《电子工程师手册》学习资料（英文版）chapter 38 Antennas.pdf_大学文库

© 2000 by CRC Press LLC 38 Antennas 38.1 Wire Short Dipole • Directivity • Magnetic Dipole • Input Impedance • Arbitrary Wire Antennas • Resonant Half-Wavelength Antenna • End Loading • Arrays of Wire Antennas • Analysis of General Arrays • Arrays of Identical Elements • Equally Spaced Linear Arrays • Planar (2-D) Arrays • Yagi–Uda Arrays • LogPeriodic Dipole Arrays 38.2 Aperture The Oscillator or Discrete Radiator • Synthetic Apertures • Geometric Designs • Continuous Current Distributions (Fourier Transform) • Antenna Parameters 38.3 Microstrip Antennas Introduction • Basic Microstrip Antenna Element • Feeding Techniques for Microstrip Antennas • Microstrip Antenna Arrays • Computer-Aided Design for Microstrip Antennas 38.1 Wire N.J. Kolias and R.C. Compton Antennas have been widely used in communication systems since the early 1900s. Over this span of time scientists and engineers have developed a vast number of different antennas. The radiative properties of each of these antennas are described by an antenna pattern. This is a plot, as a function of direction, of the power Pr per unit solid angle W radiated by the antenna. The antenna pattern, also called the radiation pattern, is usually plotted in spherical coordinates q and j. Often two orthogonal cross sections are plotted, one where the E-field lies in the plane of the slice (called the E-plane) and one where the H-field lies in the plane of the slice (called the H-plane). Short Dipole Antenna patterns for a short dipole are plotted in Fig. 38.1. In these plots the radial distance from the origin to the curve is proportional to the radiated power. Antenna plots are usually either on linear scales or decibel scales (10 log power). The antenna pattern for a short dipole may be determined by first calculating the vector potential A [Collin, 1985; Balanis, 1982; Harrington, 1961; Lorrain and Corson, 1970]. Using Collin’s notation, the vector potential in spherical coordinates is given by A = - a a (38.1) - m p 0 q q q 0 4 I dl e r jk r r ( cos sin ) N.J. Kolias Raytheon Company R.C. Compton Cornell University J. Patrick Fitch Lawrence Livermore Laboratory David M. Pozar University of Massachusetts at Amherst

© 2000 by CRC Press LLC Directivity The directivity D(q,j) and gain G(q,j) of an antenna are defined as (38.5) Antenna efficiency, h, is given by (38.6) For many antennas h ª1 and so the words gain and directivity can be used interchangeably. For the short dipole (38.7) The maximum directivity of the short dipole is 3/2. This single number is often abbreviated as the antenna directivity. By comparison, for an imaginary isotropic antenna which radiates equally in all directions, D(q,j) = 1. The product of the maximum directivity with the total radiated power is called the effective isotropic radiated power (EIRP). It is the total radiated power that would be required for an isotropic radiator to produce the same signal as the original antenna in the direction of maximum directivity. Magnetic Dipole A small loop of current produces a magnetic dipole. The far fields for the magnetic dipole are dual to those of the electric dipole. They have the same angular dependence as the fields of the electric dipole, but the polarization orientations of E and H are interchanged. (38.8) where M = p r 0 2 I for a loop with radius r0 and uniform current I. Input Impedance At a given frequency the impedance at the feedpoint of an antenna can be represented as Za = Ra + jXa. The real part of Za (known as the input resistance) corresponds to radiated fields plus losses, while the imaginary part (known as the input reactance) arises from stored evanescent fields. The radiation resistance is obtained from Ra = 2Pr /|I| 2 where Pr is the total radiated power and I is the input current at the antenna terminals. For electrically small electric and magnetic dipoles with uniform currents D P P G P P r r r ( , ) ( , ) ( , ) ( , ) q j p q j p q j p q j p = = = = Radiated power per solid angle Total radiated power/4 / / Radiated power per solid angle Total input power/4 / / in D DW D DW 4 4 h q j q j º = P P G D r in ( , ) ( , ) D(q j, ) = sin q 3 2 2 H a E a = - = - - Mk e r MZ k e r jk r jk r 0 2 0 0 2 0 0 4 4 sin sin q p q p q j

