<br><h3> Chapter One </h3> <b>Antenna Array Basics</b> <p> <p> Big antennas can detect faint signals much better than small antennas. A big antenna collects a lot of electromagnetic waves just like a big bucket collects a lot of rain. The largest single aperture antenna in the world is the Arecibo Radio Telescope in Puerto Rico (Figure 1.1). It is 305 m wide and was build inside a giant sinkhole. Mechanically moving this reflector is out of the question. <p> Another approach to collecting a lot of rain is to use many buckets rather than one large one. The advantage is that the buckets can be easily carried one at a time. Collecting electromagnetic waves works in a similar manner. Many antennas can also be used to collect electromagnetic waves. If the output from these antennas is combined to enhance the total received signal, then the antenna is known as an array. An array can be made extremely large as shown by the Square Kilometer Array radio telescope concept shown in Figure 1.2. This array has an aperture that far exceeds any antenna ever built (hundreds of times larger than Arecibo). It will be capable of detecting extremely faint signals from far away objects. <p> An antenna array is much more complicated than a system of buckets to collect rain. Collecting <i>N</i> buckets of rain water and emptying them into a large bucket results in a volume of water equal to the sum of the volumes of the <i>N</i> buckets (assuming that none is spilled). Since electromagnetic waves have a phase in addition to an amplitude, they must be combined coherently (all the same phase) or the sum of the signals will be much less than the maximum possible. As a result, not only are the individual antenna elements of an array important, but the combination of the signals through a feed network is also equally important. <p> An array has many advantages over a single element. Weighting the signals before combining them enables enhanced performance features such as interference rejection and beam steering without physically moving the aperture. It is even possible to create an antenna array that can adapt its performance to suit its environment. The price paid for these attractive features is increased complexity and cost. <p> This chapter introduces arrays through a short historical development. Next, a quick overview of electromagnetic theory is given. Some basic antenna definitions are then presented ends before a discussion of some system considerations for arrays. Many terms and ideas that will be used throughout the book are presented here. <p> <p> <b>1.1. HISTORY OF ANTENNA ARRAYS</b> <p> The first antenna array operated in the kilohertz range. Today, arrays can operate at virtually any frequency. Figure 1.3 is a chart of the electromagnetic frequency spectrum most commonly used for antenna arrays. Antenna arrays are extremely popular for use in radars in the microwave region, so that spectrum is shown in more detail. <p> The development of antenna arrays started over 100 years ago. Brown separated two vertical antennas by half a wavelength and fed them out of phase. He found that there was increased directivity in the plane of the antennas. Forest also noted an increase in gain by two vertical antennas that formed an array. Marconi performed several experiments involving multiple antennas to enhance the gain in certain directions. These initial array experiments proved vital to the development of radar. <p> World War II motivated countries into building arrays to detect enemy aircraft and ships. The first bistatic radar for air defense was a network of radar stations named "Chain Home (CH)" that received the formal designation "Air Ministry Experimental Station (AMES) Type 1" in 1940 (Figure 1.4). The original wavelength of 26 m (11.5 MHz) interfered with commercial broadcast, so the wavelength was reduced to 13 m (23.1 MHz). At first, the developers thought that the signal should have a wavelength comparable to the size of the bombers they were trying to detect in order to obtain a resonance effect. Shorter wavelengths would also reduce interference and provide greater accuracy. Unfortunately, the short wavelengths they desired were too difficult to generate with adequate power to be useful. By April 1937, Chain Home was able to detect aircraft at a distance of 160 km. By August 1937, three CH stations were in operation. The transmitter towers were about 107 m tall and spaced about 55 m apart. Cables hung between the towers formed a "curtain" of horizontally half-wavelength transmitting dipoles. The curtain had a main array of eight horizontal dipole transmitting antennas above a secondary "gapfiller" array of four dipoles. The gapfiller array covered the low angles that the main array could not. Wooden towers for the receiving arrays were about 76 m tall and initially had three receiving dipole antennas, vertically spaced on the tower. As the war progressed, better radars were needed. A new radar called the SCR-270 (Figure 1.5) was available in Hawaii and detected the Japanese formation attacking Pearl Harbor. Unlike Chain Home, it could be mechanically rotated in azimuth 360 degrees in order to steer the beam and operated at a much higher frequency. It had 4 rows of 8 horizontally oriented dipoles and operates at 110 MHz. <p> After World War II, the idea of moving the main beam of the array by changing the phase of the signals to the elements in the array (originally tried by F. Braun) was pursued. Friis presented the