Kolias, N.J., Compton, R.C., Fitch, J P, Pozar, D.M. Antennas The Electrical Engineering Handbook Ed. Richard C. Dorf Boca raton crc Press llc. 2000
Kolias, N.J., Compton, R.C., Fitch, J.P., Pozar, D.M. “Antennas” The Electrical Engineering Handbook Ed. Richard C. Dorf Boca Raton: CRC Press LLC, 2000
38 A antennas 38.1 Wire Short Dipole· Directi Impedance. Arbitrary Wire Antennas. Resonant Half-way Antenna· End Loading· Arrays of Wire Antennas· Analysis of N Kolias General Arrays. Arrays of ldentical Elements. Equally Spaced Raytheon Company Linear Arrays. Planar(2-D) Arrays. Yagi-Uda Arrays.Log Periodic Dipole Arrays R.C. Compton 38.2 Aperture The Oscillator or Discrete Radiator. Synthetic J. Patrick Fitch Apertures.Geometric Designs. Continuous Current Distributions Lawrence Livermore Laboratory Fourier Transform). Antenna Parameters 38.3 Microstrip Antennas David m. pozar Introduction. Basic Microstrip Anter iversity of Massachusetts Techniques for Microstrip Antennas Arrays. Computer-Aided Design for 38.1 Wire N 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 P per unit solid angle Q2 radiated by the antenna. The antenna pattern, also called the radiation pattern, is usually plotted in spherical coordinates 0 and p. 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 scales(10 log power) he 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 Collins notation, the vector in spherical coordinates is given by oI dl-(a, cos 8-ag sin 0) (38.1) 47 c 2000 by CRC Press LLC
© 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
in0 120 (c) FIGURE 38.1 Radiation pattern for a short dipole of length dl(d<<ho). These are plots of power density on linear scales. (a)E-plane;(b)H-Plane; (c) three-dimensional view with cutout. where k= 2T/Mo and I is the current, assumed uniform, in the short dipole of length dl(dl<< no). Here the assumed time dependence et has not been explicitly shown. The electric and magnetic fields may then be determined us V×A The radiated fields are obtained by calculating these fields in the so-called far-field region where r>>A Doing this for the short dipole yields E=∠2 Idlko sin e e~% (38.3) H jldl ko sin e where Zo=Ho/Eg. The average radiated power per unit solid angle Q2 can then be found to be △B9=129ExH*a}=1|1zdn)k日 (384) △Q 32π
© 2000 by CRC Press LLC where k0 = 2p/l0, and I is the current, assumed uniform, in the short dipole of length dl (dl << l0). Here the assumed time dependence ejwt has not been explicitly shown. The electric and magnetic fields may then be determined using (38.2) The radiated fields are obtained by calculating these fields in the so-called far-field region where r >> l. Doing this for the short dipole yields (38.3) where Z0 = . The average radiated power per unit solid angle W can then be found to be (38.4) FIGURE 38.1 Radiation pattern for a short dipole of length dl (dl << l0). These are plots of power density on linear scales. (a) E-plane; (b) H-plane; (c) three-dimensional view with cutout. E A A =- + H A —— × j = —¥ j w wm e m 00 0 1 E a H a = = - - jZ Idl k e r jIdl k e r jk r jk r 0 0 0 0 0 4 4 sin sin q p q p q j m0 e0 § D DW P r I Z dl k r r (, ) { } () qj q sin p = ¬ ¥ ×= 1 2 32 2 2 0 2 0 2 2 2 e E H* a * *
Directivity The directivity D(0. )and gain G(e, ) of an antenna are defined as D(e, o)- Radiated power per solid angle AP(e, )/AQ2 Total radiated power/4t 38.5) G(,g) s Radiated power per Solid angle△P(6,φ)/△s Total input power/4π P./4兀 Antenna efficiency, n, is given by n P_G(6,q) 386) Pin D(e, p) For many antennas n =l and so the words gain and directivity can be used interchangeably. For the short dipole D(e, p n26 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(8, p)=l. 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. 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 polar ization orientations of E and H are interchanged. ko sin 0-ae 4πr 388) -jkr E= MOko sin 8 4πr where M=T o I for a loop with radius ro and uniform current L. put Mpeda At a given frequency the impedance at the feedpoint of an antenna can be represented as Z, =R,+ iX the real part of Z,(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 R,= 2P, /ln2 where P, is the total radiated power and I is the input current at the antenna terminals For lectrically small electric and magnetic dipoles with uniform currents c 2000 by CRC Press LLC
© 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
R,=80 dl electric dipole 入 3205 (2o/magnetic dipole The reactive component of Za can be determined from X,=40(Wm -We)/ln where Wm is the average magnetic energy and w is the average electric energy stored in the near-zone evanescent fields. The reflection coefficient T. of the antenna is just (38.10) Za t zo where Zo 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 E)=20m-(an,,-a]1 (38.11) where the integral is over the contour C of the wire, a is a unit vector tangential to the wire, and ris 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 stems. Factors contributing to its popularity are its well-understood radiation pattern, its simple construction, its high efficiency, and its capability for easy impec dance matching The electric and magnetic fields for the half-wave dipole can be calculated by substituting its current distribution, I= Io cos(koz), into Eq (38.11)to obta COS e ilo e 2 The total radiated power, Pr, can be determined from the electric and magnetic fields by integrating the expression 1/2 :e(ExH.a)over a surface of radius r Carrying out this integration yields P =36.565 IlI The radiation resistance of the half-wave dipole can then be determined from
© 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