakenbach, Mass High Tech Magazine, Wednesday, Jul. 6,
2011, at pp. 8-9 (print edition), published by American City
Business Journals.
[0005] Traditional design or optimization ("D/O") paradigms,
methods, techniques, algorithms, frameworks, approaches, processes,
or procedures (collectively and individually hereinafter
"methodology") view the antenna feed system characteristic
impedance or the apparatus internal impedance, denoted herein
Z.sub.0, as a fixed parameter with a constant value specified at
the start of the methodology, even if multiple parametric values
are employed. Z.sub.0 therefore is not a variable quantity whose
value is determined by the methodology. This distinction is subtle
but extremely important, because traditional methodology
automatically excludes from the outset all antenna system
configurations that could provide better performance by using some
other value of Z.sub.0.
[0006] What is needed is a system and method that provides antenna
devices with improved performance specifications, including, but
not limited to, impedance bandwidth (IBW). Variable Z.sub.0 System
and Method addresses this need.
SUMMARY OF THE INVENTION
[0007] Embodiments include a system and method for designing an
antenna system comprising wherein an antenna feed system
characteristic impedance or apparatus internal impedance is treated
as a variable quantity whose value is determined by a design
methodology of the antenna system, instead of its being specified
as a fixed design parameter.
[0008] Another embodiment includes a system and method for
optimizing an antenna system comprising wherein an antenna feed
system characteristic impedance or apparatus internal impedance is
treated as a variable quantity whose value is determined by an
antenna system optimization methodology, instead of its being
specified as a fixed optimization parameter.
[0009] An embodiment is a variable impedance method and system for
designing an antenna system comprising varying an input value of
the impedance of an antenna feed system of the antenna system to
produce a selected value of the impedance; determining the selected
value of the impedance by a methodology; wherein the input value of
the impedance of the antenna system is not specified as a fixed
design parameter; and applying to an antenna system the design of
the antenna system that fulfills specified characteristics. Another
embodiment includes defining electromagnetic characteristics of the
antenna system other than the impedance; specifying ranges of the
electromagnetic characteristics; and calculating parameter values
of the antenna system from the specified electromagnetic
characteristics other than the impedance. In a further embodiment,
the antenna feed system impedance is an antenna feed system
characteristic impedance. For a yet further embodiment, the antenna
feed system impedance comprises an antenna feed system internal
impedance. In still further embodiments, the methodology comprises
a design methodology. For yet other embodiments, the methodology
comprises an optimization methodology. In additional embodiments,
minimum and maximum values are specified for the variable
impedance. In still other embodiments, minimum and maximum values
are specified for the electromagnetic characteristics of the
antenna system other than the impedance. Continuing embodiments
provide that the electromagnetic characteristics comprise design
parameters. In an ongoing embodiment, the electromagnetic
characteristics comprise optimization parameters. Subsequent
embodiments provide that the methodology comprises at least one of
the group consisting of a deterministic algorithm, Central Force
Optimization (CFO), Dominating Cone Line Search (DCLS), extended
Wu-King impedance loading, seat of the pants design,
experience-based design, and best guess. Another following
embodiment provides that the methodology comprises at least one of
the group consisting of a stochastic algorithm, Particle Swarm
Optimization (PSO), Ant Colony Optimization (ACO), Differential
Evolution (DE), and Genetic Algorithm.
[0010] An embodiment is a variable impedance method for designing
antenna systems comprising the steps of defining parameters of the
antenna system, including a variable antenna feed system impedance;
specifying ranges of the parameters, including a minimum value and
a maximum value for the antenna feed system impedance; iteratively
executing a methodology to calculate antenna system characteristics
from the parameters including the variable antenna feed system
impedance; selecting values for the antenna system parameters
determined from the methodology. In another embodiment, the
parameters of the antenna system comprise design parameters. In a
further embodiment, the parameters of the antenna system comprise
optimization parameters. For a yet further embodiment, the
methodology includes performance objective iteration, the iteration
comprising inputting initial performance objectives; executing a
design methodology; determining if performance objectives have been
met; modifying the initial performance objectives if the
performance objectives have not been met, then re-executing the
design methodology with the modified performance objectives; and
ending the iteration if performance objectives have been met,
selecting antenna system design parameters resulting in meeting the
performance objectives. In still further embodiments, the
methodology includes optimization iteration, the iteration
comprising defining a fitness function; executing an optimization
methodology; determining if termination criteria have been met;
re-executing the optimization methodology if the termination
criteria have not been met; and ending the iteration if the
termination criteria have been met, selecting antenna system design
parameters resulting in meeting the termination criteria. Other
embodiments further comprise an external antenna modeling engine
interfacing with the optimization methodology. Yet other
embodiments, further comprise applying to an antenna system the
design of the antenna system that fulfills specified
characteristics including a determined value of the variable
antenna feed system impedance.
[0011] An embodiment is one or more computer-readable storage media
comprising computer-executable instructions for a variable
impedance method for designing antenna systems, the
computer-executable instructions directed to steps comprising
defining parameters of the antenna system, including a variable
antenna feed system impedance; specifying ranges of the parameters,
including a minimum value and a maximum value for the antenna feed
system impedance; iteratively executing a methodology to calculate
antenna system characteristics from the parameters including the
variable antenna feed system impedance; and selecting values for
the antenna system parameters determined from the methodology.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a schematic representation of an antenna system in
transmit mode.
[0013] FIG. 2 is a schematic representation of a generalized
antenna system in transmit mode.
[0014] FIG. 3 is representative antenna system design flowchart
showing Variable Z.sub.0 System and Method configured in accordance
with an embodiment of the invention.