theory behind the antenna pattern for a two element array of loop antennas and experimental results that validated his theory. Two elements were also used for finding the direction of incidence of an electromagnetic wave. Mutual coupling between elements in an array was recognized to be very important in array design at a very early date. A phased array in which the main beam was steered using adjustable phase shifters was reported in 1937. The first volume scanning array (azimuth and elevation) was presented by Spradley. The ability to scan without moving is invaluable to military applications that require extremely high speed scans as in an aircraft. As such, the parabolic dish antennas that were once common in the nose of aircraft have been replaced by phased array antennas (Figure 1.6). <p> Analysis and synthesis methods for phased array antennas were developed by Schelkunoff and Dolph. Their static weighting schemes resulted in the development of low sidelobe arrays that are resistant to interference entering the sidelobes. These later formed that basis of the theory of digital filters. In the 1950s, Howells and Applebaum invented the idea of dynamically changing these weights to reject interence. Their work laid the foundation for adaptive, smart, and reconfigurable antenna arrays that are still being researched today. <p> Improvements in electronics allowed the increase in the number of elements as well as an increase in the frequency of operation of arrays. The development of transmit-receive (T/R) modules have reduced the cost and size of phased array antennas. Computer technology improved the modeling and design of array antennas as well as the operation of the phased arrays. Starting in the 1960s, new solid-state phase shifters resulted in the first practical large-scale passive electronically scanned array (PESA). A PESA scans a volume of space much more quickly than a mechanically rotating antenna. Typically, a klystron tube or some other high-power source provided the transmit power that was divided amongst the radiating elements. These antennas were ground- and ship-based until the electronics became small and light enough to place on aircraft. The Electronically Agile Radar (EAR) is an example of a large PESA that had 1818 phase shifting modules (Figure 1.7). Active electronically scanned arrays (AESA) became possible with the development of gallium arsenide components in the 1980s. These arrays have many transmit/receive (T/R) modules that control the signals at each element in the array. <p> Today, very complex phased arrays can be manufactured over a wide range of frequencies and performing very complex functions. As an example, the SBX-1 is the largest X-band antenna array in the world (Figure 1.8). It is part of the US Ballistic Missile Defense System (BMDS) that tracks and identifies long-range missiles approaching the United States. The radar is mounted on a modified, self-propelled, semi-submersible oil platform that travels at knots and is designed to be stable in high winds and rough seas. Through mechanical and electronic scanning, the radar can cover 360 in azimuth and almost 90 in elevation. There are 45,000 GaAs transmit/receive modules that make up the 284-[m.sup.2] active aperture. Figure 1.9 shows the array being placed on the modified oil platform. A radome is placed over the array to protect it from the elements (Figure 1.10). <p> <p> <b>1.2. ELECTROMAGNETICS FOR ARRAY ANALYSIS</b> <p> Before delving into the theory of antenna arrays, a review of some basic electromagnetic theory is in order. The frequency of an electromagnetic wave depends on the acceleration of charges in the source. Accelerating charges produce time-varying electromagnetic waves and vice versa. The radiated waves are a function of time and space. Assume that the electromagnetic fields are linear and time harmonic (vary sinusoidally with time). The total electromagnetic field at a point is the superposition of all the time harmonic fields at that point. If the field is periodic in time, the temporal part of the wave has a complex Fourier series expansion of the form <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.1) <p> where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = Fourier coefficients and [<i>f</i>.sub.0] is the fundamental frequency. The fundamental frequency determines where the wave is centered on the frequency spectrum in Figure 1.3. If the electromagnetic field is periodic or aperiodic, it has the following temporal Fourier transform pair: <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.2) <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.3) <p> Equations (1.1), (1.2) and (1.3) illustrate how any time-varying electromagnetic field may be represented by a spectrum of its frequency components. <i>E(t)</i> is the superposition of properly weighted fields at the appropriate frequencies. Superimposing and weighting the fields of the individual frequencies comprising the waveform. Traditional electromagnetics analysis examines a single-frequency component, and then it assumes that more complex waves are generated by a weighted superposition of many frequencies. <p> Equations (1.1), (1.2) and (1.3) do not take the vector nature of the fields into account. A single-frequency electromagnetic field (Fourier component) is represented in rectangular coordinates as <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.4) <p> where [??], [??], and [??] are the unit vectors in the <i>x, y,</i> and <i>z</i> directions; <i>[E.sub.x]</i>, <i>[E.sub.y]</i>, and <i>[E.sub.z]</i> are the magnitudes of the electric fields in the <i>x, y,</i> and <i>z</i> directions; and [[psi].sub.