U.S. patent number RE48,528 [Application Number 15/842,793] was granted by the patent office on 2021-04-20 for antenna array with wide-band reactance cancellation.
This patent grant is currently assigned to HRL Laboratories, LLC. The grantee listed for this patent is HRL LABORATORIES, LLC. Invention is credited to Jonathan J. Lynch, Carson R. White.
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United States Patent |
RE48,528 |
White , et al. |
April 20, 2021 |
Antenna array with wide-band reactance cancellation
Abstract
An antenna array containing two or more radiating elements, with
nearest neighbor radiating elements connected together with a
non-Foster circuit at terminals of the radiating elements such that
mutual reactance of the elements is reduced over a wider bandwidth
than which would be obtained if the non-Foster circuits were
omitted.
Inventors: |
White; Carson R. (Augora Hills,
CA), Lynch; Jonathan J. (Oxnard, CA) |
Applicant: |
Name |
City |
State |
Country |
Type |
HRL LABORATORIES, LLC |
Malibu |
CA |
US |
|
|
Assignee: |
HRL Laboratories, LLC (Malibu,
CA)
|
Family
ID: |
49512143 |
Appl.
No.: |
15/842,793 |
Filed: |
December 14, 2017 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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61620384 |
Apr 4, 2012 |
|
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Reissue of: |
13856375 |
Apr 3, 2013 |
9214724 |
Dec 15, 2015 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
H01Q
21/20 (20130101); H03H 7/52 (20130101); H03H
7/48 (20130101); H01Q 3/26 (20130101); H03H
7/485 (20130101); H01Q 21/0006 (20130101); H01Q
21/14 (20130101); H01Q 1/523 (20130101); H01Q
21/28 (20130101) |
Current International
Class: |
H01Q
21/00 (20060101); H01Q 21/20 (20060101); H03H
7/52 (20060101); H03H 7/48 (20060101); H01Q
1/52 (20060101); H01Q 3/26 (20060101); H01Q
21/14 (20060101); H01Q 21/28 (20060101) |
Field of
Search: |
;343/810,816,850,852,853,893 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
Other References
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.
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2004, pp. 1-14. cited by examiner .
R.C. Hansen, "Fundamental Limitations in Antennas", Proceedings of
the IEEE, 69(2), 1981, pp. 170-182. cited by applicant .
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Array", IEEE Transactions on Antennas and Propogation, 55(4), 2007,
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in Arrays of Radiating Elements Fed by Microwave Transistors",
Proceedings of the 4th European Microwave Conference, Montreux,
Switzerland, 1974, pp. 278-282. cited by applicant .
C.K. Edwin Lau, et al., "Minimum Norm Mutual Coupling Compensation
with Applications in Direction of Arrival Estimation", IEEE
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2034-2041. cited by applicant .
C. Volmer, et al. "Broadband Decopuling and Matching of a
Superdirective Two-Port Antenna Array", IEEE Antennas and Wireless
Propagation Letters, vol. 7, 2008, pp. 613-616. cited by applicant
.
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Electrically-Small Antennas", IEEE Transactions on Antennas and
Propagation, 57(8), 2009, pp. 2230-2241. cited by applicant .
J.G. Linvill, "Transistor Negative-Impedance Converters",
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725-729. cited by applicant .
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Impedances to Match Electrically-Small Antennas and Arrays",
Proceedings of the Antenna Applications Symposium, 2005, pp.
89-108. cited by applicant .
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Microwave and Optical Technology Letters38(6), 2003, pp. 453-455.
cited by applicant .
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Linear N-Node Circuits from Network Determinants and the
Appropriate Role of the Stability Factor K of their Reduced
Two-Ports,", Third International Workshop on Integrated Nonlinear
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an Eigenmode Feed Network", IEEE Transactions on Antennas and
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117. cited by applicant .
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as US 2014-0300431 A1), Application and Office Actions. cited by
applicant .
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from PCT/US2013/035183 dated Sep. 15, 2014. cited by applicant
.
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.
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from PCT/US2013/035185 issued on Oct. 7, 2014. cited by applicant
.
White, Carson R., "A non-foster monopole array," Antennas and
Propagation Society International Symposium (APSURSI), 2012 IEEE, 2
pages. cited by applicant .
White, Carson R., et al., "A Non-Foster VHF Monopole Antenna," IEEE
Antennas and Wireless Propagation Letters, vol. 11, 2012, pp.
584-587. cited by applicant .
ISR and WO for related PCT/US2013/035185 mailed on Jul. 25, 2013.
cited by applicant .
ISR and WO for related PCT/US2013/035183 mailed on Jul. 25, 2013.
cited by applicant .
Chua, Ping Tyng, et al. "Microstrip Decoupling Networks for
Low-Order Multi-Port Arrays with Reduced Element Spacing",
Microwave and Optical Technology Letters, Sep. 20, 2005, vol. 46,
Issue 6, pp. 592-597. cited by applicant .
Yazdanbakhs, P., et al. "Optimization of Monopole four-Square Array
Antenna using a decoupling network and a neural network to model
ground plane effects", In: Antennas and Propagation, 2009. cited by
applicant .
EuCAP2009, 3.sup.rd European Conference, Mar. 23-27, 2009, pp.
3014-3018. cited by applicant .
Zhang, et al. "Design and Investigation of Broadband Monopole
Antenna Loaded with Non-Foster Circuit," 2010, Progress in
Electromagnetics Research C. vol. 17, pp. 245-255. cited by
applicant .
From U.S. Appl. No. 13/856,403 (now published as US 2014/0300431
A1), Office Action mailed on May 8, 2015. cited by applicant .
Allen, John L., "Gain and impedance variation in scanned dipole
arrays," IRE Transactions on Antennas and Propagation, Sep. 1962,
pp. 566-572. cited by applicant .
Coetzee, Dual-Frequency Decoupling Networks for Compact Antenna
Arrrays, Hindawi Publishing Corporation, International Journal of
Microwave Science and Technology, vol. 2011, Article ID 249647 (4
pages). cited by applicant .