© 2000 by CRC Press LLC (38.9) The reactive component of Za can be determined from Xa = 4w(Wm-We)/|I| 2 where Wm is the average magnetic energy and We is the average electric energy stored in the near-zone evanescent fields. The reflection coefficient, G , of the antenna is just (38.10) where Z0 is the characteristic impedance of the system used to measure the reflection coefficient. Arbitrary Wire Antennas An arbitrary wire antenna can be considered as a sum of small current dipole elements. The vector potential for each of these elements can be determined in the same way as for the short dipole. The total vector potential is then the sum over all these infinitesimal contributions and the resulting E in the far field can be found to be (38.11) where the integral is over the contour C of the wire, a is a unit vector tangential to the wire, and r¢ is the radial vector to the infinitesimal current element. Resonant Half-Wavelength Antenna The resonant half-wavelength antenna (commonly called the half-wave dipole) is used widely in antenna systems. Factors contributing to its popularity are its well-understood radiation pattern, its simple construction, its high efficiency, and its capability for easy impedance matching. The electric and magnetic fields for the half-wave dipole can be calculated by substituting its current distribution, I = I0 cos(k0z), into Eq. (38.11) to obtain (38.12) The total radiated power, Pr, can be determined from the electric and magnetic fields by integrating the expression 1/2 Re {E ¥ H* · ar} over a surface of radius r. Carrying out this integration yields Pr = 36.565 |I0| 2 . The radiation resistance of the half-wave dipole can then be determined from R dl R r a a = Ê Ë Á ˆ ¯ ˜ = Ê Ë Á ˆ ¯ ˜ 80 320 2 0 2 6 0 0 4 p l p l electric dipole magnetic dipole G = - + Z Z Z Z a a 0 0 E a aa a a r r ( ) [( ) ] ( ) r jk Z e r I l e dl jk r r r c jk = ×- ¢ ¢ - × ¢ 0 0 Ú 0 0 4p E a H a = Ê Ë Á ˆ ¯ ˜ = Ê Ë Á ˆ ¯ ˜ - - jZ I e r j I e r jk r jk r 0 0 0 2 2 2 2 0 0 cos cos sin cos cos sin p q q p p q q p q j

739 (38.13) This radiation resistance is considerably higher than the radiation resistance of a short dipole. For example, if we have a dipole of length 0.017, its radiation resistance will be approximately 0.08 Q2(from Eq 38.9). This resistance is probably comparable to the ohmic resistance of the dipole, thereby resulting in a low efficiency The half-wave dipole, having a much higher radiation resistance, will have much higher efficiency. The higher resistance of the half-wave dipole also makes impedance matching easier. End loading At many frequencies of interest, for example, the broadcast band, a half-wavelength becomes unreasonably long. Figure 38.2 shows a way of increasing the effective ngth of the dipole without making it longer. Here, additional wires have been added to the ends of the dipoles. These wires increase the end capacitance of the dipole, thereby increasing the effective electrical length. Arrays of Wire Antennas Often it is advantageous to have several antennas operating together in an array. Arrays of antennas can be made to produce highly directional radiation patterns. Also, small antennas can be used in an array to obtain the level of performance of FIGURE 38.2 Using end a large antenna at a fraction of the ar ding to increase the The radiation pattern of an array depends on the number and type of antennas effective electrical length of used, the spacing in the array, and the relative phase and magnitude of the excitation an electric dipole currents. The ability to control the phase of the exciting currents in each element of the array allows one to electronically scan the main radiated beam. An array that varies the phases exciting currents to scan the radiation pattern through space is called an electronically scanned phased Phased arrays are used extensively in radar applications Analysis of General Arra To obtain analytical expressions for the radiation fields due to an array one must first look at the fields produced by a single array element. For an isolated radiating element positioned as in Fig. 38.3, the electric field at a far field point P is given by E,=a K, (0, o)e/lk(R1 -a, I (3814) where K, (0, p) is the electric field pattern of the individual element, a, eai is the excitation of the individual element,R, is the position vector from the phase reference point to the element, i, is a unit vector pointing toward the far-field point P and k is the free space wave vector. Now, for an array of n of these arbitrary radiating elements the total E-field at position P is given by the vector sum E a K, (0, ( p)e' (38.15) This equation may be used to calculate the total field for an array of antennas where the mutual coupling between the array elements can be neglected. For most practical antennas, however, there is mutual coupling, c 2000 by CRC Press LLC

