Dipole Antennas - Fundamentals of Electromagnetics and Transmission Lines | ECE 3300, Lab Reports of Electrical and Electronics Engineering

Download Dipole Antennas - Fundamentals of Electromagnetics and Transmission Lines | ECE 3300 and more Lab Reports Electrical and Electronics Engineering in PDF only on Docsity! DIPOLE ANTENNAS 575 x y F φ θ z h Figure 1. Dipole antenna variations. radiation is independent of  (rotationally symmetric about the z axis). Dipole antennas and arrays of dipoles are com- monly used for high-frequency (HF) and ultrahigh-frequency (UHF) communications, TV, and FM broadcasting, and as electric field probes. This article will describe the basic nature and applications of dipole antennas and some of their varia- tions such as biconical and bowtie antennas, slot dipoles, folded dipoles, sleeve dipoles, and shunt-fed dipoles. The com- monly used broadband log-periodic and Yagi–Uda dipole arrays are also discussed. INFINITESIMAL DIPOLE (HERTZIAN DIPOLE) An infinitesimal dipole (L  ) is a small element of a linear dipole that is assumed to be short enough that the current (I) can be assumed to be constant along its length L. It is also called a Hertzian dipole. The electric and magnetic field com- ponents of this dipole are (1) H = 1 4π IL sin θ e− jβ0 r
jβ0 r + 1 r 2  φ (1) E = jη0IL 2πβ0 cos θ
jβ0 r 2 + 1 r 3  e− jβ0 rr − jη0IL 4πβ0 sin θ  −β 2 0 r + jβ0 r 2 + 1 r 3  e− jβ0 rθ (2) where 0
(0/ 0)1/2 is the intrinsic impedance (
377 ) for free space, and
0
(0 0)1/2 is the propagation con- stant (
/c, where c is the speed of light). The fields decay rapidly (1/r3 variation) very near the antenna, and less rapidly (1/r variation) farther away. The fields with terms 1/r2 and 1/r3 (the induction terms) provide energy that is stored near the antenna. The fields with 1/r varia- tion (the radiation terms) represent actual energy propaga- tion away from the antenna. The distance away from the antenna where the induction and radiation terms are equalDIPOLE ANTENNAS is d
/2. When d /2, one is in the near field of the antenna, and the induction terms dominate. When d A dipole antenna is most commonly a linear metallic wire or /2, one is in the far field, and the radiation terms domi-rod with a feed point at the center as shown in Fig. 1. Most nate. In the far field, the wave propagation is in the trans-often, this type of antenna has two symmetrical, aligned, ra- verse electromagnetic (TEM) mode, which is characteristicdiating arms. Because of the symmetry of the antenna rela- tive to the xy plane containing the feed point, the resultant of far-field radiation from finite structures. J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc. 576 DIPOLE ANTENNAS these elements. The resultant fields far from the antenna at a distance r0 are E = jηI(0) 2πr sin kh F(θ )e j(ωt−kr)θ (6) and H = jI(0) 2πr sin kh F(θ )e j(ωt−kr)φ (7) x y z where
(/ )1/2, and where the  dependence F() of the Figure 2. Radiation pattern for an infinitesimal (or Hertzian) dipole. radiated fields is called the pattern factor and is given by the following: The far-zone radiated fields of the Hertzian dipole follow from (1) and (2) by retaining the 1/r varying terms: F(θ ) = cos(kh cos θ ) − cos kh sin θ (8) The radiated power density P() is given byH = j 4πr IL sin θ e− jβ0rφ (3) P(θ ) = E · E ∗ 2η = ηI 2(0) 8π2r2 sin2 kh F2(θ ) (9)E = jη0 4πr IL sin θ e− jβ0 rθ (4) Using
0
120, this can also be expressed in terms ofAs expected for TEM wave propagation, the E and H fields the total radiated power W [
I2(0)Ra/2] and the feedpointare perpendicular to each other and to the outward propaga- resistance Ra as follows:tion in the r direction. Also, the ratio E /H
0
(0/ 0)1/2, which is the intrinsic impedance of free space. The radiation pattern of this Hertzian dipole is shown in Fig. 2, and exhibits the classical symmetry expected of dipole P(θ ) = 30 πr2 W Ra F2(θ ) sin2 kh (10) antennas, being both independent of  and symmetric about the xy plane through the center (feedpoint) of the dipole. The magnitude of the total radiated power is Prad
40 2I20 (L/ )2. From Eqs. (3) and (4) it is interesting to note that even for this constant-current infinitesimal dipole, the radiated power density is proportional to sin2 . Hence, it is maximum for 
90 (i.e. in the xy plane normal to the orientation of the dipole) and zero for the directions along the length of the di- pole (
0 and 180). The latter property for zero radiation along the length of the dipole will be seen for all linear dipoles regardless of length. It follows from the fact that a linear an- tenna may be considered as composed of infinitesimal dipoles do not create E and H fields or radiated power density for the 