Hirvonen et al., Bandwidth Limitations of Dipoles Matched With
Non-Foster Impedances, Proceedings of European Conference on
Antennas Propagat. Eucap 2007, Nov. 2007 (5 pages). cited by
applicant .
Chaloupka, H.j., Wang, X. and Coetzee, J.C., "A superdirective
3-element array for adaptive beamforming," Microwave and Optical
Technology Letters, vol. 36, No. 6, pp. 425-430, 2003. cited by
applicant .
Chen, S.C., Wang, Y.S., and Chung, S.J., "A decoupling technique
for increasing the port isolation between two strongly coupled
antennas," IEEE Transactions on Antennas and Propagation, vol. 56,
No. 12, pp. 3650-3658, 2008. cited by applicant .
Chua, P.T. and Coetzee, J.C., "Microstrip decoupling networks for
low-order multi-port arrays with reduced element spacing,"
Microwave and Optical Technology Letters, vol. 46, No. 6, pp.
592-597, 2005. (16 pages). cited by applicant .
Coetzee, J.C. and Yu, Y., "Closed-form design equations for
decoupling networks of small arrays," Electronics Letters, vol. 44,
No. 25, pp. 1441-1442, 2008. cited by applicant .
Coetzee, J.C. and Yu, Y., "Design of decoupling networks for
circulant symmetric antenna arrays," IEEE Antennas and Wireless
Propagation Letters, vol. 8, pp. 291-294, 2009. cited by applicant
.
Ludwig, A.C., "Mutual coupling, gain and directivity of an array of
two identical antennas," IEEE Transactions on Antennas and
Propagation, vol. 24, No. 6, pp. 837-841, 1976. cited by applicant
.
Pozar, D.M. Microwave Engineering, John Wiley & Sons, Hoboken,
NJ, USA, 2005.(16 pages, preface and table of contents). cited by
applicant .
Weber, J., Volmer C., Blau, K., Stephan, R. and Hein, M.A.,
"Miniaturized antenna arrays using decoupling networks with
realistic elements," IEEE Transactions on Microwave Theory and
Techniques, vol. 54, No. 6, pp. 2733-2740, 2006. cited by
applicant.
|
Primary Examiner: Whittington; Kenneth
Attorney, Agent or Firm: Ladas & Parry
Parent Case Text
CROSS REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of U.S. Provisional Patent
Application No. 61/620,384 filed Apr. 4, 2012, the disclosure of
which is hereby incorporated herein by this reference. This
application is also related to U.S. patent application Ser. No.
13/856,403 filed on Apr. 3, 2013 and entitled "Broadband non-Foster
Decoupling Networks for Superdirective Antenna Arrays" the
disclosure of which is also hereby incorporated herein by
reference.
Claims
What is claimed is:
1. An antenna array comprising two or more radiating elements, with
nearest neighbor radiating elements connected together with a
non-Foster circuit between terminals of the radiating elements such
that a mutual reactance between the nearest neighbor radiating
elements is reduced over a wider bandwidth than which would be
obtained if the non-Foster circuits were omitted.Iadd., wherein the
non-Foster circuit at terminals of the radiating elements is
implemented as a series circuit of a negative capacitor and a
negative resistor.Iaddend..
2. The antenna of claim 1 wherein the radiating elements are
monopole type antennas.
3. The antenna of claim 1 wherein the radiating elements are dipole
type antennas.
4. The antenna of claim 1 further comprising additional non-Foster
circuits connected in series with each radiating element such that
the self-reactance of each radiating element is cancelled over said
wider bandwidth.
5. The antenna of claim 1 further including a decoupling
network.
6. The antenna of claim 1 further including a beam-forming
network.
.[.7. The antenna of claim 1 wherein the non-Foster circuit at
terminals of the radiating elements implement a negative
capacitor..].
.[.8. The antenna of claim 1 wherein the non-Foster circuit at
terminals of the radiating elements implemented a series circuit of
a negative capacitor and a negative resistor..].
9. The antenna of claim 1 wherein said two or more radiating
elements comprise four or more radiating elements, wherein all
nearest neighbor elements are all equally spaced relative to each
other.
10. The antenna of claim 1 wherein said two or more radiating
elements are arranged in an Adcock antenna array.
11. The antenna of claim 1 wherein said non-Foster circuit is
connected between feed points of said radiating elements.
12. The antenna of claim 1 wherein said radiating elements are
arranged in an Adcock array of radiating antenna elements.
13. The antenna of claim 1 wherein said non-Foster circuit realizes
a negative capacitor wired in series with a negative resistor.
.[.14. An antenna network for coupling a antenna array having two
driven antenna elements with a sum-difference network having two
outputs, the sum-difference network comprising three negative
capacitors, first and second ones of the three negative capacitors
each being coupled in series between one of the outputs of the
sum-difference network and one of the two driven antenna elements,
with the third one of the three negative capacitors being coupled
between the two driven antenna elements..].
15. .[.The antenna network of claim 14.]. .Iadd.An antenna network
for coupling an antenna array having two driven antenna elements to
a sum-difference network having two outputs, the antenna network
comprising three negative capacitors, first and second ones of the
three negative capacitors each being coupled in series between one
of the outputs of the sum-difference network and one of the two
driven antenna elements, with the third one of the three negative
capacitors being coupled between the two driven antenna elements,
and .Iaddend.further including a first negative resistor coupled in
series with the third one of the three negative capacitors between
the two driven antenna elements.
16. The antenna network of claim 15 further including second and
third negative resistors each one of which is coupled in series
with one of the first and second ones of the three negative
capacitors coupled between one of the outputs of the sum-difference
network and one of the two driven antenna elements.
17. A method of improving stability of the odd mode of an antenna
system having one or more negative capacitors coupling neighboring
driven elements to one another, the method comprising inserting a
negative resistor in series with each of the negative capacitors
coupling neighboring driven elements to one another.
