# Antenna Theory EELE 5445

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1 Antenna Theory EELE 5445 Lecture 6: Dipole Antenna Dr. Mohamed Ouda Electrical Engineering Department Islamic University of Gaza 2013

2 The dipole and the monopole The dipole and the monopole are arguably the two most widely used antennas across the UHF, VHF and lower-microwave bands. Arrays of dipoles are commonly used as base-station antennas in land-mobile systems. The monopole and its variations are perhaps the most common antennas for portable equipment, such as cellular telephones, cordless telephones, automobiles, trains, etc. It has attractive features such as simple construction, sufficiently broadband characteristics for voice communication, small dimensions at high frequencies. An alternative to the monopole antenna for hand-held units is the loop antenna, the microstrip patch antenna, the spiral antennas, inverted-l and inverted-f antennas, and others. 2

3 Small dipole Assuming occur is, The maximum phase error βr in that can at θ=0 Reminder: A maximum total phase error of π/8 is acceptable since it does not affect substantially the integral solution for the vector potential A. The assumption is made here for both, the amplitude and the phase factors in the kernel of the VP integral. 3

4 The current is a triangular function of : 'z 4

5 The solution for A is simple when we assume that Note that A is exactly one-half of the result obtained for A of an infinitesimal dipole of the same length, if I m were the current uniformly distributed along the dipole. This is expected because we made the same approximation for R, as in the case of the infinitesimal dipole with a constant current distribution, and we integrated a triangular function along l, whose average is Therefore, we need not repeat all the calculations of the field components, power and antenna parameters. We make use of our knowledge of the infinitesimal dipole field. 5

6 The far-field components of the small dipole are simply half those of the infinitesimal dipole: The normalized field pattern is the same as that of the infinitesimal dipole: 6

7 7

8 The beam solid angle: The directivity As expected, the directivity, the beam solid angle as well as the effective aperture are the same as those of the infinitesimal dipole because the normalized patterns of both dipoles are the same. 8

9 The radiated power is four times less than that of an infinitesimal dipole of the same length and current because the far fields are twice smaller in magnitude: I 0 = I m As a result, the radiation resistance is also four times smaller than that of the infinitesimal dipole: 9

10 Finite-length infinitesimally thin dipole A good approximation of the current distribution along the dipole s length is the sinusoidal one: It can be shown that the VP integral 10 has an analytical (closed form) solution, however, we follow a standard approach used to calculate the far field for an arbitrary wire antenna.

11 The dipole is subdivided into a number of infinitesimal dipoles of length dz'. Each such dipole produces the elementary far field as Where and denotes the value of the current element at z'. Using the far-zone approximations, We obtain 11

12 The first factor is the element factor. Which is the far field produced by an infinitesimal dipole of unit current element. The element factor is the same for any current element, Іl=1(Axm) provided the angle θ is always associated with the current axis. The second factor is the space factor (or pattern factor, array factor). The pattern factor is dependent on the amplitude and phase distribution of the current at the antenna (the source distribution in space). 12

13 For the specific current distribution described in page 10, the pattern factor is The above integrals are solved having in mind that The far field of the finite-length dipole is obtained as 13

14 Amplitude pattern 14

15

16 16

17 17

18 Power pattern Note: The maximum F θ, φ of is not necessarily unity, but for l < 2λ the major maximum is always at θ = 900. Radiated power First, the far-zone power flux density is calculated as 18

19 19

20 20

22 Directivity The directivity is obtained as where the power pattern is Finally 22

23 Input resistance The radiation resistance given is not necessarily equal to the input resistance because the current at the dipole center I in (if its center is the is not necessarily equal to I m. In particular, I in Im if l > λ/2, and l 2(2n + 1)λ/2, n is any integer. Note that when l > λ, I in = Im. To obtain a general expression for the current magnitude I in at the center of the dipole (assumed also to be a feed point), we note that if the dipole is lossless, the input power is equal to the radiated power. Therefore, 23