© 2000 by CRC Press LLC (38.13) This radiation resistance is considerably higher than the radiation resistance of a short dipole. For example, if we have a dipole of length 0.01l, its radiation resistance will be approximately 0.08 W (from Eq. 38.9). This resistance is probably comparable to the ohmic resistance of the dipole, thereby resulting in a low efficiency. The half-wave dipole, having a much higher radiation resistance, will have much higher efficiency. The higher resistance of the half-wave dipole also makes impedance matching easier. End Loading At many frequencies of interest, for example, the broadcast band, a half-wavelength becomes unreasonably long. Figure 38.2 shows a way of increasing the effective length of the dipole without making it longer. Here, additional wires have been added to the ends of the dipoles. These wires increase the end capacitance of the dipole, thereby increasing the effective electrical length. Arrays of Wire Antennas Often it is advantageous to have several antennas operating together in an array. Arrays of antennas can be made to produce highly directional radiation patterns. Also, small antennas can be used in an array to obtain the level of performance of a large antenna at a fraction of the area. The radiation pattern of an array depends on the number and type of antennas used, the spacing in the array, and the relative phase and magnitude of the excitation currents. The ability to control the phase of the exciting currents in each element of the array allows one to electronically scan the main radiated beam. An array that varies the phases of the exciting currents to scan the radiation pattern through space is called an electronically scanned phased array. Phased arrays are used extensively in radar applications. Analysis of General Arrays To obtain analytical expressions for the radiation fields due to an array one must first look at the fields produced by a single array element. For an isolated radiating element positioned as in Fig. 38.3, the electric field at a far- field point P is given by (38.14) where Ki(q,j) is the electric field pattern of the individual element, ai e–jai is the excitation of the individual element, Ri is the position vector from the phase reference point to the element, i p is a unit vector pointing toward the far-field point P, and k0 is the free space wave vector. Now, for an array of N of these arbitrary radiating elements the total E-field at position P is given by the vector sum (38.15) This equation may be used to calculate the total field for an array of antennas where the mutual coupling between the array elements can be neglected. For most practical antennas, however, there is mutual coupling, R P I a r = ª 2 73 0 2 * * W FIGURE 38.2 Using end loading to increase the effective electrical length of an electric dipole. E K R i i i i j k a e i p i = × - ( , ) [ ( ) ] q j 0 a E E K R i tot = = × - = - = - Â i Â i i j k i p i i N i N a ( , )e [ ( ) ] q j 0 a 0 1 0 1

