Timed Arrays E-Book

Randy L. Haupt

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley - IEEE
• Sprache: Englisch

Seitenzahl: 274

Veröffentlichungsjahr: 2015

Beschreibung

Introduces timed arrays and design approaches to meet the new high performance standards

The author concentrates on any aspect of an antenna array that must be viewed from a time perspective. The first chapters briefly introduce antenna arrays and explain the difference between phased and timed arrays. Since timed arrays are designed for realistic time-varying signals and scenarios, the book also reviews wideband signals, baseband and passband RF signals, polarization and signal bandwidth. Other topics covered include time domain, mutual coupling, wideband elements, and dispersion. The author also presents a number of analog and digital beamforming networks for creating and manipulating beams. The book concludes with an overview of the methods to integrate time delay into the array design and of several other adaptive arrays that prove useful in many different systems. 

• Examines RF signal concepts such as polarization and signal bandwidth and their applications to timed antenna arrays
• Covers arrays of point source, elements in timed antenna arrays, active electronically scanned array technology, and time delay in corporate fed arrays
• Includes complete design examples for placing time delay in arrays

Timed Arrays: Wideband and Time Varying Antenna Arrays is written for practicing engineers and scientists in wireless communication, radar, and remote sensing as well as graduate students and professors interested in advanced antenna topics.