[0015] FIG. 4 is a representative antenna system optimization
flowchart showing Variable Z.sub.0 System and Method configured in
accordance with an embodiment of the invention.
[0016] FIG. 5 is Central Force Optimization pseudocode.
[0017] FIG. 6 is a graph of VSWR relative to Z.sub.0 for a
6-element Yagi antenna system configured in accordance with an
embodiment of the invention.
[0018] FIG. 7 is a graph of Forward Gain for a 6-element Yagi
antenna system configured in accordance with an embodiment of the
invention.
[0019] FIG. 8 is a graph of Front-to-Back Ratio for a 6-element
Yagi antenna system configured in accordance with an embodiment of
the invention.
[0020] FIG. 9 is a graph of VSWR relative to Z.sub.0 for a Meander
Monopole antenna system configured in accordance with an embodiment
of the invention.
[0021] FIG. 10 is a graph of Maximum Gain for a Meander Monopole
antenna system configured in accordance with an embodiment of the
invention.
[0022] FIG. 11 is a graph of VSWR relative to Z.sub.0 for a 3-Stub
Multi-Stub Matching Network configured in accordance with an
embodiment of this invention.
[0023] FIG. 12 is a graph of VSWR relative to Z.sub.0 for a 5-Stub
Multi-Stub Matching Network configured in accordance with an
embodiment of this invention.
[0024] FIG. 13 is a graph of VSWR relative to Z.sub.0 for a 7-Stub
Multi-Stub Matching Network configured in accordance with an
embodiment of this invention.
DETAILED DESCRIPTION
[0025] The invention is susceptible of many embodiments. What
follows is illustrative, but not exhaustive, of the scope of the
invention.
[0026] The Variable Z.sub.0 System and Method disclosed herein
mitigates many antenna limitations by departing dramatically from
the traditional approach to antenna system design or optimization
("D/O"). The Variable Z.sub.0 System and Method ("Variable
Z.sub.0") provides that the value of an antenna's feed system
characteristic impedance or apparatus internal impedance (impedance
of an antenna feed system), herein denoted Z.sub.0, be allowed to
change as a true variable quantity during the antenna system design
or optimization methodology and whose value be allowed to be
determined by the methodology, because different values of Z.sub.0
result in different antenna system performance that often is
considerably improved. Variable Z.sub.0 removes the limitation of
specifying a value for Z.sub.0 in advance, and this invention
yields unexpected benefits by doing so. The term "design" refers to
specifying a complete set of antenna system parameters that meets
minimum user-specified performance objectives or requirements, such
as bandwidth, radiation pattern, and so on, as nonlimiting
examples. The term "optimization" refers to specifying a complete
set of antenna system parameters that best meets user-specified
performance objectives or requirements, often but not necessarily
formulated in a mathematical "fitness function" or "objective
function" that is optimized using a computer algorithm. In the
design setting, Variable Z.sub.0 can achieve superior antenna
system designs that are unattainable using traditional D/O
methodology. This also is true in the optimization setting, in
which multiple values of a variable Z.sub.0 value, instead of fixed
values for Z.sub.0, for a "best" design may correspond to a single
or to multiple global optima that may be discovered by using an
optimization algorithm, which may be stochastic or deterministic,
and which also may converge on local instead of global optima.
[0027] The Variable Z.sub.0 System and Method provides many
advantages over traditional antenna D/O methodology. It can be
applied without limitation to any antenna system design or
optimization problem wherein Z.sub.0 is an explicit or implicit
parameter against any set of performance goals or, in the case of
optimization, against any fitness or objective function.
Embodiments are especially useful for improving impedance
bandwidth, as illustrated by the examples in this disclosure, but
Variable Z.sub.0 is not limited to that application alone.
Significantly, the Variable Z.sub.0 System and Method "product by
process" approach also can be used in conjunction with any design
or optimization methodology, deterministic ones like Central Force
Optimization (CFO) or Dominating Cone Line Search (DCLS);
stochastic algorithms like Particle Swarm Optimization (PSO), Ant
Colony Optimization (ACO), Differential Evolution (DE), or Genetic
Algorithm (GA); analytic approaches such as extended Wu-King
impedance loading; even "seat of the pants" design or optimization
based on experience, intuition, or even a "best guess." For
additional discussion of impedance loading, see, as examples
without limitation, R. A. Formato, "New Techniques for Increasing
Antenna Bandwidth with Impedance Loading," Progress in
Electromagnetics Research B, Vol. 29, 2011, pp. 269-288; and R. A.
Formato, "Issues in Antenna Optimization--A Monopole Case Study,"
2011, Cornell Univ. Library, both of which are fully incorporated
herein by reference.
[0028] The Variable Z.sub.0 System and Method, which treats Z.sub.0
as a design or optimization variable instead of a fixed parameter
can be used with any design or optimization methodology, rendering
it surprisingly flexible in its breadth of applicability. Because
of this unexpected and unrestricted applicability, Variable Z.sub.0
embodiments are especially useful with algorithm-independent
approaches in which various design or optimization algorithms can
be used singly or in combination with others (see, for example, R.
A. Formato, "Dynamic Threshold Optimization--A New Approach?" June
2012, Cornell University Library, which is fully incorporated
herein by reference).
[0029] The features and advantages described herein are not
all-inclusive and, in particular, many additional features and
advantages will be apparent to one of ordinary skill in the art in
view of the drawings, specification, and claims. Moreover, it
should be noted that the language used in the specification has
been selected principally for readability and instructional
purposes, and not to limit in any way the scope of the inventive
subject matter.