Phased Arrays By adjusting the phase of the elements of the array it is possible to vary the direction of the maximum of the rray s radiation pattern. For arrays where all the excitation currents are equal in magnitude but not necessarily phase, the array factor is a maximum when y=0. From the definition of w, one can see that at the pattern maximum kd cos e Thus, the direction of the array factor maximum is given by (38.21b) Note that if one is able to control the phase delay, a, the direction of the maximum can be scanned without physically moving the antenna Planar(2-D) Arrays Suppose there are M linear arrays, all identical to the one pictured in Fig. 38. 4, lying in the yz-plane with element spacing d in both the y and the z direction. Using the origin as the phase reference point, the array factor can be determined to be elin( o d cos 8-a2 )+jm(o d sin sin p-ay )1 .2) where a, and a, are the phase differences between the adjacent elements in the y and z directions, respectively. The formula can be derived by considering the 2-D array to be a 1-D array of subarrays, where each subarray has an antenna pattern given by eq (38. 19) If all the elements of the 2-D array have excitation currents equal in magnitude and phase(all the amm are equal and a,=a,=0), then the array will be a broadside array and will have a normalized array factor given by Mkd cos 0 sin sin e sin p f(,q)= (38.23) N sin Ka cos e Msin 2 sIn 0 sin (p Yagi-Uda arrays The Yagi-Uda array can be found on rooftops all over the world-the standard TV antenna is a Yagi-Uda array. The Yagi-Uda array avoids the problem of needing to control the feeding currents to all of the array elements by driving only one element. The other elements in the Yagi-Uda array are excited by near-field coupling from the driven element The basic three-element Yagi-Uda array is shown in Fig. 38.5. The array consists of a driven antenna of length I, a reflector element of length L, and a director element of length L3. Typically, the director element is shorter than the driven element by 5% or more, while the reflector element is longer than the driven element by 5% or more Stutzman and Thiele, 1981]. The radiation pattern for the array in Fig. 38.5 will have a maximum in the +z direction c 2000 by CRC Press LLC

© 2000 by CRC Press LLC Phased Arrays By adjusting the phase of the elements of the array it is possible to vary the direction of the maximum of the array’s radiation pattern. For arrays where all the excitation currents are equal in magnitude but not necessarily phase, the array factor is a maximum when y = 0. From the definition of y, one can see that at the pattern maximum Thus, the direction of the array factor maximum is given by (38.21b) Note that if one is able to control the phase delay, a, the direction of the maximum can be scanned without physically moving the antenna. Planar (2-D) Arrays Suppose there are M linear arrays, all identical to the one pictured in Fig. 38.4, lying in the yz-plane with element spacing d in both the y and the z direction. Using the origin as the phase reference point, the array factor can be determined to be (38.22) where ay and az are the phase differences between the adjacent elements in the y and z directions, respectively. The formula can be derived by considering the 2-D array to be a 1-D array of subarrays, where each subarray has an antenna pattern given by Eq. (38.19). If all the elements of the 2-D array have excitation currents equal in magnitude and phase (all the amn are equal and az = ay = 0), then the array will be a broadside array and will have a normalized array factor given by (38.23) Yagi–Uda Arrays The Yagi–Uda array can be found on rooftops all over the world—the standard TV antenna is a Yagi–Uda array. The Yagi–Uda array avoids the problem of needing to control the feeding currents to all of the array elements by driving only one element. The other elements in the Yagi–Uda array are excited by near-field coupling from the driven element. The basic three-element Yagi–Uda array is shown in Fig. 38.5. The array consists of a driven antenna of length l1, a reflector element of length l2, and a director element of length l3. Typically, the director element is shorter than the driven element by 5% or more, while the reflector element is longer than the driven element by 5% or more [Stutzman and Thiele, 1981]. The radiation pattern for the array in Fig. 38.5 will have a maximum in the +z direction. k d0 cos q = a q a = Ê Ë Á ˆ ¯ ˜ - cos 1 0 k d f a e mn jn k d jm k d m M n N z y ( , ) [ ( cos ) ( sin sin )] q j q a q j a = - + - = - = - Â Â 0 0 0 1 0 1 ¢ = Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ Ê Ë Á ˆ ¯ ˜ f Nk d N k d Mk d M k d ( , ) sin cos sin cos sin sin sin sin sin sin q j q q q j q j 0 0 0 0 2 2 2 2