24 Since the current at the center of the dipole (z' =0) is Then, In summary, the dipole s input resistance, regardless of its length, depends on the integral,as long as the feed point is at the center. 24

25 Loss can be easily incorporated in the calculation of R in bearing in mind that the power-balance relation can be modified as We have already obtained the expression for the loss of a dipole of length l: 25

26 Half-wavelength dipole This is a classical and widely used thin wire antenna: l=λ 26

27 3-D power pattern (not in db) of the half-wavelength dipole: 27

28 Radiated power The radiated power of the half-wavelength dipole is a special case of the integral in 28

29 29

30 30 The imaginary part of the input impedance is approximately +j42.5ω. To acquire maximum power transfer, this reactance has to be removed by matching (e.g., shortening) the dipole: thick dipole l 0.47λ thin dipole l 0.48λ The input impedance of the dipole is very frequency sensitive; i.e., it depends strongly on the ratio l/ λ. This is to be expected from a resonant narrow-band structure operating at or near resonance such as the half-wavelength dipole. Also, the input impedance is influenced by the capacitance associated with the physical junction to the transmission line. The structure used to support the antenna, if any, can also influence the input impedance. That is why the curves below describing the antenna impedance are only representative.

31 Measurement results for the input impedance of a dipole 31

32 32

33 Method of images revision 33

34 Vertical electric current element above perfect conductor 34

35 Using the total far field approximation and the VP integral 35

36 The total far field is The far-field expression can be again decomposed into two factors: the field of the elementary source g(θ) and the pattern factor (also array factor) f(θ). The normalized power pattern is 36

37 The elevation plane patterns for vertical infinitesimal electric dipoles of different heights above a perfectly conducting plane are plotted : 37

38 As the vertical dipole moves further away from the infinite conducting (ground) plane, more and more lobes are introduced in the power pattern. This effect is called scalloping of the pattern. The number of lobes is 38

39 Total radiated power Note: 39

40 Radiation resistance As βh 0, the radiation resistance of the vertical dipole above ground approaches twice the value of the radiation resistance of a dipole of the same length in free space: As βh, the radiation resistance of both dipoles becomes the same. 40

41 Radiation intensity The maximum of U(θ) occurs at θ=π/2: This value is 4 times greater than of a free-space dipole of the same length. 41

42 Maximum directivity If βh = 0, Do = 3, which is twice the maximum directivity of a free-space current element (D id o =1.5 ). The maximum of D o as a function of the height h occurs when βh =2.881 (h=0.4585λ). Then, D o =6.566 /βh =

43 43

44 Monopoles A monopole is a dipole that has been divided into half at its center where it is fed against a ground plane. It is normally λ long (a 4 quarter-wavelength monopole). 44

45 45

46 Several important conclusions follow from the image theory The field distribution in the upper half-space is the same as that of the respective free-space dipole. The currents and charges on a monopole are the same as on the upper half of its dipole counterpart but the terminal voltage is only half that of the dipole. The input impedance of a monopole is therefore only half that of the respective dipole: The total radiated power of a monopole is half the power radiated by its dipole counterpart since it radiates in half-space (but its field is the same). As a result, the beam solid angle of the monopole is half that of the respective dipole and its directivity is twice the directivity of the dipole: 46

47 47

48 Some approximate formulas for rapid calculations of the input resistance of a dipole and the respective monopole: 48

49 Horizontal current element above a perfectly conducting plane 49

50 Where Using the far field approximation 50

51 The fare field normalized pattern 51

52 As the height increases beyond a wavelength (h>λ), scalloping appears with the number of lobes being 52

53 The radiated power and the radiation resistance It is also obvious that if h=0, then R r and Π=0. This is to be expected because the dipole is short-circuited by the ground plane. 53

54 Radiation Intensity The maximum value depends on whether βh is less than π/2 or greater: Maximum directivity For small βh 54

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