[0030] Embodiments disclose a novel and proprietary antenna system
design or optimization System and Method called "Variable Z.sub.0,"
Z.sub.0 being the antenna feed system characteristic impedance or
apparatus internal impedance (impedance of an antenna feed system).
Design refers to the specification of a complete set of parameters
that defines an antenna system meeting specific performance
objectives. Optimization refers to the specification of a complete
set of parameters that defines the antenna system best meeting
specific performance objectives to the extent possible. Variable
Z.sub.0 embodiments are particularly useful for improving impedance
bandwidth (IBW). In addition, Variable Z.sub.0 embodiments are
useful for meeting any performance objectives, even ones that do
not consider IBW at all, for any antenna system for which Z.sub.0
is a design or optimization parameter. Z.sub.0 may be included as a
parameter explicitly, for example without limitation, by utilizing
one or the other or both of its real and imaginary parts
(resistance and reactance, respectively), or implicitly, for
example without limitation, as the reference impedance for
computing a standing wave ratio.
[0031] FIG. 1 is a schematic representation of an antenna system
100 in transmit mode comprising: RF (radio-frequency) apparatus 110
with characteristic impedance or apparatus internal impedance
(impedance of an antenna feed system) Z.sub.0; antenna feed 120
that conducts RF energy shown as propagating electric field 140;
antenna input terminals a and b; and antenna 150. The antenna
system may function in transmit mode, receive mode (not shown), or
both, and in each case antenna feed 120 typically is a transmission
line or matching network or combination of the two. In transmit
mode, RF apparatus 110 is a source of RF energy, typically a radio
transmitter. The sequence of dots 130 denotes repetition of the
electric field pattern. Antenna 150 is "That part of a transmitting
or receiving system that is designed to radiate or to receive
electromagnetic waves" as defined in IEEE Std 145-1993 IEEE
Standard Definitions of Terms for Antennas, 1993 (definition 2.12
at page 4), published by The Institute of Electrical and
Electronics Engineers, Inc. (IEEE), 345 East 47.sup.th Street, New
York, N.Y. 10017-2394 USA (ISBN 1-55937-317-2), fully incorporated
herein by reference. Terminology employed herein is intended to be
consistent with this standard to the fullest extent. In transmit
mode, antenna 150 emits into the surrounding space a radiated
electromagnetic (EM) wave 160 comprising coupled electric and
magnetic fields, which for simplicity is represented schematically
only by its electric field 140. When the antenna system functions
in receive mode radiated EM wave 160 is replaced by an incident EM
wave, and RF apparatus 110 typically is a receiver. In many cases
RF apparatus 110 comprises a transceiver that functions both as a
transmitter and a receiver.
[0032] FIG. 2 is a schematic representation 200 of a generalized
antenna system in transmit mode in which RF hardware 210
incorporates elements 110 and 120 in FIG. 1. RF hardware 210 has a
generalized complex apparatus internal impedance denoted Z.sub.0,
this nomenclature deriving from the fact that the RF apparatus 110
of FIG. 1 usually is impedance-matched to antenna feed 120 in FIG.
1 which typically is a transmission line with characteristic
impedance Z.sub.0, Hence the Z.sub.0 nomenclature, which has no
special significance beyond its being a common notation in the
antenna art. In the context of this invention, Z.sub.0 represents
the internal impedance of RF hardware 210 in FIG. 2 regardless of
the hardware's specific configuration or mode of operation
(transmit, receive, or both), although, as pointed out above,
Z.sub.0 typically is a transmission line's characteristic
impedance. These concepts are discussed more generally in the
textbook "Antenna Theory: Analysis and Design," by C. A. Balanis,
Harper & Row, Publishers, New York, 1982 ("Balanis") at pages
1-4 and 52-57, which is incorporated herein by reference. In
particular, FIGS. 1 and 2 herein are adapted from Balanis FIGS. 1.1
and 2.18(a) in Sections 1.2 and 2.13, respectively, of that
textbook; and Z.sub.0 herein corresponds to internal impedance
Z.sub.g in Balanis FIG. 2.18(a) and to Z.sub.T in Balanis FIG.
2.19(a). Additional discussion of antenna feed systems in the
context of impedance bandwidth appears in Y. Zehforoosh, et al.,
"Antenna Design for Ultra Wideband Application Using a New
Multilayer Structure," PIERS Online, vol. 2, No. 6, pp. 544-549,
2006, at page 546, which is fully incorporated herein by reference,
doi:10.2529/PIERS060531145356, "doi" being the paper's "digital
object identifier."
[0033] In transmit mode, RF hardware 210 in FIG. 2 excites antenna
220 at its input terminals a and b, and antenna 220 emits radiated
EM wave 230 into the surrounding space. Maximum power is absorbed
by antenna 220 when impedance Z.sub.0 is conjugated-matched to the
antenna input impedance Z.sub.in seen between terminals a and b;
that is, there is zero reflected power when this condition is met
(note that in Balanis' notation Z.sub.in is denoted Z.sub.A in his
equation (2-72) at page 54). The antenna input impedance Z.sub.in
is determined by the antenna's source current distribution.
Constraining this current distribution to yield a value of antenna
input impedance, Z.sub.in, that is as close as possible to
Z.sub.0's complex conjugate unnecessarily eliminates all other
current distributions that will provide better antenna performance
against a specific set of user-specified performance objectives
with a different value of Z.sub.0. This limitation, which is
inherent in all traditional antenna D/O methodology, is removed by
using the Variable Z.sub.0 System and Method instead of traditional
methodology, and the results often are quite surprising.