Leseprobe

CONTENTS

COVER

TITLE PAGE

LIST OF FIGURES

PREFACE

1 TIMED AND PHASED ARRAY ANTENNAS

1.1 LARGE ANTENNAS

1.2 COLLECTION OF ELEMENTS

1.3 OVERVIEW OF AN ARRAY ARCHITECTURE

1.4 TRANSIENT VERSUS STEADY STATE

1.5 TIME VERSUS PHASE

1.6 BOOK OVERVIEW

REFERENCES

2 RF SIGNALS

2.1 THE CARRIER AND MODULATION

2.2 NOISE AND INTERFERENCE

2.3 POLARIZATION

2.4 SIGNAL BANDWIDTH

REFERENCE

3 ARRAYS OF POINT SOURCES

3.1 POINT SOURCES

3.2 FAR FIELD

3.3 ARRAY SAMPLING IN THE TIME DOMAIN

3.4 ARRAY SAMPLING IN THE FREQUENCY DOMAIN

3.5 GRATING LOBES: SPATIAL ALIASING

3.6 SUBARRAYS AND PANELS

3.7 ELECTRONIC BEAM STEERING

3.8 AMPLITUDE WEIGHTING

3.9 THINNED ARRAYS

REFERENCES

4 ELEMENTS IN TIMED ARRAYS

4.1 ELEMENT CHARACTERISTICS

4.2 ELEMENTS

4.3 MUTUAL COUPLING

4.4 ELEMENT DISPERSION

4.5 SCALED ARRAYS

4.6 INTERLEAVED ARRAYS

REFERENCES

5 ARRAY BEAMFORMING

5.1 PCB TRANSMISSION LINES

5.2 S-PARAMETERS

5.3 MATCHING CIRCUITS

5.4 CORPORATE FEEDS

5.5 DISTRIBUTED VERSUS CENTRALIZED AMPLIFICATION

5.6 BLASS MATRIX

5.7 BUTLER MATRIX

5.8 LENSES

5.9 REFLECTARRAYS

5.10 DIGITAL BEAMFORMING

REFERENCES

6 ACTIVE ELECTRONICALLY SCANNED ARRAY TECHNOLOGY

6.1 SEMICONDUCTOR TECHNOLOGY FOR T/R MODULES

6.2 T/R MODULE LAYOUT

6.3 AMPLIFIERS

6.4 SWITCHES

6.5 PHASE SHIFTER

6.6 ATTENUATORS

6.7 LIMITER

6.8 CIRCULATOR

6.9 CORRECTING ERRORS THROUGH CALIBRATION AND COMPENSATION

REFERENCES

7 TIME DELAY IN A CORPORATE-FED ARRAY

7.1 PULSE DISPERSION

7.2 PHASED ARRAY BANDWIDTH

7.3 TIME DELAY STEERING CALCULATIONS

7.4 TIME DELAY UNITS

7.5 UNIT CELL CONSTRAINTS

7.6 TIME DELAY BIT DISTRIBUTION AT THE SUBARRAY LEVEL

REFERENCES

8 ADAPTIVE ARRAYS

8.1

SIGNAL CORRELATION MATRIX

8.2

OPTIMUM ARRAY WEIGHTS

8.3

ADAPTIVE WEIGHTS WITHOUT INVERTING THE CORRELATION MATRIX

8.4

ALGORITHMS FOR NONDIGITAL BEAMFORMERS

8.5

RECONFIGURABLE ARRAYS

8.6

RECONFIGURABLE ELEMENTS

8.7

TIME-MODULATED ARRAYS

8.8

ADAPTIVE THINNING

8.9

OTHER ADAPTIVE ARRAY ALTERNATIVES

REFERENCES

LIST OF SYMBOLS AND ABBREVIATIONS

INDEX

END USER LICENSE AGREEMENT

List of Tables

Chapter 02

TABLE 2.1 Frequency bands

Chapter 06

TABLE 6.1 Semiconductor technologies for T/R modules

TABLE 6.2 Beam Locations When Two Tones Are Transmitted

TABLE 6.3 Estimates of Important Power Points

TABLE 6.4 Characteristics of Switch Technologies

TABLE 6.5 Settings for 1 Bit Phase Shifter in I-Q Vector Modulator

TABLE 6.6 Phase Shifter Characteristics

Chapter 07

TABLE 7.1 Microstrip Line Length and Corresponding Time Delay for Each of the 9 Bits in the Example Planar Array

Chapter 08

TABLE 8.1 Element weights and switching times for 30 and 40 dB Chebyshev average array factors

List of Illustrations

Chapter 01

FIGURE 1.1 (a) Green Bank Telescope reflector [4]. (b) PAVE PAWS radar [5].

FIGURE 1.2 Four different geometrical layouts of an array: (a) linear array, (b) planar array, (c) conformal array, and (d) random array.

FIGURE 1.3 Concept of an antenna phase center.

FIGURE 1.4 Three different element lattices and corresponding unit cells.

FIGURE 1.5 Generic array architecture.

FIGURE 1.6 Two signals adding in and out of phase.

FIGURE 1.7 Pulse dispersion: (a) Two identical pulses (coherent) added together. (b) Two identical pulses (not coherent) that start at different times added together. (c) Two identical pulses (coherent) that start at different times are added together.

Chapter 02

FIGURE 2.1 A stream of bits corresponds to a signal amplitude. The baseband signal modulates the carrier. Examples of OOK, BPSK, and QPSK are shown here.

FIGURE 2.2 OOK, BPSK, and QPSK with an SNR of 10 dB.

FIGURE 2.3 Pulse dispersion or spreading occurs when high frequencies are attenuated.

FIGURE 2.4 When the direct and attenuated reflected signal add together, the pulse is dispersed.

FIGURE 2.5 Wave polarization.

FIGURE 2.6 CP Gaussian pulse.

Chapter 03

FIGURE 3.1 Antenna far field definition.

FIGURE 3.2 Plane wave incident on linear array.

FIGURE 3.3 Array sampling of plane wave from broadside and endfire directions (a)

θ

s

 = 0°, (b)

θ

s

 = 90°, and (c)

θ

s

arbitrary.

FIGURE 3.4 Directivity of a linear uniform array as a function of element spacing for five different array sizes.

FIGURE 3.5 Directivity of a

planar uniform array as a function of element spacing for square and triangular element lattices.

FIGURE 3.6 Power of 2 subarrays in a linear array.

FIGURE 3.7 Beam squint as a function of frequency and steering angle.

FIGURE 3.8 Beam squint associated with a 32-element phased array when the main beam is steered to 60° at the center frequency.

FIGURE 3.9 Array factors at the center, high, and low frequencies of a 32-element timed array when the main beam is steered to 60°.

FIGURE 3.10 Beam steering a 32-element array to 60°: (a) time delay (b) time delay translated into phase at three frequencies.

FIGURE 3.11 Amplitude weights for a 30 dB Chebyshev taper.

FIGURE 3.12 Array factor for a 30 dB Chebyshev taper.

FIGURE 3.13 Amplitude weights for a 30 dB

Taylor taper.

FIGURE 3.14 Array factor for a 30 dB

Taylor taper.

FIGURE 3.15 Amplitude weights for a 30 dB

Bayliss taper.