18. The method of claim 17 where the negative resistor has a value
which is sufficiently large in absolute value to assure that in a
signal analysis that all zeros are in a left half of an s plane
analysis thereof.
.[.19. An antenna array comprising two or more antenna elements,
with nearest neighbor antenna elements connected together at feed
points of said antenna elements by a non-Foster circuit..].
20. .[.The antenna of claim 19.]. .Iadd.An antenna array comprising
two or more antenna elements, with nearest neighbor antenna
elements connected together at feed points of said antenna elements
by a non-Foster circuit, .Iaddend.wherein said non-Foster circuit
realizes a negative capacitor wired in series with a negative
resistor.
.[.21. A method of reducing the self reactance of a plurality of
antenna elements disposed in an array of parallel antenna elements,
the parallel antenna elements each having an axis which is
laterally spaced the axes of other antennas in said array, the
method comprising: a. providing a plurality of first non-Foster
circuits each connected in series between a transmitter and/or a
receiver and a connection point of each antenna element disposed in
said array, and b. providing a plurality of second non-Foster
circuits connected between the connection points of neighboring
antenna elements disposed in said array..].
22. .[.The method of claim 21.]. .Iadd.A method of reducing the
self reactance of a plurality of antenna elements disposed in an
array of parallel antenna elements, the parallel antenna elements
each having an axis which is laterally spaced the axes of other
antennas in said array, the method comprising: a. providing a
plurality of first non-Foster circuits each connected in series
between a transmitter and/or a receiver and a connection point of
each antenna element disposed in said array, and b. providing a
plurality of second non-Foster circuits connected between the
connection points of neighboring antenna elements disposed in said
array, .Iaddend.wherein (i) said plurality of antenna elements
comprise N antenna elements, (ii) the plurality of first non-Foster
circuits comprise N first non-Foster circuits and (iii) the
plurality of second non-Foster circuits comprise N second
non-Foster circuits, and wherein the value of N is the same for the
numbers of antenna elements, first non-Foster circuits and second
non-Foster circuits.
23. The method of claim 22 wherein the first and second non-Foster
circuit each realize a negative capacitor connected in series with
a negative resistor.
.Iadd.24. In combination, an antenna array having two driven
antenna elements, a sum-difference network having two outputs, and
a network comprising three negative capacitors, first and second
ones of the three negative capacitors each being coupled in series
between one of the outputs of the sum-difference network and one of
the two driven antenna elements, with the third one of the three
negative capacitors being coupled between the two driven antenna
elements and further including a first negative resistor coupled in
series with the third one of the three negative capacitors between
the two driven antenna elements..Iaddend.
.Iadd.25. The combination of claim 24 further including second and
third negative resistors each one of which is coupled in series
with one of the first and second ones of the three negative
capacitors coupled between one of the outputs of the sum-difference
network and one of the two driven antenna elements..Iaddend.
.Iadd.26. The antenna array of claim 20 wherein the antenna
elements each comprise an antenna with a corresponding feed point
and wherein the non-Foster circuits connected between antenna feed
points reduce mutual reactance between the antennas in said
array..Iaddend.
.Iadd.27. The antenna array of claim 20 wherein the feed points of
the antenna elements are connected to a beamforming network via
additional non-Foster circuits..Iaddend.
Description
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT
None.
TECHNICAL FIELD
An antenna array having greater efficiency than prior art. The
array (i) is capable of producing superdirective beams; (ii) may be
electrically small; and (iii) may be both capable of producing
superdirective beams and also be electrically small at the same
time.
BACKGROUND
Superdirective antennas typically comprise two or more radiating
elements in close proximity (the spacing of the radiating (or
receiving) elements is <.lamda./4, where .lamda. is the
wavelength of the signal to be radiated and/or received by the
antenna).
Antenna arrays are used in numerous applications: communications,
radar, signal intelligence, etc. Perhaps the most attractive
features of antenna arrays are beam-synthesis and
reconfigurability. For example, phased arrays have one or more
beams that may be reconfigured to point in different directions or
have different beam characteristics by changing the weight (phase
and/or amplitude) applied to the signal at each antenna element. In
digital beamforming arrays, the signal may be recorded
independently at each element, and beams may be formed in post
processing. Multiple-Input and Multiple-Output (MIMO) technology,
known in the art, can be important in wireless communications
systems since because it offers data throughput improvements
without using additional bandwidth or increasing transmit
power.
Array synthesis techniques are available in the literature that
show how to a) increase the directivity of the array without
increasing the physical size and b) generate nulls in the radiation
pattern that will provide immunity to interfering or jamming
signals. However, these techniques have severe limitations in real
arrays due to mutual coupling. Specifically, it is well known that
prior art superdirective antenna arrays have a high Q, and
therefore suffer from a corresponding efficiency/bandwidth
limitation. Due to this limitation, superdirective antenna arrays
are widely regarded as problematic and are not widely deployed.
This invention reduces the Q of superdirective antennas by more
than 10 times, providing greater than a 10 dB improvement in the
realized gain (RF efficiency) of superdirective antennas. This
reduction in Q is also helpful in generating pattern nulls.
Electrically small antennas are antennas which are rather small (or
short) compared to the wavelengths of the radio frequencies they
are intended to receive. Conventional full length antennas are
typically a'4 or 1/2 wavelength in size. At the frequencies used
for some handheld device applications, antennas which are much
smaller are called for. Electrically small antennas can be defined
as antennas whose elements are 1/10 (or less) of a wavelength of
the radio frequencies they are intended to receive. Electrically
small antennas also tend to have high Qs, so they tend to have a
small bandwidth compared to conventional antennas.
The prior art may include:
Passive Superdirective Arrays:
There is plentiful academic work (starting with Oseen in 1922) that
reveals the difficulty of realizing significant bandwidth and
efficiency. Two key conclusions are that optimum directivity leads
to extremely high Q and that mutual coupling makes for difficult
feed network design. Few arrays have been realized, and these
arrays have efficiencies <-20 dB. The practical limitations
are:
(1) High Antenna Q small bandwidth;
(2) Low radiation resistance low efficiency; and
(3) Tight tolerances difficult to realize feed network.