[0034] IBW is defined as the frequency band or bands within which
Z.sub.in, the antenna input impedance, is matched within specified
limits to Z.sub.0, the characteristic impedance or apparatus
internal impedance of RF hardware 210 in FIG. 2. The required
degree of matching can be specified in terms of the antenna's
actual input impedance [resistance, R.sub.in, and reactance,
X.sub.in, where Z.sub.in=R.sub.in+jX.sub.in, j=(-1).sup.1/2] as a
function of frequency, or, as is more often the case, in terms of a
maximum voltage standing wave ratio (VSWR). IBW typically is
specified as VSWR//Z.sub.0.ltoreq.2:1 (// denoting "relative to"),
which is equivalent to a return loss (scattering parameter
S.sub.11) approximately less than -10 dB. Other VSWR thresholds can
be used instead, and frequently are. Zehforoosh et al., cited
above, describe the design of an Ultra Wideband (UWB) microstrip
antenna and provide a useful summary of Z.sub.0's significance as a
design or optimization parameter in the context of IBW. Following
traditional methodology, Zehforoosh's work treats the feed system
characteristic impedance Z.sub.0 as a fixed parameter, not a
variable quantity as it is in Variable Z.sub.0. While IBW is an
important consideration in modern wireless device antenna system
design, other performance measures often are as well, for example,
without limitation, directivity, radiation pattern, sidelobe level,
or radiation efficiency, which also can be addressed using the
Variable Z.sub.0 System and Method.
[0035] FIG. 3 flowchart 300 is a representative antenna system
design methodology illustrating a Variable Z.sub.0 embodiment
including steps 390, 395. Flowchart 300 applies generally to any
design methodology 315. As an example, without limitation, in the
case of designing a Yagi-Uda array antenna system ("Yagi"), design
methodology 315 might be based on the essentially graphical
methodology formulated in P. B. Viezbicke, "Yagi Antenna Design,"
National Bureau of Standards Technical Note 688, U.S. Dept. of
Commerce, December, 1976 which is fully incorporated herein by
reference. Alternatively, design methodology 315 may be based on
one of the many computer programs or textbooks available from or
recommended by the American Radio Relay League (ARRL), 225 Main
Street, Newington, Conn. 06111 USA, on its antenna technology
website, or, as an example, not a limitation, the various methods
described in The ARRL Antenna Book.
[0036] In flowchart 300, arrows 370 trace the sequence of design
steps, which begins with definition of design parameters 305, in
which each of N parameters P.sub.i, i=1,N, is defined. In the case
of the Yagi array, for example, the length, diameter, and spacing
of each array element are typical design parameters. For other
types of antennas, other parameters may be specified. For example,
a helical antenna might be defined by its number of turns, wire
gauge, helix diameter, and turn pitch. These typical antenna types
and parameters are provided for illustrative purposes only, in no
way limiting the types of antennas or the range of antenna system
parameters that may be designed or determined using the Variable
Z.sub.0 System and Method according to this invention.
[0037] In step 310, each antenna system design parameter typically
is bounded by minimum and maximum acceptable values, that is,
P.sub.min.ltoreq.P.sub.i.ltoreq.P.sub.max, i=1, N, where P.sub.min
and P.sub.max, respectively, are the minimum and maximum acceptable
values. These bounds define the antenna system "design space." For
example, in the case of the Yagi array, the acceptable driven
element length might be no shorter than 10 centimeters (minimum)
and no longer than 50 centimeters (maximum), while similarly in the
helix example, the number of turns might be restricted to no fewer
than 5 or more than 20, these examples being provided only for
purposes of illustration and not in any way limiting the Variable
Z.sub.0 System and Method according to this invention.
[0038] Design methodology 315 processes the design parameters to
develop an antenna system design whose performance is evaluated
against a set of user-specified performance objectives shown as
input data 380 or 360 feeding design methodology 315. Performance
objectives 380 or modified performance objectives 360 pass through
OR function 350 as shown. If the design objectives are met in
decision step 320 then the design methodology 315 is terminated at
End step 330. If, on the other hand, objectives 380 are not met,
path 345, then the objectives may be preserved and another
iteration 340 of the design methodology undertaken using the
original performance objectives 380. Alternatively, as shown in OR
step 350, the objectives may be modified by following path 355 to
create modified performance objectives 360, whereupon OR 350 is
performed to input new modified performance objectives to design
methodology 315. The process outlined in flowchart 300 continues
until an acceptable antenna system design has been developed.
Modifications to representative flowchart 300 often are made by
practitioners skilled in the art of antenna system design, and such
modifications are fully anticipated herein.
[0039] Introducing Z.sub.0 as a new design parameter results in
better antenna system designs because the design space has been
expanded by introducing into it another degree of freedom, namely,
the variable instead of fixed value of Z.sub.0. Steps 390 and 395
create an entirely new range of possible antenna source current
distributions, which, without Variable Z.sub.0, are forever
inaccessible using traditional methodology, and which, with
Variable Z.sub.0, can result in improved antenna system
performance. These new distributions often result in remarkably
better antenna performance, the possible tradeoff then being
between working with a "non-standard" value for Z.sub.0 and
achieving a much better antenna system, or insisting on a
pre-determined "standard" value for Z.sub.0 at the expense of
performance. This trade-off generally favors the Variable Z.sub.0
design, often by a very wide margin.