FIGURE 3.16 Array factor for a 30 dB

Bayliss taper.

FIGURE 3.17 25 dB Taylor taper for the 64 × 64 planar array.

FIGURE 3.18 64 × 64 element array thinned to get a 25 dB

Taylor taper.

FIGURE 3.19 Solid line is an array factor cut of the 64 × 64 element array thinned to get a 25 dB

Taylor pattern. The dashed line is a cut from the desired low sidelobe pattern. The dotted line is the rms average sidelobe level predicted by (3.49).

FIGURE 3.20 Photograph of the random arrangement of elements in the LWA1 array.

Chapter 04

FIGURE 4.1 Combining two linear polarized elements to get circular polarization (in this case, LHCP).

FIGURE 4.2 Four linearly polarized patches are rotated and phased to get circular polarization: (a) phasing and placement for limited scan and (b) phasing and placement for wide scan.

FIGURE 4.3 (a) Four linearly polarized broadband horns are rotated and phased to get circular polarization. (b) Measured (dotted) and calculated (solid) pulses transmitted by array at boresight.

FIGURE 4.4 Currents on a coax-fed dipole antenna.

FIGURE 4.5 Dipole type antennas: (a) thin dipole, (b) monopole, (c) fat dipole, (d) bicone, (e) bicone with spherical caps, and (f) ellipsoidal.

FIGURE 4.6 Bent wire dipole element in the LWA1 array.

FIGURE 4.7 Dipole arrays. (a) Dipoles in MERA array. [5]© 2013 Wiley. (b) Crossed dipoles in HAARP array.

FIGURE 4.8 8 × 8 planar array of patches.

FIGURE 4.9 Broadband patch antennas: (a) coplanar and (b) stacked.

FIGURE 4.10 Examples of spiral antennas: (a) 2 arm Archimedes [5]© 2010, (b) two-arm logarithmic spiral. Reprinted by permission of Ref. [21]; © 2009 IEEE, and (c) conical log spiral [22]© 2010.

FIGURE 4.11 Photograph of the (a) front and (b) side views of a sinuous antenna.

FIGURE 4.12 Geometry of a 4 × 4 helical array.

FIGURE 4.13 (a) Exploded view of the stripline notch element and (b) linear array of five elements.

FIGURE 4.14 Antipodal TSA.

FIGURE 4.15 Measured cross-pol and co-pol patterns of an 8 × 8 planar array for broadside scan and the center element co-pol pattern.

FIGURE 4.16 Measured versus calculated (FDTD) VSWR of planar arrays at (a) broadside scan, (b) E-plane 50 scan, and (c) H-plane 50 scan.

FIGURE 4.17 A 324-element dual-polarized TSA array.

FIGURE 4.18 The BOR element array is 16 × 9 cm.

FIGURE 4.19 Diagram of a PUMA array: (a) Top view of dipole layer; (b) crosssectional view of a unit-cell, showing the location where a module split occurs; and (c) isometric view of a PUMA module with exploded dielectric cover layers.

FIGURE 4.20 Three 8 × 8 PUMA modules.

FIGURE 4.21 Broadside VSWR of three dual-polarized PUMA arrays: (a) 5 GHz maximum frequency. (b) 21 GHz maximum frequency. (c) 45 GHz maximum frequency. (d) Models of the PUMAv2 (left) and the PUMAv3 (right) compared to a penny.

FIGURE 4.22 8 × 8 element array of overlapping dipoles above a ground plane.

FIGURE 4.23 (a) Unit cell of a tightly coupled bowtie array with resistive FSS and superstrate and (b) top view of unit cell (dimensions in mm).

FIGURE 4.24 Unit cell of a fragmented array.

FIGURE 4.25 VSWR of fragmented element in planar array.

FIGURE 4.26 Gain of fragmented element in planar array.

FIGURE 4.27 Mutual coupling in an array.

FIGURE 4.28 Graphs of the direct pulses and echoes for a 4-element array when

and (a)

(b).

.

FIGURE 4.29 Pulse transmitted and received by two elliptical dipole antennas [49].

FIGURE 4.30 Pulse transmitted and received by two conical log spiral antennas [49].

FIGURE 4.31 Relative group delay of a Vivaldi antenna and a log-periodic antenna.

FIGURE 4.32 Scaled planar array with a 10° beamwidth in the principle planes from 4 to 18 GHz.