For a paper on the subject, see R. C. Hansen, "Fundamental
Limitations in Antennas," Proceedings of the IEEE, v. 69, no. 2,
February 1981.
The Use of Metamaterials Placed Between Radiating Elements to
Decouple them:
See, for example, K. Buell, et al. "Metamaterial Insulator Enabled
Superdirective Array," IEEE Trans. Antenn. Prop., April, 2007. The
disadvantages of this approach are:
(1) Narrow bandwidth;
(2) Only applicable to printed antennas;
(3) Complicated fabrication; and
(4) Not easily tuned.
Active Antennas:
Directly feed antennas with transistor active impedance matching
networks. This works because transistor active component inputs and
outputs are approximated by open circuits and hard sources,
respectively. Therefore, mutual coupling has no effect. However,
the antennas are not matched, resulting in low receiver sensitivity
and low transmit efficiency. For example, see M. M. Dawoud and A.
P. Anderson, "Superdirectivity with appreciable Bandwidth in Arrays
of Radiating Elements Fed by Microwave Transistors," European
Microwave Conference, 1974.
Digital Beamforming:
An analog-to-digital converter at each antenna element digitizes
the signal so that arbitrary beams may be formed in the digital
domain. In addition, mutual coupling can be accounted for in the
beamforming (see C. K. Edwin Lau, Raviraj S. Adve, and Tapan K.
Sarkar, "Minimum Norm Mutual Coupling Compensation With
Applications in Direction of Arrival Estimation," IEEE Transactions
on Antennas and Propagation, Vol. 52, No. 8, August 2004, pp.
2034-2041). However, the physical impedance match is only valid for
a single radiation pattern, which results in limited receive
sensitivity for other patterns. Furthermore, high resolution and
high dynamic range analog-to-digital converters are needed to
realize superdirective patterns.
Decoupling Networks:
Decoupling Networks result in independent modes with orthogonal
patterns from the antenna array. These modes can be matched
independently and used to synthesize arbitrary radiation patterns.
However, this approach does not reduce antenna Q. For reference,
see Christian Volmer, Metin Sengul, Jorn Weber, Ralf Stephan, and
Matthias A. Hein, "Broadband Decoupling and Matching of a
Superdirective Two-Port Antenna Array, IEEE AWPL, vol. 7, 2008.
Multimode Antenna Structure:
This technology connects nearby antennas with conductors to
decouple them. The approach is narrowband and alters the radiation
modes of the structure. Furthermore, seems to only be applicable to
small numbers of elements. See U.S. Pat. No. 7,688,273.
Non-Foster Matching Circuits for Single Antennas:
See the following documents and the comment below:
S. E. Sussman-Fort and R. M. Rudish, "Non-Foster impedance matching
of electrically-small antennas," IEEE Trans. Antennas Propagat.,
vol. 57, no. 8, August 2009. J. G. Linvill, "Transistor Negative
Impedance Converters," Proc. IRE, vol. 41, no. 6, pp. 725-729, June
1953.
This prior art technology pertains to single antennas rather than
to antenna arrays.
Non-Foster Matching Circuits Connected in Series with Array
Elements or Between Dipole Ends in Large Arrays:
See the following documents and the comments below:
(1) S. E. Sussman-Fort and R. M. Rudish "Progress in use of
non-Foster impedances to match electrically-small antennas and
arrays," Antenna Applications Symposium Digest, 2005. (2) R. C.
Hansen, "Wideband Dipole Arrays Using Non-Foster Coupling,"
Microwave and Optical Technology Letters, 38(6), Sep. 20, 2003, pp.
453-455. (3) Applicable to large arrays, not to superdirectivity.
Calculations are valid for conventional phased array scanning. (4)
Does not match all modes simultaneously.
Superdirectivity has been sought after for 90 years, and is still
regarded as impractical due to the resulting high antenna Q. The
prior art in superdirectivity is not capable of reducing the
antenna Q. Previous approaches produce either narrowband results or
low efficiency.
BRIEF DESCRIPTION OF THE INVENTION
This invention relates to an antenna array capable of producing
superdirective beams with higher RF efficiency than available in
the prior art. This is achieved by canceling the array self and
mutual reactance using non-Foster circuits (NFCs), thereby
significantly reducing the antenna quality factor, Q (where Q is
used here as the ratio of reactance to radiation resistance).
Non-Foster circuits employ active devices and therefore are not
bound by Foster's reactance theorem (which states that the
reactance or susceptance of any passive lossless one-port network
must increase with increasing frequency). Typical NFCs are negative
capacitors (which have reactance given by
.omega. ##EQU00001## where C is the capacitance and .omega. is the
radian frequency) and negative inductors (which have reactance
given by X=-.omega.|L|, where L is the inductance and w is the
radian frequency).
This invention can be used in many antenna applications--it is not
limited to use with superdirective arrays. Superdirective arrays
are just one example of antenna systems with high Qs and hence
small bandwidth. Electrically small antennas are another example of
antenna systems with high Qs and hence small bandwidth. This
invention can improve the bandwidth of any antenna or antenna
system and therefore it is not limited to either superdirective
arrays or electrically small antennas. This invention may be used
in MIMO applications.
BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1a-1d are schematic representations of a 3-element antenna
array illustrating in FIG. 1a the mutual coupling impedances
(Z.sub.21, Z.sub.31 and Z.sub.32) and in FIG. 1b the self- and
mutual-coupling mitigation circuits (Z.sub.S1, Z.sub.S2, and
Z.sub.S3; and Z.sub.c12 and Z.sub.C23). In addition, FIGS. 1c and
1d depict beamforming networks that may produce single (FIG. 1c)
and multiple simultaneous (FIG. 1d) beams, respectively. FIG. 1e is
a schematic representation of a 3-element antenna array coupled via
a decoupling network, amplifiers and phase controllers to a common
port.