[0040] FIG. 4 flowchart 400 is a representative antenna system
optimization methodology illustrating a Variable Z.sub.0 embodiment
including steps 485, 490. Flowchart 400 applies generally to any
optimization methodology 440. Optimization methodology 440 is
completely unrestricted as to type and function, and it may perform
maximization or minimization. It may be computer-based, which most
often is the case, or analytical in nature, or a combination of
these or other approaches, for example without limitation,
graphical, approaches. Widely used computer search and optimization
algorithms include, as examples and not limitations, Central Force
Optimization, Dominating Cone Line Search, Particle Swarm
Optimization, Genetic Algorithm, Ant Colony Optimization,
Differential Evolution, and many others well known in the art. For
additional discussion of antenna system optimization algorithms,
see, for example, without limitation, E. A. Jones et al., "Design
of Yagi-Uda Antennas Using Genetic Algorithms," IEEE Trans.
Antennas and Propagation, vol. 45, no. 9, 1997, pp. 1386-1392; R.
A. Formato, "Improved CFO Algorithm for Antenna Optimization,"
Prog. Electromagnetics Research B, Vol. 19, 2010, pp. 405-425; R.
A. Formato, "Central Force Optimization Applied to the PBM Suite of
Antenna Benchmarks," 2010, each of which is fully incorporated
herein by reference.
[0041] Flowchart 400 begins with definition of optimization
parameters 410 followed by specification of the "decision space"
420 by bounding these parameters (steps 410 and 420 are analogous
to steps 305 and 310 in FIG. 3) and by definition of the fitness
function to be optimized 430, which may be maximized or
minimized.
[0042] Whereas design methodology 315 in flowchart 300 usually
comprises a capability to assess antenna system performance, as a
general rule optimization methodology 440 does not. Most
optimization algorithms are "stand alone" computer programs that
are useful across a wide range of disparate problems, not only
antenna system design. As an example, Ant Colony Optimization has
been used for array antenna synthesis (see, for example,
Quevedo-Teruel et al., "Ant Colony Optimization for Array
Synthesis," IEEE Antennas and Propagation Society International
Symposium, 23 Oct. 2006, Albuquerque, N. Mex, pp. 3301-3304, doi:
10.1109/APS.2006.1711318, which is fully incorporated herein by
reference), and also for solving protein folding problems, which is
a quite different discipline (see, for example, Hu et al., "Protein
Folding in Hydrophobic-Polar Lattice Model: A Flexible Ant-Colony
Optimization Approach," Protein & Peptide Letters, 2008, 15,
469-477, which is fully incorporated herein by reference).
[0043] Because optimization methodology 440 typically does not
comprise an antenna system modeling capability, an optional
external antenna modeling engine 495 usually is required (but not
necessarily, with the dashed line being used to distinguish blocks
485 and 490). Many modeling engines are available, and one of the
most popular is the Numerical Electromagnetics Code (NEC), which is
available in several versions. NEC-2, for example, is freeware
downloadable from various websites.
[0044] NEC has been used to compute Yagi array and Meander Monopole
antenna system performance using an embodiment of Variable Z.sub.0
System and Method, and the results are described below. Details of
NEC theory, implementation, and use may be found in the following
publications: G. J. Burke, "Numerical Electromagnetics
Code--NEC-4.2 Method of Moments, Part I: User's Manual," Jul. 15,
2011, LLNL-SM-490875; G. J. Burke, "Numerical Electromagnetics
Code--NEC-4, Method of Moments, Part I: User's Manual and Part II:
Program Description--Theory," January 1992, UCRL-MA-109338; G. J.
Burke and A. J. Poggio, "Numerical Electromagnetics Code
(NEC)--Method of Moments," Parts I, II and III, January 1981,
UCID-19934, all published by Lawrence Livermore National
Laboratory, Livermore, Calif., USA.
[0045] Optimization methodology 440 continues to operate until
user-specified termination criteria 450 are met, whereupon path 460
is followed to termination step 470. If, however, termination
criteria 450 are not met, then path 455 is followed, and
optimization methodology 440 continues its operation. Typical
termination criteria are a certain number of iterations (often
referred to as "generations" or "steps"); saturation of a fitness
function (changes over some number of steps within a specified
tolerance); meeting or exceeding a specific fitness threshold
value; or a combination of these and possibly other measures of how
"good" the value of the fitness function is. The user is free to
define whatever termination criterion or criteria, respectively, is
or are appropriate, singly or in combination with others.
Modifications to this representative flowchart 400 often are made
by practitioners skilled in the art of antenna system design, and
such modifications are fully anticipated herein.
[0046] In some example embodiments of the Variable Z.sub.0 System
and Method, the Central Force Optimization (CFO) algorithm has been
used as optimization methodology 440, and FIG. 5 provides CFO
pseudocode 500. Procedure CFO [f({right arrow over (x)}), N.sub.d,
.OMEGA.] optimizes (maximization, not minimization) a scalar-valued
function f({right arrow over (x)}) of N.sub.d-dimensional decision
vector
x .fwdarw. = i = 1 N d x i e ^ i , ##EQU00001##
where .sub.i is the i.sup.th unit vector in the decision space
defined by
.OMEGA. = { x i x i min .ltoreq. x i .ltoreq. x i max ,
##EQU00002##
i=1, . . . , N.sub.d}. N.sub.t is the number of CFO "time" steps;
F.sub.rep.sup.init the starting value for CFO's repositioning
factor F.sub.rep ; .DELTA.F.sub.rep the increment in F.sub.rep;
F.sub.rep.sup.min its minimum value; N.sub.p the number of CFO
probes;
( N p N d ) MAX ##EQU00003##
the maximum number of CFO probes per dimension; and
.gamma..sub.start, .gamma..sub.stop, .DELTA..gamma., respectively,
CFO's .gamma.-parameter starting, stopping, and increment values
for CFO's probe line distribution. As an optimization run
progresses, CFO computes a fitness matrix M.sub.j.sup.p at each
probe's location specified by position vector {right arrow over
(R)}.sub.j.sup.p, j being the time step index and p the probe
number. Pseudocode 500 has been reproduced from R. A. Formato,
"Parameter-Free Deterministic Global Search with Simplified Central
Force Optimization," in Advanced Intelligent Computing Theories and
Applications (ICIC2010), Lecture Notes in Computer Science (D.-S.