0 and 180 directions. LINEAR DIPOLE ANTENNAS The geometry of a linear dipole antenna of length 2h is shown in Fig. 1. The current distribution is sinusoidal and is approx- imately given by I(z′) = I(0) sin kh sin k(h − |z′|) for − h < z′ < h (5) where I(0) is the current at the feedpoint of the antenna, h
L/2 is the half length of the antenna, and k
( )1/2 is the propagation constant in the material surrounding the di- pole. The current distributions for several lengths of dipole antennas are shown in Fig. 3. h = 3 /4 h = /2λ h = /4λ λ The electric and magnetic fields around the dipole are cal- culated by modeling the antenna as a series of Hertzian or Figure 3. Current distributions and associated radiation patterns for several different lengths of dipole antennas.elemental dipoles and integrating the fields from each of DIPOLE ANTENNAS 579 Figure 12. A broadband dipole curtain. Dots indicate feed point loca- tions. α2 (a) (b) Rn + 1 Ln + 1 Rn Ln Figure 10. Log-periodic dipole array: (a) geometry of a log-periodic array, showing how the phase-reversal feed system for this antenna results in unwanted reflections and erratic impedance behav-is constructed (from Ref. 1), (b) equivalent antenna model of the log- periodic array. ior, known as end effect. An effective way to further increase the bandwidth of a log-periodic array is to change from dipole elements to ele- geometry of a log-periodic array is shown in Fig. 10(a), which ments with individual broader bandwidths, similarly to shows how the phase-reversal feed system for this antenna is changing from a dipole antenna to a biconical antenna. This constructed. The equivalent antenna model of this array is is accomplished for log-periodic arrays by using a configura- shown in Fig. 10(b). The elements of the array are dipole an- tion of wires such as is shown in Fig. 11, where each element tennas that increase in both length and spacing according to is a sawtooth element and therefore has broader bandwidth the formula than the individual dipole elements. BROADBAND DIPOLE CURTAIN ARRAYSτ = Rn+1 Rn = Ln+1 Ln = dn+1 dn < 1 (13) A broadband dipole curtain as shown in Fig. 12 is commonlywhere 
fn/fn1 is the ratio of the resonant frequencies used for high-power (100 kW to 500 kW) HF ionosphericfn and fn1 of adjacent dipole elements. Since lengths and broadcasting and short-wave broadcasting stations. The cur-spacings are interrelated, the choice of one initial value tain is composed of several dipoles, usually half a wavelengthcontrols the design of the remaining elements. The spacing long, mounted horizontally or vertically in a rectangular orbetween one dipole and its adjacent shorter neighbor is square array, often backed by a reflecting plane or wire mesh.given by This array has several desirable features, including high gain, broad bandwidth, independent control of horizontal and vertical radiation patterns, ease of matching (low VSWR), andσ = dn 2Ln = 1 − τ 4 cot α (14) the ability to broadcast high power efficiently. Using a phased-feeds system, this array allows beam steering of theLog-periodic arrays are generally constructed with small radiation pattern in both the azimuthal and the elevationvalues of  [10    45 (2)] and large values of  [0.7  plane, providing a very high degree of flexibility.  0.95 (3)], which essentially gives a traveling wave propa- gating to the left in the backfire direction, away from the an- tenna array. The mechanism of this array is that only the VHF–UHF COMMUNICATION APPLICATIONS elements that are approximately half-wavelength long radi- ate, and since they are radiating to the left, the smaller ele- Yagi–Uda Dipole Array ments do not interfere with them. This is accomplished by the Yagi–Uda arrays are commonly used as general-purpose an-phase reversal of the feeds. An array that is built without the tennas from 3 MHz to 3000 MHz, and in particular as homephase reversal radiates in the end-fire direction. The interfer- TV antennas. They are inexpensive, have reasonable band-ence of the longer elements to the right of radiating elements width, and have gains up to 17 dBi or more if multiple arrays are used. They have unidirectional beams with moderate side lobes (1). A typical Yagi–Uda array is shown in Fig. 13. This array is a simple end-fire array of dipole antennas where only one Figure 11. Log-periodic array with sawtooth wire elements for in- creased bandwidth. Dots indicate feed point locations. Heavy wires indicate dipole antennas. Light wires indicate wires for structural support only. Figure 13. Yagi–Uda array. 580 DIPOLE ANTENNAS Figure 14. Typical E- and H-plane pat- terns of a Yagi–Uda array. Total number of elements