can increase the gain of the Yagi-Uda array by Reflector additional director elements. Adding additional elemen Directo or elements. however has little effect because the field behind the first reflector element is small Yagi-Uda arrays typically have directivities between 10 and 100, depending on the number of directors [Ramo et al., 1984. TV antennas usually have several directors. Log-Periodic Dipole Arrays Another variation of wire antenna arrays is the log-perI- FIGURE 38.5 Three-elemer odic dipole array. The log-periodic is popular in applica-(Source: Shintaro Uda and Yasut tions that require a broadband, frequency-independent Antenna, Sendai, Japan: Sasaki antenna. An antenna will be independent of frequency if Company, 1954, p 100. With permission.) its dimensions, when measured in wavelengths, remain constant for all frequencies. If, however, an antenna is designed so that its characteristic dimensions are periodic with the logarithm of the frequency, and if the characteristic dimensions do not vary too much over a period of time, then the antenna will be essentially frequency independent. This is the basis for the log-periodic array, shown in Fig. 38 zn+1⊥Lm+1 (38.24) Also note that there is a mechanical phase reversal between successive elements in the array caused by the tossing over of the interconnecting feed lines. This phase reversal is necessary to obtain the proper phasing tween adjacent array elements This half-wave resonant dipole and its immediate neighbors are called the active region of the log-periodic array. As the operating frequency changes, the active region shifts to a different part of the log-periodic. Hence, the frequency range for the log-periodic array is roughly given by the frequencies at which the longest and shortest dipoles in the array are half-wave resonant(wavelengths such that 2LN<2< 2L,)[Stutzman and Thiele, 1981 2 QX L FIGURE 38.6 The log-periodic dipole array. Source: D.G. Isbell, "Log peri IRE Transactions on antenna and Propagation, voL. AP-8, P. 262, 1960. With permission. c 2000 by CRC Press LLC

© 2000 by CRC Press LLC One can increase the gain of the Yagi–Uda array by adding additional director elements. Adding additional reflector elements, however, has little effect because the field behind the first reflector element is small. Yagi–Uda arrays typically have directivities between 10 and 100, depending on the number of directors [Ramo et al., 1984]. TV antennas usually have several directors. Log-Periodic Dipole Arrays Another variation of wire antenna arrays is the log-periodic dipole array. The log-periodic is popular in applications that require a broadband, frequency-independent antenna. An antenna will be independent of frequency if its dimensions, when measured in wavelengths, remain constant for all frequencies. If, however, an antenna is designed so that its characteristic dimensions are periodic with the logarithm of the frequency, and if the characteristic dimensions do not vary too much over a period of time, then the antenna will be essentially frequency independent. This is the basis for the log-periodic dipole array, shown in Fig. 38.6. In Fig 38.6, the ratio of successive element positions equals the ratio of successive dipole lengths. This ratio is often called the scaling factor of the log-periodic array and is denoted by (38.24) Also note that there is a mechanical phase reversal between successive elements in the array caused by the crossing over of the interconnecting feed lines. This phase reversal is necessary to obtain the proper phasing between adjacent array elements. To get an idea of the operating range of the log-periodic antenna, note that for a given frequency within the operating range of the antenna, there will be one dipole in the array that is half-wave resonant or is nearly so. This half-wave resonant dipole and its immediate neighbors are called the active region of the log-periodic array. As the operating frequency changes, the active region shifts to a different part of the log-periodic. Hence, the frequency range for the log-periodic array is roughly given by the frequencies at which the longest and shortest dipoles in the array are half-wave resonant (wavelengths such that 2LN < l < 2L1 ) [Stutzman and Thiele, 1981]. FIGURE 38.6 The log-periodic dipole array.(Source: D.G. Isbell, “Log periodic dipole arrays,” IRE Transactions on Antennas and Propagation, vol. AP-8, p. 262, 1960. With permission.) FIGURE 38.5 Three-element Yagi–Uda antenna. (Source: Shintaro Uda and Yasuto Mushiake, Yagi–Uda Antenna, Sendai, Japan: Sasaki Printing and Publishing Company, 1954, p. 100. With permission.) t = = + + z z L L n n n n 1 1