Huang, Z. Zhao, V. Bevilacqua and J. C. Figueroa, Eds.), LNCS 6215,
pp. 309-318, Springer-Verlag Berlin Heidelberg, 2010, which
contains a detailed explanation of the CFO algorithm and which is
fully incorporated herein by reference. Additional explanation of
CFO theory and operation appears in R. A. Formato, "Central Force
Optimization with Variable Initial Probes and Adaptive Decision
Space," Applied Mathematics and Computation, Vol. 217,2011, pp.
8866-8872, and in R. A. Formato, "Central Force Optimization: A New
Metaheuristic with Applications in Applied Electromagnetics," Prog.
Electromagnetics Research, PIER 77, 2007, pp. 425-491, both of
these publications being fully incorporated herein by
reference.
[0047] FIGS. 6 through 13, inclusive, illustrate the improvement in
antenna system performance achievable by using the Variable Z.sub.0
System and Method with three quite different example systems: (1) a
6-element Yagi-Uda array antenna system; (2) a Meander Monopole
antenna system; and (3) a transmission line Multi-Stub Matching
Network.
6-Element Yagi-Uda Array Results
[0048] A Yagi array usually comprises a single reflector element
(REF), a single driven element (DE), and a plurality of director
elements (D.sub.i) all arranged parallel to one another along a
perpendicular boom. If each element has the same circular
cross-section, which often is the case, then the array is
completely specified by assigning to each element a length and its
spacing from the previous one. For example, a 6-element Yagi is
completely specified by 11 geometrical parameters (six lengths for
REF, DE, D.sub.1, D.sub.2, D.sub.3, D.sub.4; and five spacings for
DE-REF, D.sub.1-DE, D.sub.2-D.sub.1, D.sub.3-D.sub.2,
D.sub.4-D.sub.3). These parameters and others used in specifying an
antenna system typically are termed "design" or "optimization"
"parameters" or "variables" or "decision variables," or, depending
on context, other like terminology which is common in the art and
anticipated herein.
[0049] In traditional antenna system D/O methodology the impedance
Z.sub.0 is assigned a fixed value at the beginning of the
methodology, typically Z.sub.0=50.OMEGA. because this is a
"standard" value. By contrast, using Variable Z.sub.0 Method and
System according to this invention, Z.sub.0 is not assigned any
value, and instead is allowed to "float" as a true variable
quantity whose ultimate value is determined by the methodology.
Thus, in applying a design or optimization methodology to the
Variable Z.sub.0 6-element Yagi array antenna system, Z.sub.0 is
added to the list of design parameters as a twelfth design
parameter or decision variable whose value is to be determined by
the design or optimization methodology, an improvement that,
surprisingly, has been overlooked through many decades of antenna
system design or optimization.
[0050] FIGS. 6, 7 and 8, respectively, plot the Voltage Standing
Wave Ratio (VSWR), Forward Gain (G.sub.fwd), and Front-to-Back
Ratio (FBR) for a 6-element Yagi optimized using traditional
methodology, that is keeping Z.sub.0 fixed, and also using the
improved Variable Z.sub.0 System and Method according to this
invention. The traditional methodology assumed a "standard" value
of 50.OMEGA. for Z.sub.0 and used two different deterministic
optimization algorithms: Central Force Optimization (CFO) and
Dominating Cone Line Search (DCLS). For the Variable Z.sub.0 case,
Z.sub.0 was treated as a true variable quantity according to this
invention whose value is determined by the optimization algorithm
(CFO), instead of being specified as a fixed value input to the
algorithm.
[0051] DCLS and the fitness (objective) function that was used for
a DCLS-optimized 6-element Yagi are described in A. C. Lisboa, et
al., "Monotonically Improving Yagi-Uda Conflicting Specifications
Using the Dominating Cone Line Search Method," IEEE Trans.
Magnetics, vol. 45, no. 3, 2009, pp. 1494-1497, which is fully
incorporated herein by reference.
[0052] For the CFO runs, the Yagi array antenna system was
optimized against the fitness function
k = 1 3 c k G fwd ( f k , x .fwdarw. ) - i = 1 3 c i VSWR // Z 0 (
f i , x .fwdarw. ) ##EQU00004##
where f is the antenna operating frequency and {right arrow over
(x)} the decision vector defined as {right arrow over
(x)}=(Z.sub.0, L.sub.REF, L.sub.DE, L.sub.D.sub.1, L.sub.D.sub.2,
L.sub.D.sub.3, L.sub.D.sub.4, X.sub.DE, X.sub.D.sub.1,
X.sub.D.sub.2, X.sub.D.sub.3, X.sub.D.sub.4). The fitness function
coefficients were:
TABLE-US-00001 i c.sub.i k c.sub.k f.sub.i, k (MHz) 1 5.0 1 0.2
239.8 2 8.0 2 0.8 299.8 3 0.9 3 1.0 359.8
[0053] The fitness (to be maximized in this case) increases with
increasing forward gain G.sub.fwd and decreasing VSWR//Z.sub.0,
VSWR//Z.sub.0 being the voltage standing wave ratio relative to
Z.sub.0 (// denotes "relative to"). This fitness function optimizes
the antenna system both for VSWR and for gain, not just one or the
other, and it provides an example, without limitation, of how
various antenna system performance measures can be combined. There
are no restrictions on how a suitable objective or fitness function
may be defined or what performance measures may be included. Yagi
system performance in this case was computed using NEC as the
modeling engine.