FIG. 2a depicts the antenna geometry of a 4-element Adcock array
made from four monopole antennas 10, while FIG. 2b shows a
configuration for mutual reactance cancellation using four
non-Foster negative capacitors (-C.sub.C) with the 4-element Adcock
array of FIG. 2a and FIG. 2c depicts modal reactance with
Non-Foster Circuits (NFCs) connected between adjacent antenna
elements 10 and without the mutual-reactance cancellation
(unmatched). Only the lower portion of a 4-element Adcock array
made from four monopole antennas 10 is shown in FIG. 2b so that the
four non-Foster negative capacitors (-C.sub.C) can be more easily
depicted.
FIG. 3a shows a configuration of the 4-element Adcock array with
both self and mutual reactance cancellation using negative
capacitors and FIG. 3(b) shows the improvement in Signal-to-Noise
Ratio using series only and both series and inter-element ideal
NFCs.
FIG. 4a depicts a configuration of the mutual reactance
cancellation circuits for the 8-element Adcock array. Improvement
in Signal-to-Noise Ratio using series only and both series and
inter-element ideal NFCs is shown in FIG. 4b.
FIGS. 5a and 5b depict two possible embodiments of 2-element Adcock
arrays wherein the individual radiating elements are dipoles.
FIG. 6a depicts the geometry of a 2-element antenna array where
radiating elements are monopoles and capacitors C.sub.S and C.sub.P
are negative and cancel the self and mutual reactance,
respectively, while FIG. 6b depicts far field radiation
resistance.
FIG. 7 depicts fours graphs of simulated even and odd mode
reactance for a passive array (graph (a)), an odd mode matched
array (graph (b)), an even mode matched array (graph (c)) and a
both modes matched array (graph (d)).
FIG. 8 depicts simulated transducer gain (ratio of power accepted
by the antenna array to the available power) of the even and odd
modes of the passive (in black) and non-Foster enhanced (in grey)
arrays with ideal negative capacitors assuming Z.sub.0=50 Ohms for
the antenna of FIG. 6a.
FIG. 9a is an equivalent circuit of the two element array of FIG.
6a (within the dotted enclosure), but with an added negative
resistor Rps, and with port impedances Z.sub.o also shown for ports
P1 and P2.
FIG. 9b is the same as FIG. 6a except the negative resistor Rps is
added as are two optional negative resistors Rs.
FIGS. 10a-10c depict stability and gain diagrams comparing various
values of Cp, Cs and Rps for the antenna of FIG. 9b.
FIG. 11 is a simplified schematic of three non-Foster networks, two
of which (Series NFC) are coupled between the ports (used to couple
the antenna to a receiver for example, typically via beamforming
networks and/or decoupling networks (if used)) to the elements 10
while the remaining non-Foster network (the Parallel NFC) is
coupled directly between neighboring antenna elements 10.
FIG. 12 is a detailed schematic diagram of a preferred embodiment
of the NFC used to implement the Series and Parallel NFCs of FIG.
11 as a single circuit.
FIG. 13 depicts the imulated improvement in transducer gain of both
the even and odd modes relative to the unmatched case using the
circuit in FIG. 12.
FIG. 14 is very similar to FIG. 4a with negative resistors shown in
series with the negative capacitors -Cp.
DETAILED DESCRIPTION
Three attractive features of antenna arrays are MIMO operation,
beam-synthesis and reconfigurability. Array synthesis techniques
are available in the literature that show how to (a) increase the
directivity of the array without increasing its physical size (i.e.
superdirectivity) and (b) generate nulls in the radiation pattern
that will provide immunity to jamming signals. However, these
techniques have severe limitations in real arrays due to mutual
coupling; the input impedance at any given element is a function of
the array excitation. For example, referring to FIGS. 1a-1e, which
present schematic representations of a 3-element antenna array
depicting mutual coupling:
.times..times..times..times..times..times. ##EQU00002##
where Z.sub.in,2 is the input impedance at antenna element 2,
i.sub.m is the excitation current of the m.sup.th element and
Z.sub.mn are elements in the impedance matrix of the array. The
array of antenna elements may be a linear or a non-linear array.
When the array is excited in order to generate a superdirective
pattern, mutual coupling drives the real part of the input
impedance to zero, while having a much weaker effect on the
imaginary (i.e. reactive) part. This results in the well-known
property of superdirective arrays: high antenna Q and the
corresponding efficiency/bandwidth limitation. In addition, the
input impedance varies as the beam is reconfigured. Due to these
limitations, superdirective antenna arrays are widely regarded as
problematic and are not widely deployed outside of direction
finding (DF). The present invention can be used with DF, if
desired, as it should improve DF performance either by improving
sensitivity with the same directivity or by further improving
directivity.
It should also be noted that while three element arrays are
depicted in FIGS. 1a-1e, the mathematics is not so limited. The
number of antenna elements can be equal to or greater than the
number two. Typically, a larger number of elements improves
directivity.
This invention can reduce the Q of electrically-small and
superdirective antennas by >10.times. by placing NFCs both in
series with the elements and in between nearest neighbor elements.
See FIG. 1b, where Z.sub.C12 and Z.sub.C23 are NFCs that reduce the
mutual reactance, and Z.sub.S1-Z.sub.S3 are NFCs that cancel the
self reactance.
With passive circuit elements, reactance may be cancelled over
narrow bandwidths by resonating negative (capacitive) reactance
with an inductor and positive (inductive) reactance with a
capacitor. But due to the narrow bandwidth when using passive
circuit elements, the passive circuit elements need to be
continually retuned when used in a wider bandwidth application.