FIGURE 4.33 Layout of the prototype dual-pol. flared-notch WSA. [51]© 2012

FIGURE 4.34 Modular construction and assembly of the planar WSA prototype: (a) 8 × 8 sub-array, 8:1 bandwidth (1–8 GHz); (b) 4 × 4 sub-array, 4:1 bandwidth (1–4 GHz); (c) 2 × 2 sub-array, 2:1 bandwidth (1–2 GHz); and (d) assembled dual-polarized WSA prototype.

FIGURE 4.35 E-plane radiation patterns at the three breakpoints: (a) 2 GHz, (b) 4 GHz, and (c) 8 GHz, showing agreement between simulations and measurement.

FIGURE 4.36 Diagram of an interleaved array of dipoles.

FIGURE 4.37 Sum array factor for a 120-element aperture that has sum and difference arrays interleaved.

FIGURE 4.38 Difference array factor for a 120-element aperture that has sum and difference arrays interleaved.

FIGURE 4.39 Example of a dual polarization spiral array, 1001100110. E.

FIGURE 4.40 Characteristics of an 80-spiral antenna array. These spirals are standard 2-arms center-fed Archimedean spirals, they have five turns, for a diameter of 34 mm. The distance center to center in the array is 38 mm. (a) Axial ratio. (b) VSWR at 250 Ω. Samples of the radiation patterns for a standard array. (c) At 3 GHz and at broadside. (d) At 5 GHz and steered at 30° from broadside.

FIGURE 4.41 Bandwidth of a simple interleaved array of spiral with alternating polarization, following the three criteria.

Chapter 05

FIGURE 5.1 Three types of planar transmission lines.

FIGURE 5.2 Examples of power dividers/combiners. (a) Resistive, (b) quadrature hybrid, and (c) Wilkinson.

FIGURE 5.3 AESA beamforming (a) RF and (b) IF.

FIGURE 5.4 Diagram of a Blass matrix.

FIGURE 5.5 Diagram of a four port Butler matrix and its four orthogonal beams.

FIGURE 5.6 Waveguide lens antenna for the Nike AJAX MPA-4 radar.

FIGURE 5.7 Diagram of a Rotman lens.

FIGURE 5.8 Microstrip version of a Rotman lens.

FIGURE 5.9 Measured antenna patterns at 2.5 GHz a Rotman lens array.

FIGURE 5.10 Measured antenna patterns at 4 GHz a Rotman lens array.

FIGURE 5.11 AN/MPQ-53 Patriot radar system [19].

FIGURE 5.12 Diagram of reflect array.

FIGURE 5.13 Experimental reflect array.

FIGURE 5.14 Diagram of a digital beamforming array.

FIGURE 5.15 DBF with on-site coding and one ADC.

FIGURE 5.16 Photograph of DBF transmitter array.

FIGURE 5.17 Block diagram of DBF transmitter antenna.

Chapter 06

FIGURE 6.1 Diagram of a T/R module.

FIGURE 6.2 Semiconductor technology for T/R modules [4].

FIGURE 6.3 Picture of the MERA T/R module [5]© 2010 Wiley.

FIGURE 6.4 Picture of the ATF T/R module [5]© 2010 Wiley.

FIGURE 6.5 Photograph of the T/R module for the X-band phase-tilt radar array.

FIGURE 6.6 Block diagram of quasi-MMIC approach to a power amplifier.

FIGURE 6.7 Tile architecture with array elements on the front and components on the back.

FIGURE 6.8 Output power versus input power for an amplifier.

FIGURE 6.9 Intermodulation products resulting from two tones input to the amplifier.

FIGURE 6.10 Diagram of a multi-beam corporate fed array.

FIGURE 6.11 Amplitude and frequencies at the output of the T/R module when the input has 6 and 8.4 GHz tones.

FIGURE 6.12 Magnitude and locations of the beams corresponding to the frequencies in Figure 6.11.

FIGURE 6.13 Pass band spectrum of Figure 6.11.

FIGURE 6.14 Magnitude and locations of the beams corresponding to the frequencies in Figure 6.13.

FIGURE 6.15 Location of the main beams and IMP beams in

u–v

space.

FIGURE 6.16 Experimental multi-beam array.

