Linear Wire Antennas. EE-4382/ Antenna Engineering

Transcription

1 EE-4382/ Antenna Engineering

2 Outline Introduction Infinitesimal Dipole Small Dipole Finite Length Dipole Half-Wave Dipole Ground Effect Constantine A. Balanis, Antenna Theory: Analysis and Design 4 th Ed., Wiley, Stutzman, Thiele, Antenna Theory and Design 3 rd Ed., Wiley,

3 Introduction 3

4 Wire Antennas - Introduction Wire antennas are the simplest, cheapest, and many times most effective antennas for many applications. The easiness of configuration and analysis is why we begin with these types of antennas. Slide 4

5 Infinitesimal Dipole 5

6 Infinitesimal Dipole An infinitesimal dipole is in the order of l λ, a λ, where l is the length of the antenna, and a is the thickness. z The simplest antenna, it is just an open wire fed at the center with an alternating source. L λ To simplify the mathematical analysis, we will assume an infinitesimal vertical dipole placed along the z-axis, and the current is constant throughout the wire. I z = a z I 0 I 0 I Slide 6

7 Infinitesimal Dipole Slide 7

8 Infinitesimal Dipole - Fields For an electric current source, the magnetic field is equal to The electric field is equal to H θ = H r = 0 H φ = j ki 0l sin θ 4πr jkr e jkr E φ = 0 E r = η I 0l cos θ 2πr jkr e jkr E θ = jη ki 0l sin θ 4πr jkr 1 kr 2 e jkr Slide 8

9 Infinitesimal Dipole - Fields Slide 9

10 Infinitesimal Dipole Near-Field At the near-field region kr 1, the fields with higher order terms dominate: E φ = H θ = H r = 0 H φ = j ki 0l sin θ 4πr jkr e jkr = I 0le jkr 4πr 2 sin(θ) E r = η I 0l cos θ 2πr jkr e jkr = jη I 0le jkr 2πkr 3 cos(θ) E θ = jη ki 0l sin θ 4πr jkr 1 kr 2 e jkr = jη I 0le jkr 2πkr 3 sin(θ) Slide 10

11 Infinitesimal Dipole - Far-field At the far-field region kr 1, the fields with lower order terms dominate: E φ = H θ = H r = 0 H φ = j ki 0l sin θ 4πr jkr e jkr = j ki 0le jkr 4πr sin(θ) E r = η I 0l cos θ 2πr jkr e jkr 0 E θ = jη ki 0l sin θ 4πr jkr 1 kr 2 e jkr = jη ki 0le jkr 4πr sin(θ) Slide 11

12 Infinitesimal Dipole Power Density Power Density: For a lossless antenna, the real part of the input resistance is designated as radiation resistance. Through the mechanism of radiation resistance, the power from guided waves transfers to free-space waves. Recall the complex Poynting Vector: W = 1 2 E H = 1 2 a re r + a θ E θ a φ H φ = 1 2 ( a re θ H φ a θ E r H φ ) Thus we get two components for power: W r = η 8 I 0 l λ 2 sin 2 (θ) r 2 1 j 1 kr 3 W θ = jη k I 0l 2 cos θ sin θ 16π 2 r kr 2 Slide 12

13 Infinitesimal Dipole Power Density Power Density: The complex power in the radial direction is obtained by integrating the components over the closed sphere: 2π π P = W ds = න න S 0 0 a r W r + a θ W θ a r r 2 sin θ dθdφ And we obtain P = η π 3 I 0 l λ 2 1 j 1 kr 3 For real power in the far field, we only care about the first term. Reactive (imaginary power) is more intense in the near-field region, but does not contribute to the far-field power. Slide 13

14 Infinitesimal Dipole Power Density and Radiation Resistance Power Density: From the power calculated we obtain P rad = η π 3 I 0 l λ 2 = 1 2 I 0 2 R r Radiation Resistance: Where R r is the radiation resistance given by R r = η 2π 3 l λ 2 = 80π 2 l λ 2 Assumes antenna is in free-space Slide 14

15 Infinitesimal Dipole Directivity We can calculate the directivity from the average power. W rad = W ave = η 2 I 0 l sin 2 (θ) 8 λ r 2 = η 2 ki 0 l sin 2 (θ) 2 4π r 2 U = r 2 W rad = η 8 D 0 = U max U 0 I 0 l λ = 4πU max P rad = 2 4π η 8 η π 3 sin 2 (θ) ki 0 λ I 0 l λ 2 2 = 3 2 D 0 = 3 = 1.76 dbi 2 U n = sin 2 (θ) Slide 15

16 Infinitesimal Dipole Radiation Pattern Slide 16

17 Infinitesimal Dipole Radiation Resistance Example Example 4.1 (page 150 Balanis) Find the radiation resistance of an infinitesimal dipole whose length is l = λ 50 R r = 80π 2 l λ 2 = 80π = Ω Slide 17

18 Short Dipole 18

19 Short (Small) Dipole The short dipole is a more practical, real antenna, usually has lengths from λ 50 to λ 10. A better representation of current distribution of wire antennas is the triangular distribution. Slide 19

20 Short Dipole Current Distribution z I e x, y, z = a z I l z, 0 z l 2 a z I l z, l 2 z 0 l I 0 I Slide 20

21 Short Dipole Geometry Slide 21

22 Far-Field E- and H- Fields For an electric current source, the magnetic field is equal to The electric field is equal to H r = H θ = 0 H φ = j ki 0l 8πr e jkr sin θ E r = E φ = 0 E θ = jη ki 0l 8πr e jkr sin θ The fields of the short dipole are one-half of the infinitesimal dipole Slide 22

23 Short Dipole - Directivity and Radiation Resistance The radiation pattern is the same for the short and infinitesimal dipole. Since the directivity is controlled by the power pattern of the antenna, it is also the same as the infinitesimal dipole. D 0 = 3 = 1.76 dbi 2 U n = sin 2 (θ) The power radiated by the short dipole is one-fourth dipole. R r = 20π 2 l λ of the infinitesimal Slide 23

24 Short Dipole Radiation Pattern Slide 24