NFCs, on the other hand, employ active devices and therefore are
not bound by Foster's reactance theorem. Typical NFCs are negative
capacitors (which have reactance given by
.omega. ##EQU00003## where C is the capacitance and w is the radian
frequency) and negative inductors (which have reactance given by
X=-.omega.|L|, where L is the inductance). Therefore, capacitive
reactance may theoretically be cancelled over all frequencies using
a negative capacitor. In practice, this reactance cancellation has
been limited to 1-2 decades to date by the frequency range of the
devices and other practical aspects of the circuit design. In
addition, the circuits may become unstable (leading to oscillation
or latchup) if they are not correctly designed to operate in the
particular antenna.
The performance of two exemplary antenna arrays has been calculated
using modal decomposition. The first example (see FIGS. 2a and 2b)
is a 4-element Adcock antenna array (four monopole antennas in a
square arrangement) having a height of 150 mm and a separation of
30 mm (0.05.lamda. and 0.01.lamda., respectively at 100 MHz, such
that this embodiment is also an electrically small and
superdirective antenna system). Due to the symmetries of this
4-element array, the four independent (i.e. decoupled) modes can be
generated by even/odd symmetry (note that these modes are not
normalized):
.times. ##EQU00004##
The numbers in Eqn, 2 are antenna excitation weights produced by a
beamforming network. "1" means that the antenna is excited with a
magnitude 1 and phase 0; "-1" means magnitude 1 and phase 180 deg,
and "0" means that the antenna is weighted with magnitude 0 for the
beam. The subscripts reflect the mode numbers. Adding the -C.sub.C
NFCs does not affect the modes because it does not affect the
symmetry (neglecting any mismatch between them).
The modal reactance is plotted in the top plot of FIG. 2c; it is
apparent that the reactance of mode 1 is significantly larger in
magnitude than that of modes 2-4. Therefore, the self reactance of
all modes cannot be cancelled simultaneously using the -C.sub.S
NFCs that are placed in series with the antenna elements and
substantially cancel the reactance of all modes (shown in the
bottom plot of FIG. 2c for the 4-element array). However,
connecting negative capacitors, -C.sub.C, between nearest neighbor
elements (see FIG. 2b) reduces the effect of the mutual reactance,
thereby bringing the reactance of all modes to nearly the same
value (see the bottom plot of FIG. 2c) so that the series reactance
of all modes can be substantially cancelled simultaneously. This is
illustrated for four and eight element Adcock antenna arrays in
FIGS. 3a and 4a, respectively. In both embodiments, the realized
gain of all modes is improved using only series NFCs (the -C.sub.S
capacitors). However, when inter-element NFCs (the -C.sub.C
capacitors) are also included, significant further improvement is
achieved. To a first order, the self and mutual (nearest neighbor)
reactances of the array are well approximated over broad bandwidth
as capacitors. -C.sub.S is chosen to provide the negative of the
self reactance over frequency and -C.sub.C is chosen to provide the
negative of the mutual reactance over frequency. A first step to
choosing -C.sub.C is to calculate the impedance matrix of the
array, approximate the mutual reactance between nearest neighbors
(i.e. the imaginary part of the terms of the impedance matrix that
relate the coupling between nearest neighbors) by a capacitor, and
take the negative of that capacitance. Alternatively, one can
calculate the impedance of the array loaded by the -C.sub.C NFCs
(omitting the -C.sub.S NFCs) and adjusting the -C.sub.C NFCs until
the reactances of the modes are nearly identical.
The Adcock array embodiments depicted by FIGS. 2a, 3a, and 4a, are
implemented with monopole antenna elements 10. The depicted
monopole antenna elements 10 can be replaced with dipole antenna
elements 12 as shown in the embodiments of FIGS. 5a and 5b. In the
embodiment of FIG. 5a the -C.sub.C NFCs and -C.sub.S NFCs are
applied to only one element 10 of each the two dipoles depicted. In
the embodiment of FIG. 5b the -C.sub.C NFCs and -C.sub.S NFCs are
applied to both elements 10 of each the two dipoles depicted,
however their values are changed compared to the embodiment of FIG.
5a. In the embodiments of FIGS. 5a and 5b, port P1 is the antenna
port for the first dipole antenna while port P2 is the antenna port
for the second dipole antenna. In the embodiment of FIG. 5a, the
negative capacitive loading is unbalanced while the negative
capacitive loading is balanced in FIG. 5b, so between these two
embodiments, FIG. 5b may be preferred.
If monopole antenna elements 10 are used, they are essentially one
half of a dipole, with a ground plane (which is not shown in Adcock
array embodiments depicted by FIGS. 2a, 3a, and 4a) serving as the
other half of the dipole.
Referring again to FIGS. 1a-1e, it should be recalled that the
discussion above started with a discussion of impedances and then
when it came to a presentation of the embodiments of FIGS. 2a, 3a,
4a, 5a and 5b, and the impedances were implemented with negative
capacitors. But it is believed that still better results can be
obtained if a negative resistance (-R.sub.C) is placed in series
with the negative capacitance -C.sub.C implemented by the NFCs.
Simulations have been done on an electrically small 2-element array
of monopoles 10 (see FIG. 6a). Without implying a limitation,
dipoles can be used instead of the monopoles 10 as is discussed
above. The ground plane for the monopoles is not shown. It could be
earth ground or an electrically grounded plate from which the
monopoles would project (but be electrically isolated
therefrom).
FIG. 6a depicts the geometry of a 2-element antenna array where
radiating elements A1 and A2 are monopoles (they also could be
dipoles, without implying a limitation) formed, for example, as
wire antennas (again without implying a limitation). Capacitors Cs
and Cp are negative and preferably cancel the self and mutual
reactance, respectively, of monopoles A1 and A2. A sum-difference
network 20 may be used to decompose the antenna array into even and
odd modes. The circuits depicted in FIG. 5 or 5a of U.S. patent
application Ser. No. 13/856,403 filed on Apr. 3, 2013 and entitled
"Broadband non-Foster Decoupling Networks for Superdirective
Antenna Arrays" may be used to implement network 20. Alternatively,
passive 180 degree hybrid couplers known per se in the prior art
could alternatively be used to implement network 20.