<i>y</i>] and [[psi].sub.<i>z</i>] are the phases of the <i>y</i> and <i>z</i> components relative to the x component. Using Euler's identity, (1.4) may also be written as <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.5) <p> where E represents the complex steady-state phasor (time independent) of the electric field and is written as <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.6) <p> and <i>[E.sub.x]</i>, <i>[E.sub.y]</i>, and <i>[E.sub.z]</i> are functions of <i>x, y</i>, and <i>z</i> and are not a function of <i>t</i>. <p> Maxwell's equations in differential and integral form are shown in Table 1.1. Note that the [<i>e</i>.sup.j[??]t] time factor is omitted, because it is common to all components. Variables in these equations are defined as follows: <p> <b>E</b> electric field strength (volts/m) <b>D</b> electric flux density (coulombs/[m.sup.2]) <b>H</b> magnetic field strength (amperes/m) <b>B</b> magnetic flux density (webers/[m.sup.2]) <b>J</b> electric current density (amperes/[m.sup.2]) [[rho].sub.ev] electric charge density (coulombs/[m.sup.3]) <b>[J.sub.m]</b> magnetic current density (volts/[m.sup.2]) [[rho].sub.mv] magnetic charge density (webers/[m.sup.3]) <i>[Q.sub.e]</i> total electric charge contained in <i>S</i> (coulombs) <i>[Q.sub.m]</i> total magnetic charge contained in <i>S</i> (coulombs) <i>S</i> closed surface ([m.sup.2]) ITLITL closed contour line (m) <p> <p> Electric sources are due to charge. Magnetic sources are fictional but are often useful in representing fields in slots and apertures. <p> Each of the equations in Table 1.1 is a set of three scalar equations. There are too many unknowns to solve these equations, so additional information is necessary and comes in the form of constitutive parameters that are a function of the material properties. The constitutive relations for a linear, isotropic, homogeneous medium provide the remaining necessary equations to solve for the unknown field quantities. <p> <b>D</b> = [epsilon] <b>E</b> (1.7) <p> <b>B</b> = [mu] <b>H</b> (1.8) <p> <b>J</b> = [sigma] <b>E</b> (1.9) <p> where the constitutive parameters describe the material properties and are defined as follows: <p> [mu] permeability (henries/m) <p> [epsilon] permittivity or dielectric constant (farads/m) <p> [sigma] conductivity (siemens/m) <p> <p> Assuming the constant to be scalars is an over simplification. In today's world, antenna designers must take into account materials with special properties, such as <p> Composites <p> Semiconductors <p> Superconducting materials <p> Ferroelectrics <p> Ferromagnetic materials <p> Ferrites <p> Smart materials <p> Chiral materials <p> Conducting polymers <p> Ceramics <p> Electromagnetic bandgap (EBG) materials <p> <p> Antenna design relies upon a complex repitroire of different materials that will provide the desired performance characteristics. <p> Spatial differential equations have only general solutions until boundary conditions are specified. If these equations still had the time dependence factor, then initial conditions would also have to be specified. The boundary conditions for the field components at the interface between two media are given by <p> The tangential electric field: <p> [??] x ([<b>E</b>.sub.1] - [<b>E</b>.sub.2]) = -<b>[J.sub.m]</b> (1.10) <p> The normal magnetic flux density: <p> [??] ([<b>B</b>.sub.1] - [<b>B</b>.sub.2]) = -[[rho].sub.m] (1.11) <p> The tangential magnetic field: <p> [??] x ([<b>H</b>.sub.1] - [<b>H</b>.sub.2]) = -<b>[J.sub.s]</b> (1.12) <p> The normal electric flux density: <p> [??] x ([<b>D</b>.sub.1] - [<b>D</b>.sub.2]) = -[[rho].sub.es] (1.13) <p> <p> where subscripts 1 and 2 refer to the two different media, [[rho].sub.ms] is the magnetic surface charge density (coulombs/[m.sup.2]), and [[rho].sub.es] is the electric surface charge density (webers/[m.sup.2]). <p> Maxwell's equations in conjunction with the constitutive parameters and boundary conditions allow us to find quantitative values of the field quantities. <p> Power is an important antenna quantity and has units of watts or volts times amps. Multiplying the electric field and the magnetic field produces units of W/[m.sup.2] or power density. The complex Poynting vector describes the power flow of the fields via <p> <b>S</b> = 1/2 Re {<b>E</b> <b>H</b>*} (1.14) Note that the direction of propagation (direction that <b>S</b> points) is perpendicular to the plane containing the <b>E</b> and <b>H</b> vectors. <b>S</b> is the power flux density, so [nabla] <b>S</b> is the volume power density leaving a point. A conservation of energy equation can be derived in the form of <p> [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1.15) <p> The terms 1/2 [epsilon] [absolute value of <b>E</b>] and 1/2 [mu] [absolute value of [[<b>H</b>].sup.2] are the electric and magnetic energy densities, respectively. Finally, <b>E</b> <b>J</b>* represents the power density dissipated. <p> <i>(Continues...)</i> <p> <!-- copyright notice --> <br></pre> <blockquote><hr noshade size='1'><font size='-2'> Excerpted from <b>Antenna Arrays</b> by <b>Randy L. Haupt</b> Copyright © 2010 by John Wiley & Sons, Inc.. Excerpted by permission.<br> All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.<br>Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.