27, number of directors
25, number of reflectors
1, number of driven elements
1, total length of re- flector
0.5 , total length of feeder
0.47 , total length of each director
0.406 , spacing between reflector and feeder
0.125 , spacing between adja- cent directors
0.34 , radius of wires
0.003 . From G. A. Thiele, ‘‘Analysis of Yagi–Uda Antennas,’’ IEEE Trans. Anten- nas & Propag., 17: 1969,  IEEE. 120° 90° 60° 30° 90° 60° 30° 90° 60° 30° E plane 90° 60° 30° 120°120° 150° 180° E plane pattern (a) 150° 120° 0.75 0.50 0.25 1.0 R e la tiv e e le ct ri c fie ld H plane 150° 180° 0° 0° H plane pattern (b) 150° 0.75 0.50 R e la tiv e e le ct ri c fie ld 0.25 1.0 of the elements is driven and the rest are parasitic. The para- Dipoles for Circular Polarization sitic elements operate as either reflectors or directors. In gen- For applications that require a circularly polarized antenna eral (1), the longest antenna, which is about /2 in length, is such as TV and FM broadcasts and space communications, at the main reflector, and is generally spaced /4 behind the least two dipoles, each of which has a linear polarization, driven dipole. The feed element is commonly a folded dipole must be combined in an array, often referred to as crossed antenna 0.45 to 0.49 long. Adding directors, which are gen- dipoles. In a crossed-dipole configuration, dipoles are mounted erally 0.4 to 0.45 , to the front of the driven element in- perpendicular to each other for circular polarization or at creases the gain of the array. The directors are not always of other angles for elliptical polarization. Currents are fed 90 the same length, diameter, or spacing. Common arrays have out of phase between the two dipoles. These can also be used 6 to 12 directors and at most two reflectors. Additional im- as probes for sensing vector fields to isolate individual compo- provements in gain by adding more elements are limited, but nents of the electric field. Adaptations of the crossed dipole arrays have been designed with 30 to 40 elements (3). A gain are shown in Figs. 15(a) and (b). Dipole arrays such as the (relative to isotropic) of 5 to 9 per wavelength of array length is typical for Yagi–Uda arrays, for an overall gain of 50 to 54 (14.8 dB to 17.3 dB). The Yagi–Uda array is characterized by a main lobe of ra- diation in the direction of the director elements and small side lobes. The beamwidth is small, generally 30 to 60 (3). Typical E- and H-plane patterns of a Yagi–Uda array are shown in Fig. 14. Typically, the performance of a Yagi–Uda array is computed using numerical techniques (4). For the simple case where all of the elements are approximately the same size, the electric field pattern can be computed from the array factors of the various elements. The input impedance of a Yagi–Uda array is often small. For example, for a 15-element array with reflector length 0.5 , director spacing 0.34 , and director length 0.406 , the input impedance is 12 , 22 , 32 , 50 , or 62  for reflec- tor spacings of 0.10 , 0.13 , 0.15 , 0.18 , and 0.25 , respec- tively. This can make matching to typical transmission lines (50, 75, or 300 ) difficult. Folded dipoles used for the driven element are therefore used to boost the input impedance by a (a) (b) (c)factor of 4 or more. Extensive studies of the design of Yagi–Uda arrays have Figure 15. Cross-dipole applications for circular or elliptical polar- been made (5), and tables are provided to optimize the Yagi– ization: (a) two shunt-feed slanted V dipoles, (b) series-fed slanted dipoles, (c) circularly polarized Yagi–Uda array. From Ref. 1.Uda array for a desired gain (2). DIRECTIONAL COUPLERS 581 Yagi–Uda can also be combined to provide circular polariza- tion, as shown in Fig. 15(c). BIBLIOGRAPHY 1. R. C. Johnson and H. Jasik (eds.), Antenna Engineering Handbook, New York: McGraw-Hill, 1984. 2. W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 2nd ed., New York: Wiley, 1998, pp. 172, 173. 3. C. A. Balanis, Antenna Theory—Analysis and Design, 2nd ed., New York: Wiley, 1997. 4. C. A. Balanis, ibid., p. 541. 5. C. A. Chen and D. K. Cheng, Optimum element lengths for Yagi– Uda arrays, IEEE Trans. Antennas Propag., AP–23: 8–15, 1975. 6. J. D. Kraus, Antennas, 2nd ed., New York: McGraw-Hill, 1988. 7. M. F. Iskander, Electromagnetic Fields and Waves, Englewood Cliffs, NJ: Prentice-Hall, 1992. 8. O. P. Gandhi, Microwave Engineering and Applications, New York: Pergamon, 1985. CYNTHIA M. FURSE Utah State University OM P. GANDHI GIANLUCA LAZZI University of Utah