[0054] The 6-element Yagi antenna system optimization problem is
12-dimensional with the following decision variables: Z.sub.0, the
feed system characteristic impedance (or apparatus internal
impedance if there is no feed line) according to this invention;
and the eleven geometric variables corresponding to the Yagi
element lengths ("L") and boom coordinates ("X"), each subscripted
with the corresponding element name (note that REF is placed
symmetrically on the Y-axis, that is, at X=0, in a rectangular
Cartesian coordinate system). The fitness is evaluated at three
frequencies using the empirically determined coefficients c.sub.i
and c.sub.k shown above. G.sub.fwd is evaluated in the direction of
the +X-axis (.theta.=90.degree., .phi.=0.degree. in NEC's
right-handed spherical polar coordinate system). Additional details
and discussion of this optimization example appear in R. A.
Formato, "Improving Bandwidth of Yagi-Uda Arrays," Wireless
Engineering and Technology, January 2012, 3, pp. 18-24
(doi:10.4236/wet.2012.31003), which is fully incorporated herein by
reference.
[0055] FIG. 6 graph 600 shows that the Variable Z.sub.0 6-element
Yagi VSWR 610 exhibits considerably better IBW for the usual VSWR
threshold of 2:1, and, indeed, surprisingly better performance
throughout the VSWR range than the traditional fixed-Z.sub.0
systems 620, 630. This improvement is a result of allowing the
optimization algorithm to determine Z.sub.0 according to this
invention, which in this case was found to be a value of
107.91.OMEGA. instead of the usual 50.OMEGA. that was used for the
fixed-Z.sub.0 antenna systems. Curve 630 was computed by NEC using
the dimension data for the fixed-Z.sub.0 6-element DCLS-optimized
"A3" Yagi array described in Lisboa et al.'s paper cited above. For
comparative purposes, FIG. 6 also shows IBW for a "perfect antenna"
(1:1 impedance match) as the dashed line 640.
[0056] FIGS. 7 and 8, graphs 700 and 800, similarly show that the
CFO-optimized Variable Z.sub.0 Yagi curves 710, 810 exhibit
generally better G.sub.fwd and FBR, respectively, than the fixed
Z.sub.0=50.OMEGA. antenna systems 720, 730, 820, 830. Additional
details describing Variable Z.sub.0 and the CFO algorithm appear in
R. A. Formato, "A Novel Methodology for Antenna Design and
Optimization: Variable Z.sub.0 (ver. 2)," 2011, Cornell University
Library and in R. A. Formato, "UWB Array Design Using Variable
Z.sub.0 Technology and Central Force Optimization, ver. 2," 2011,
Cornell University Library, both of which are fully incorporated
herein by reference.
Meander Monopole Results
[0057] As a further example of Variable Z.sub.0's effectiveness,
FIGS. 9 and 10, graphs 900 and 1000, respectively, show VSWR and
maximum gain for a CFO-optimized Meander Monopole (MM) antenna
system using Variable Z.sub.0 (curves 910, 1010) and not using it
(curves 920, 1020). The MM antenna system, like the Yagi example
above, was optimized both for VSWR and maximum gain, but a
different fitness function was employed, in this case, the weighted
gain-VSWR quotient defined as
i = 1 N w g ( f i ) G max ( f i ) w VSWR ( f i ) VSWR // Z 0 ( f i
) ##EQU00005##
wherein functions
w g ( f i ) = ( w g max - w g min ) ( f U - f i ) f U - f L + w g
min ##EQU00006## and ##EQU00006.2## w VSWR ( f i ) = ( w VSWR max -
w VSWR min ) ( f U - f i ) f U - f L + w VSWR min
##EQU00006.3##
are weighting functions, and f.sub.i,f.sub.L and f.sub.U are the
calculation frequencies and operating band lower and upper
frequencies, respectively. A detailed discussion of this Meander
Monopole optimization example appears in R. A. Formato, "Variable
Z.sub.0--A New Antenna Design Paradigm," VHF Communications (U.K.),
1/2012, March, 2012, pp. 18-23, which is fully incorporated herein
by reference.
[0058] It is seen from the curves in FIG. 9 that using the
traditional methodology in which Z.sub.0 is set to a fixed value
(50.OMEGA. in this case) results in a higher and much more variable
VSWR, 920, than does Variable Z.sub.0 according to this invention,
910, in which the CFO optimization algorithm determines Z.sub.0's
value. The difference in these curves is unexpectedly dramatic,
especially when they are compared to the perfect 1:1 match curve
930.
[0059] As shown in the annotation of curve 910, an optimum value of
Z.sub.0 computed by CFO using the Variable Z.sub.0 System and
Method is 263.91.OMEGA., which is quite different from the standard
50.OMEGA. value. Besides resulting in a VSWR curve 910 that is
surprisingly flatter and closer to the ideal 1:1 curve, Variable
Z.sub.0 eliminates the very large and undesirable spike between
3500 and 4000 MHz on curve 920. Forcing the MM antenna system
current distribution to impedance-match Z.sub.0=50.OMEGA. to the
greatest degree possible, which is what traditional antenna system
D/O does, automatically excludes the far better current
distribution discovered by CFO using Variable Z.sub.0 which results
in Z.sub.0=263.91.OMEGA..