Multiple-element antenna arrays, typically having between two and
eight elements, are useful for applications of superdirectivity,
MIMO wireless communications, and antenna diversity, among others.
When spaced much closer than one wavelength, they may be also be
building blocks for Adcock direction-finding arrays. It will be
assumed for the remainder of this discussion that the antenna
spacing is less than one tenth of a wavelength. The 2-element array
is preferably decomposed into two independent modes by a
sum-difference decoupling network. The even and odd modes have
omnidirectional and figure-8 patterns, respectively, in the x-y
plane. It should be apparent that any utility of the second antenna
may only be realized by coupling to both modes. This can be
challenging because the odd mode does not radiate efficiently;
monopoles A1 and A2 are then out of phase, so the radiation
interferes destructively in the far field, leading to low radiation
resistance (see FIG. 6b). The reactance, on the other hand, is only
slightly cancelled (see FIG. 7 graph (a)), resulting in very high
antenna Q. The Bode-Fano Criterion then dictates a
bandwidth-efficiency tradeoff when using state of the art passive
matching techniques.
Non-Foster circuits are employed to reduce the reactance preferably
by a factor of ten or more. The reactances of both the even and odd
modes are well approximated by a capacitor (i.e. -1/f where f is
the frequency), but the odd mode reactance is 30% smaller than that
of the even mode. Non-Foster matching cancels the reactance of
small wire antennas with series negative capacitors (Cs in FIG.
6a). However, it is clearly seen in FIG. 7 graphs (b) and (c) that
this technique is not capable of simultaneously matching both
modes; substantial reactance remains in the unmatched mode. This
residual reactance has a detrimental effect on the transducer gain
(the ratio of power accepted by the antenna array to the available
power), as seen in FIG. 8, where the mode that is not well matched
shows minimal improvement in gain. In this invention, on the other
hand, the reactance of the even and odd modes is set to be
approximately the same by canceling the mutual reactance with
negative capacitor Cp (FIG. 6a). It is seen in FIG. 7 graph (d) and
FIG. 8 graph (c) that this enables a simultaneous even and odd mode
match and a significant improvement in the transducer gain.
Negative capacitor Cp discussed with respect to FIGS. 6a-12
corresponds to negative capacitor C.sub.C discussed with respect to
FIGS. 1-5.
While the foregoing discussion shows the benefit of the topology of
FIG. 6a, circuit stability should also be addressed. The equivalent
circuit of the two element array of FIG. 6a (valid from 0-200 MHz
and approximate up to about 400 MHz) is shown inside the dotted box
of FIG. 9a, where +.eta..sub.0=377 Ohms, Ca=3.2 pF, La=24.5 nH,
R12=45 Ohms, C12=14.6 pF and L12=8.4 nH. The non-Foster circuits,
Cs and Cp, and port impedances Z.sub.o are also shown. Resistor
Rps, which is shown connected in series with negative capacitor Cp,
will be discussed later. Mesh currents i1, i2, and i3 are described
in the frequency domain by a 3.times.3 impedance matrix; the
natural modes are found by solving for the zeros in complex
frequency (s=j2.pi.f) of the determinant of this impedance matrix.
The network is stable if all zeros are in the left half of the s
plane. Instability means that the amplitude of the currents
(whether oscillation or not) will increase exponentially with time
despite a finite excitation. While the 3.times.3 matrix method is
rigorous, the stability of the even and odd modes by themselves has
been analyzed by looking at the loop impedances and checking for
right-half-plane zeros. In practice an unstable system exhibits
either latch up or oscillation.
FIG. 9b is the same as FIG. 6a, except that (i) a negative resistor
Rps is shown in series with negative capacitor Cp and (ii) two
optional negative resistors Rs are shown in series with negative
capacitors Cs. Negative resistors Rs are less important to stable
operation than is negative resistor Rps since the values of Rs can
be set to zero (they can be removed from the circuit) and the
resulting circuit appears to be stable. Negative resistors Rs are
discussed in greater detail below with reference to FIG. 11.
If Cs and Rps are omitted, there is no value of Cp<0 that
results in a stable network. However, the network is stabilized for
both modes by introducing Rps<-90 Ohms, for example. The
stability of the network vs. Cs and Cp is plotted in graph (a) of
FIG. 10a where Rps is selected to be -90 Ohms. The even mode is
stable if Cs<-2.65 pF and unstable otherwise, while the odd mode
stability depends on both Cs and Cp. If Cp is omitted (analogous to
Cp=0 on the right hand side of the plot), the odd mode is stable
for Cs<-4 pF. However, introducing Cp allows (with Rps=-90 Ohms)
the odd mode to be stable for higher values of Cs. The utility of
this is seen in graphs (b) and (c) of FIG. 10a, which plot the
transducer gain of the even and odd modes, respectively, at stable
values of Cp and Cs. The odd-mode gain is maximized along the right
edge of the stable region, but the even mode gain is maximized at
the top of the stable region. In one exemplary embodiment, the
optimum point is approximately Cp=-0.75 pF and Cs=-2.65 pF, which
is the same as shown in FIGS. 7 and 8.
FIG. 10b provides the same plots as described above for FIG. 10a,
but Rps is selected instead to be equal to -75 Ohms. Note that
there are no values of Cp and Cs which result in stability for both
modes when Rps is equal to -75 Ohms (only the even mode can be made
stable). On the other hand if Rps is selected to be equal to -300
Ohms (see FIG. 10c), a stable embodiment of the antenna of FIG. 9b
can still arise for both modes with appropriate selections for the
values of Cp and Cs. As can be seen, as the absolute value of the
negative resistance approaches zero, the circuit becomes unstable
for the odd mode. The precise value of Rps where stability is first
obtained for both modes will depend on the size and configuration
of the two monopole antennas A1 and A2.