FIGURE 6.17 Pattern measurements of experimental array in Figure 6.16. Mainbeams are at 4000 and 4010 MHz. Third-order IMP beams are at 3990 and 4020 MHz [19].

FIGURE 6.18 Relative far field patterns of the array at the two tone frequencies and their third and fifth order IMPs when phase steering [20]© 2013.

FIGURE 6.19 Relative far field patterns (

cut) of the array at the two tone frequencies and their third and fifth order IMPs when

 dBm time delay steering [20]© 2013.

FIGURE 6.20 Turning an RF switch on and off.

FIGURE 6.21 Diagram of a PIN diode.

FIGURE 6.22 FET switch.

FIGURE 6.23 MEMS switches in the on and off positions. (a) Cantilever off, (b) Cantilever on, (c) Ohmic contact off, and (d) Ohmic contact on.

FIGURE 6.24 Three bit switched line phase shifter.

FIGURE 6.25 I-Q vector modulator.

FIGURE 6.26 Insertion phase as a function of frequency for a switched filter phase shifter using a high pass and low pass filter.

FIGURE 6.27 Diagram (left) and photograph (right) of a GaN HEMT high-pass/low-pass phase shifter.

FIGURE 6.28 Microstrip rendition of a tunable dielectric phase shifter.

FIGURE 6.29 Two common types of RF attenuators.

FIGURE 6.30 Diagram of a stepped attenuator.

Chapter 07

FIGURE 7.1 Time delay and phase shift in the argument of a Fourier harmonic.

FIGURE 7.2 Phase shift is a constant with respect to frequency. Time delay is a linear function of frequency.

FIGURE 7.3 Narrow band signal incident on an array.

FIGURE 7.4 Wideband signal incident on an array.

FIGURE 7.5 A signal received by a 4-element array at a small scan angle (top). The envelopes of the signals at the elements can be aligned with phase shift (middle). Coherently adding them together results in an output with no dispersion (bottom).

FIGURE 7.6 A signal received by a 4-element array at a large scan angle (top). The envelopes of the signals at the elements cannot be aligned with phased shifters even though the carrier is aligned in phase (middle). Coherently adding them together results in dispersion (bottom).

FIGURE 7.7 A signal received by a 4-element array at a large scan angle (top). The envelopes of the signals at the elements can be aligned with time delay (middle). Coherently adding them together results in an output with no dispersion (bottom).

FIGURE 7.8 Bandwidth as a function of the number of elements and steering angle.

FIGURE 7.9 The array instantaneous bandwidth.

FIGURE 7.10 The maximum time delay for a narrow band (left) and wideband signal (right).

FIGURE 7.11 Maximum time delay versus frequency versus

N

versus scan angle.

FIGURE 7.12 Lumped circuit time delay.

FIGURE 7.13 A 4-bit trombone line time delay architecture (left) with a block diagram superimposed on the chip microphotograph (right).

FIGURE 7.14 Model of a varactor loaded transmission line and equivalent lumped circuit.

FIGURE 7.15 Measured time delay and insertion loss of a typical hybrid nonlinear delay line [10]

FIGURE 7.16 Diagram of a BAW delay line.

FIGURE 7.17 Cobham TDU/ASIC module.

FIGURE 7.18 Measured time delay for the Cobham TDU chip.

FIGURE 7.19 Photograph of the 256-element array with time delay steering in azimuth.

FIGURE 7.20 The 8-channel time delay beamformer.

FIGURE 7.21 Measured array patterns: (a) boresight and (b) steered to 26°.

FIGURE 7.22 Trace of the time delay MSB relative to the element unit cell.

FIGURE 7.23 Placement of time delay at various levels in a corporate feed network.

FIGURE 7.24 A 32 × 32 element array broken into power of two subarrays.

FIGURE 7.25 The main beam is scanned to

using phase shifters at the elements.

FIGURE 7.26 The main beam is scanned to

using time delay units at the elements.

FIGURE 7.27 The main beam is scanned to

using 7-bit time delay units at the elements and 2-bit time delay units at the 4 × 4 subarrays.

FIGURE 7.28 The main beam is scanned to

using 4-bit phase shifters at the elements and 5-bit time delay units at the 4 × 4 subarrays.

FIGURE 7.29 The main beam is scanned to

using 4-bit phase shifters at the elements and 5-bit time delay units at the 8 × 8 subarrays.