[0060] FIG. 10 compares the MM antenna system's maximum gains and
shows that across the band the Variable Z.sub.0 gain 1010 generally
is comparable to or better than the fixed Z.sub.0 gain 1020. These
data combined with curves 910 and 920 show clearly that the
CFO-optimized MM antenna system using the Variable Z.sub.0 System
and Method according to this invention has accomplished the
objective of improved VSWR while maintaining good maximum gain, and
that this MM's performance is surprisingly better than that
obtained with the traditional D/O approach in which Z.sub.0 is a
fixed parameter whose value cannot change. Variable Z.sub.0 is
effective because it adds another degree of freedom to the design
space or, in the case of optimization, to the decision space,
thereby leading to unexpected and surprisingly greater flexibility
in discovering good solutions to the design or optimization
problem, the MM problem described here being only an example.
Multi-Stub Matching Network Results
[0061] As a further example of Variable Z.sub.0's effectiveness,
FIGS. 11, 12 and 13, graphs 1100, 1200 and 1300, respectively, show
VSWR plots for 3, 5 and 7-stub Multi-Stub Matching Networks (MSMN)
optimized for a specific VSWR profile (not a "flat" VSWR as in the
previous examples) using both traditional D/O methodology in which
Z.sub.0 is fixed, and also using the Variable Z.sub.0 System and
Method according to this invention in which Z.sub.0 "floats." The
network comprises matching stubs on a transmission line whose
characteristic impedance is Z.sub.0. Biogeography Based
Optimization (BBO) was used for each case with and without Variable
Z.sub.0, and for comparison the 7-stub MSMN also was optimized
using Nelder-Mead Simplex (NM) with fixed-Z.sub.0 only. The
"standard" value Z.sub.0=50.OMEGA. was used for all of the
fixed-Z.sub.0 runs. In order to compare the optimized MSMN
configurations to an "ideal" response, graphs 1100, 1200, and 1300
include the desired VSWR curve as a solid line, 1130, 1230, 1330,
which unlike in the Yagi and MM examples is not flat at VSWR=1.
Discussion of the MSMN problem generally, and details of the design
objective, appear in C. Regoli, "Impedance matching by using a
multi-stub system," Proceedings of the 7th WSEAS International
Conference on Simulation, Modeling and Optimization, Beijing,
China, Sep. 15-17, 2007, pp. 340-344, which is fully incorporated
herein by reference.
[0062] FIG. 11 shows results for the 3-stub MSMN. The BBO-optimized
fixed Z.sub.0 device exhibits especially poor VSWR performance 1120
near the band-center frequency of 1.2 GHz, whereas the
BBO-optimized Variable Z.sub.0 MSMN's response 1110 comes quite
close to the desired response 1130. A similarly impressive
improvement is seen in the 5-stub case, FIG. 12, graph 1200,
wherein the fixed Z.sub.0 device's VSWR 1220 is very poor mid-band,
whereas in marked contrast the Variable Z.sub.0 device's response
1210 is surprisingly close to the desired response 1230l throughout
the entire band.
[0063] FIG. 13, graph 1300, compares two fixed-Z.sub.0 7-stub MSMNs
optimized with BBO and with NM to the 7-stub network BBO-optimized
using the Variable Z.sub.0 System and Method according to this
invention. Neither of the fixed-Z.sub.0 responses, 1320 and 1340,
is close to the desired response 1330 across the band spanning
1.1-1.3 GHz band, although both the BBO and NM devices slightly
improve the mid-band response, with BBO 1320 performing better than
NM 1340. However, even with this minor mid-band improvement, the
overall response of the traditionally-optimized 7-stub device at
best is only fair. In marked contrast, and what is nothing less
than a truly unexpected and remarkable improvement, the
BBO-optimized Variable Z.sub.0 7-stub MSMN response 1310 is
essentially indistinguishable from the desired response 1330 across
the entire band.
[0064] Because in the Variable Z.sub.0 System and Method according
to this invention the value of Z.sub.0 is determined by the design
or optimization methodology, the curves in FIGS. 11, 12 and 13 are
annotated with the different BBO-determined Z.sub.0 values, all of
which are within a factor of 3 of "standard" fixed-Z.sub.0 value of
50.OMEGA. that was employed in the traditional D/O methodology. For
the 7-stub case, the optimal value of Z.sub.0 is 128.OMEGA., which
happens to be fairly close to the 50.OMEGA. value that results in
far worse VSWR performance. These results are a compelling example
of how much better antenna systems designed using Variable Z.sub.0
according to this invention can be, compared to traditionally
designed or optimized systems.
[0065] The MSMN problem again illustrates how effective the
Variable Z.sub.0 System and Method is for solving difficult antenna
system problems that simply cannot be effectively addressed by
other methods. Additional details describing the MSMN problem
appear in N. I. Dib, A. Sharaqa, and R. A. Formato, "Variable
Z.sub.0 Applied to Biogeography Based Optimized Multi-Stub Matching
Network and to a Central Force Optimized Meander Monopole," April,
2012, which is fully incorporated herein by reference.
[0066] The foregoing description of the embodiments of the
invention has been presented for the purposes of illustration and
description. Each and every page of this submission, and all
contents thereon, however characterized, identified, or numbered,
is considered a substantive part of this application for all
purposes, irrespective of form or placement within the application.
This specification is not intended to be exhaustive or to limit the
invention to the precise form disclosed. Many modifications and
variations are possible in light of this disclosure. Other and
various embodiments will be readily apparent to those skilled in
the art, from this description, figures, and the claims that
follow. It is intended that the scope of the invention be limited
not by this detailed description, but rather by the claims appended
hereto.
* * * * *