Radiation resistance

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1 Radiation esistance Antennas ae designed fo effective adiation of electomagnetic enegy. Equivalent cicuit of an antenna I in R input adiation esistance R Repesents adiated enegy input loss esistance R L Repesents conduction and dielectic losses of the antenna input eactance X A epesents the enegy stoed in the field nea the antenna 1

2 Radiation esistance The powe adiated is equal to: W The powe losses is W loss If W in is the input powe, the adiation efficiency is: I in R L ad I in R η W W ad in R R + R L I in R

3 Diective gain, diectivity and gain Stonge in some Same intensity fo all diections diections Isotopic Antenna (the efeence antenna) 3

4 Let avg be the aveage oynting vecto which is the powe flow density pe unit aea, 1 avg Re( E H *) The total powe adiated W ad is then W W Diective gain, diectivity and gain ad ad S S avg ds U (, φ) dω ds R sinddφ dω sinddφ whee U(,φ) is the powe flow though a unit solid angle, and is called the adiation intensity (W/s). U (, φ) avg 4

5 Diective gain, diectivity and gain 5

6 Diective gain, diectivity and gain Diective gain G D (,φ) Ratio of the adiation intensity in a paticula diection(,φ) to the aveage adiation intensity. U (, φ) U (, φ) G D (, φ) U W / 4π avg Diectivity Maximum value of the diective gain in a cetain diection. D Max (, φ) { } G d owe Gain Ratio of the adiation intensity in a given diection to the adiation intensity of a lossless isotopic adiato that has the same input powe. U (, φ) G p (, φ) W / 4π in ad 6

7 Example Find the diective gain of a Hetzian dipole. avg avg 1 Re H 1 ( E *) E H φ ( Idl ) 3π U avg η o β ( Idl ) 3π sin η o β sin I H φ E 7

8 8 Example and then ( ) π φ φ φ π π 0 0 sin 3 4 / sin sin sin ), ( ), ( d d U U G avg D

9 Example 9

10 Example Diective gain and the diectivity of the Hetzian dipole 3 GD (, φ) sin 3 D G d ( π /, φ) 1.76 db I Suppose the adiation efficiency is 46%, G p 0.46D db ( W ad / W in 0.46) 10

11 Example Find the adiation esistance of a Hetzian dipole R π π 0 0 ( dl) avg I η oβ 3π I ( dl) η oβ 1π I dl 80π λ dl 80π λ sinddφ π 0 0 dl Suppose,.01 R 0. 08Ω oo adiato!! λ 0 π sin 3 ddφ 11

12 Linea dipole antenna In dipole antennas, the cuent magnitude along the dipole can be epesented like in a tansmission line, whee h is the length of the dipole and z0 at the cente feed-point of the dipole. [ ( h z )] I ( z ) I m sin β h I 1

13 Linea dipole antenna Knowing the cuent distibution I(z), we can sum up the fields due to the infinitesimal segments on the antenna using the esults of the Hetzian dipole. ˆ jη o I me E πr ˆ ji me H φ πr cos F ( ) jkr jkr F ( ) F ( ) a ( βh cos ) φ cos sin βh h I F() is called the patten function 13

14 Linea dipole antenna Antenna patten E-plane patten (patten function vesus fo a constant φ) H-plane patten (patten function vesus φ fo a constant π/) 14

15 Linea dipole antenna At cetain dipole lengths ( λ/, λ ) called esonant lengths, the input impedance is puely esistive. Fo halfwavelength dipole, Z in R 73 Ω The patten patten fo a half-wavelength dipole is cos( βh cos ) cos βh F ( ) sin D 1.64 π cos cos sin 15

16 Example -- Monopole A thin quate-wavelength vetical antenna ove a conducting gound is excited by a sinusoidal souce at its base. Find the (a) adiation patten, (b) esistance, and (c) diectivity. 16

17 Example -- Monopole (a) The electomagnetic field in the uppe half-space due to the quate-wave vetical antenna is the same as that of the half-wave antenna. (b) The magnitude of the time-aveage oynting vecto holds 0 fo π / but the quate-wave antenna adiates only into the half-space, its total adiated powe is only half of a half-wave dipole. Theefoe, the adiation esistance is R R (half wave dipole)/ 73/ 36.5 Ω (c) Same D as 1.64 half-wave dipole 17

18 Effective Aea and Fiis Equation Effective Aea The effective aea A e of a eceiving antenna is the atio of the time-aveage powe eceived to the time-aveage powe density of the incident wave at the antenna. A / e L avg It may be shown that is A e elated to the diective gain as: A λ 4π e G D (, φ) 18

19 Fiis Equation Effective Aea and Fiis Equation Conside two antennae sepaated by a distance. The tansmitting antenna tansmits a total powe t. A e1, G D1, t A e, G D, L The time-aveage powe density at the eceiving antenna is avg t 4π G D1 19

20 0 Effective Aea and Fiis Equation The powe eceived to the load is (Fiis Equation) ( ) t D D avg D e avg L G G G A π λ π λ ( ) 1 4 D D t L G G π λ

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