The self/mutual impedance compensation network for a two element
antenna array can be realized as shown in FIG. 11. Three Linvill
Negative Impedance Converter (NIC) circuits convert positive model
circuits--each comprising a variable resistor and a variable
capacitor--to their negative equivalents. The series circuits are
in the open-circuit-stable (OCS) configuration and the
mutual-element circuit is in the short-circuit-stable (SCS)
configuration. Cs, Cp, and Rps have already been discussed;
negative resistor Rs is preferably added to cancel any parasitic
series resistance that the circuit introduces. The main contributor
to this series resistance is the finite transconductance gm of the
transistors; the Linvill circuits add a resistance of 2/gm and
-2/gm in the OCS and SCS configurations, respectively. Rs, Cs, Cp,
and Rps are tunable/variable in the preferred embodiment so that
they may be configured to their optimal values in situ, despite
fabrication tolerances and other unknowns; however, scope of this
invention also includes all cases where one or more of the
component values are fixed. In addition, it is obvious to one of
ordinary skill in the art that the NPN transistors in FIG. 11 may
be replaced with PNP, NFET or PFET transistors.
A series/mutual impedance compensation network has been designed
for the IBM 8HP BiCMOS process, and the detailed schematic is shown
in FIG. 12. The circuit comprises four branches between Vdd=5V and
ground. Each branch preferably carries 2 mA of quiescent current
that is driven by current mirrors (the bottom row of NPN
transistors). Active loads (the top row of PMOS transistors)
present a high impedance to the NICs while dropping about 1.6 V.
The series NICs (Rs, Cs) are realized in the top row of NPN
transistors, which comprise two cross coupled pairs. The variable
capacitance and resistance are realized by back-to-back varactor
diodes and linear-region PFETs, respectively, that are controlled
by tuning voltages. DC blocking capacitors in the feedback loop
prevent the circuit from latching, and the transistors are
self-biased by high impedance networks that connect the collectors
and bases. These networks include diodes connected from collector
to base to prevent the device from breaking down during power-up or
when subjected to large signals. In addition, antiparallel diodes
between the collectors of each NIC prevent the circuits from
latching during powerup. In FIG. 12 Vvs controls the series
capacitance Cs, Vrs controls the series resistance Rs, Vvp controls
the parallel capacitance Cp and Vrp controls the series resistance
Rps.
The mutual-element NIC is realized by the center two NPNs of the
2.sup.nd row from the bottom, where the variable capacitance and
resistance are realized by back-to-back varactor diodes and
linear-region NFETs, respectively. Both are controlled by a tuning
voltage. The outer (diode-connected) NPNs of the 2nd row merely
provide a voltage drop for biasing the network. It is apparent that
the series and inter-element NICs share the same bias current. This
arrangement has the advantages of minimizing both circuit
parasitics and power consumption.
The circuit of FIG. 12 has been simulated using Cadence Spectre for
both stability and transducer gain. Transient simulations predict
stable operation of the circuit within similar bounds as shown in
FIG. 10. The simulated improvement in transducer gain over the
unmatched case is shown in FIG. 13. The network improves the gain
by >10 dB from 10-100 MHz.
Based on the results of the antenna of FIG. 9a having two monopole
radiating elements, the addition of a negative resistance in series
with the negative capacitor Cp can result in stability over even
and odd modes of excitation. And it is believed that this concept
can be expanded to the Adcock arrays of FIGS. 2b, 3a and 4a to
improve their stability as well by inserting a negative resistance
-R.sub.C in series with negative capacitors -C.sub.C. It is
suggested that the analysis set forth above can used as a starting
point to determine reasonable values of Rps for a two element
antenna (as in FIG. 9a), and that the Adcock arrays of FIGS. 2b, 3a
and 4a (for example) be viewed as an expansion of the two element
array of FIG. 9a for the reasonable values determined for Rps be
used for -R.sub.C in the arrays of FIGS. 2b, 3a and 4a. FIG. 14
shows an eight element Adcock array with series connected negative
capacitors -C.sub.C and negative resistors -R.sub.C coupling the
bases of the nearest neighbor radiating elements 10. Of course,
negative resistors -R.sub.S could be placed in series with negative
connected capacitors -C.sub.S (if used) Likewise, it is believed
that connecting negative resistors in series with the -C.sub.C
capacitors in the embodiment FIG. 5a and that connecting negative
resistors in series with the -0.5C.sub.C capacitors in the
embodiment FIG. 5b can improve the odd mode stability of those
embodiments as well.
Attached hereto as appendices A and B are two technical papers
(published after the date of the provisional application to which
this application claims a benefit) which provide additional
information. Appendices A and B are hereby incorporated herein by
reference.
Designing for stability starts with simplicity, minimizing circuit
parasitics and excess time delay within the feedback loops that
make up the NFCs. The stability of the array can be analyzed first
modeling the antenna array as either a) a matrix of rational
functions or b) broadband frequency domain data and then a)
extracting the poles of the full network matrix (including antenna
array, NFCs, beamforming networks, receiver, etc) or b) using the
Normalized Determinant Function (See A. Platzker and W. Struble,
"Rigorous determination of the stability of linear n-node circuits
from network determinants and the appropriate role of the stability
factor K of their reduced two-ports," Third International Workshop
on Integrated Nonlinear Microwave and Millimiterwave Circuits,
October 1994). Method a) is applicable to pole-zero models of the
NFCs, and both methods a) and b) are applicable to transistor
implementations of the NFCs.
This concludes the description of the preferred embodiments of the
present invention. Other layouts of various antenna types are
within the scope of this invention including, without implying a
limitation, linear layouts of monopole and dipole antennas,
triangular, square, hexagonal layouts of monopole, dipole and
spiral antennas. Thus, the foregoing description of one or more
embodiments of the invention has been presented for the purposes of
illustration and description. It is not intended to be exhaustive
or to limit the invention to the precise form disclosed. Many other
modifications and variations are possible in light of the above
teaching. It is intended that the scope of this invention be
limited not by this detailed description, but rather by the claims
appended hereto.
* * * * *