FIGURE 7.30 BER curve at 50 Mbps.

Chapter 08

FIGURE 8.1 Adaptive nulling places a null in the sidelobe where interference is present.

FIGURE 8.2 Non-DBF adaptive array.

FIGURE 8.3 Signal reduction in the main beam and first sidelobe as a function of number of adaptive elements.

FIGURE 8.4 SINR as a function of number of adaptive elements.

FIGURE 8.5 Adapted pattern superimposed on the quiescent pattern.

FIGURE 8.6 Algorithm improvement as a function of time.

FIGURE 8.7 Adapted pattern superimposed on the quiescent pattern.

FIGURE 8.8 Algorithm improvement as a function of time.

FIGURE 8.9 Adapted pattern superimposed on the quiescent pattern.

FIGURE 8.10 Algorithm improvement as a function of time.

FIGURE 8.11 A phased array built on a geodesic dome. The outlined triangles represent regions of activated subarrays. The solid region is the original array configuration. The dashed outlines are either the expanded or translated version of the original configuration.

FIGURE 8.12 Section of a 10 m diameter spherical array [24].

FIGURE 8.13 Atacama large millimeter/submillimeter array.

FIGURE 8.14 VLA antennas on railroad tracks (NRAO/AUI/NSF).

FIGURE 8.15 TechSat21 concept. (“TechSat21.” Licensed under Public domain via Wikimedia Commons—http://commons.wikimedia.org/wiki/File:TechSat21.jpg#mediaviewer/File:TechSat21.jpg)

FIGURE 8.16 Reconfigurable microstrip patches.

FIGURE 8.17 Reconfigurable slotted patch antenna.

FIGURE 8.18 Diagram of the reconfigurable U-slot and L-stub antennas.

FIGURE 8.19 Reconfigurable antenna that change polarization using MEMS.

FIGURE 8.20 Switches at the elements of a time-modulated array.

FIGURE 8.21 Array factor as a function of time for a 30 dB Chebyshev average taper.

FIGURE 8.22 Array factor as a function of time for a 40 dB Chebyshev average taper.

FIGURE 8.23 The directivity of the array factor as a function of time for a 30 dB Chebyshev average taper.

FIGURE 8.24 The top plots are the weights and array factor (in dB) for the time-modulated array for a 30 dB Chebyshev average. The bottom two plots are static 30 dB Chebyshev and uniform array factors.

FIGURE 8.25 The pattern on the left is from an array with 30 dB Chebyshev amplitude weights. The one on the right is a time-modulated 30 dB Chebyshev taper.

FIGURE 8.26 T/R module for adaptive thinning.

FIGURE 8.27 SINR for 100 random seeds that generate a thinning for a 25 dB Taylor taper.

FIGURE 8.28 Pattern associated with the best SINR and worst SINR.

FIGURE 8.29 Pattern cuts at

for the best and worst SINR cases.

FIGURE 8.30 SINR as a function of switching time for a 25 dB Taylor taper when two interference sources are 30 dB stronger than the desired signal.

FIGURE 8.31 Pattern cuts at

for the best and worst SINR cases.

FIGURE 8.32 SINR as a function of switching time for a 25 dB Taylor taper when two interference sources are 35 dB stronger than the desired signal.

FIGURE 8.33 Two random low sidelobe thinnings for the concentric ring array.

FIGURE 8.34 The red dashed line is a pattern cut of the array with thinning 1, while the blue solid line is the pattern cut from thinning 2.

FIGURE 8.35 Rotman lens with multiple beams.

FIGURE 8.36 Diagram of an Adcock array.

FIGURE 8.37 Plot of the direction finding spectra for an eight-element array.

FIGURE 8.38 Diagram of a retrodirective array.

FIGURE 8.39 MIMO concept.

Guide

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TIMED ARRAYS

Wideband and Time Varying Antenna Arrays

RANDY L. HAUPT

Copyright © 2015 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New JerseyPublished simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Haupt, Randy L. Timed arrays : wideband and time varying antenna arrays / Randy L. Haupt.  pages cm Includes index.

 ISBN 978-1-118-86014-4 (cloth)1. Antenna arrays. 2. Adaptive antennas. 3. Time-domain analysis. I. Title.  TK7871.67.A77H383 2015 621.3841′35–dc23    2015004892