Mutual impedance between linear elements: The induced EMF method. Persa Kyritsi September 29th, 2005 FRB7, A1-104

Transcription

1 Mutual impedance between linea elements: The induced EMF method Septembe 9th, 5 FRB7, A-4

2 Outline Septembe 9, 5 Reminde: self impedance nduced EMF method Nea-field of a dipole Self impedance vs. Mutual impedance Summay and into to the poblem set

3 Antenna paametes Septembe 9, 5 Q: What ae the dipole antenna paametes? A: Geometical popeties (length, diamete), Radiation popeties (intensity, diectivity, gain, apetue, impedance) Q: Why antenna impedance? A: optimie eceived/ adiated powe? Q3: Why multiple antennas? Custom adiation/ gain.

4 Septembe 9, 5 Antenna impedance Thevenin equivalent cicuit (small, simple antennas) Antenna (diving point) impedance R R adiation esistance (e-adiated powe) R L loss esistance (dissipated powe) nput eactance (eactive powe) X A Unbounded, scatteing fee medium A Self-impedance Scatteing medium (gound plance, othe elements) f(seld-impedance, mutual impedance) A + R + A L jx A

5 Radiation esistance Septembe 9, 5 R adiation Methodology. Find total adiated enegy (Poynting vecto and integation). Nomalie to the cuent (input o maximum) (adiated enegy) R adiation cuent nomaliation W ( ) adiated WHY DO WE CARE?

6 Septembe 9, 5 Radiation esistance of λ/ dipole θ θ π θ θ π η φ θ sin cos cos cos,h sin cos cos cos E kl kl e j kl kl e j jk jk Ω 73 R sin W sin cos cos cos ),, ( P ad adiated λ π π θ θ φ θ θ π η φ θ l P d d kl kl

7 Antenna impedance Septembe 9, 5 Methods fo calculating the antenna impedance Bounday value (simplified antenna shapes) Tansmission line (biconical antennas) Poynting vecto: integation ove a closed suface Sphee (of sufficiently lage adius) Antenna suface (induced EMF method) ntegal equation- Method of Moments (E-MoM) Pocklington s intego-diffeential equation Hállen s E

8 Dipole geomety Septembe 9, 5 l/ d R P y x l/ R a

9 Septembe 9, 5 nduced EMF method Assumptions: finite, linea, thin, wie dipole antennas Nea filed egion of finite dipole: Quasi-stationay electic and magnetic fields Dominant eactive powe density Sinusoidal cuent distibution l ( ' ) sin k ' Self and mutual impedance Poynting vecto method Small adii dipole ka <<, l >> a

10 Septembe 9, 5 Nea fields of dipole Tangential electic field component ( a ) E j π e R jkr + e R jkr 4 cos kl e jk π fee space impedance cuent maximum

11 Septembe 9, 5 Deivation of the nea field fo the dipole Sinusoidal cuent distibution l ' sin k ' Vecto potential A ( ) A ˆ μ ˆ 4π ( ' ) Magnetic and electic fields C jkr H A, E μ jωε e R d' H

12 Septembe 9, 5 Deivation () ntegation contou fo eo adius wie (a): Cylindical coodinates (ρ,φ) with no φ vaiation Aimuthal symmety and fo ( ) ( ) ', ' ' l l y x y x R ρ ρ y ρ π φ ρ μ φ φ φ A H H ˆ ˆ

13 Septembe 9, 5 Deivation (3) Magnetic field Electic field (φπ/), cos l R l R e kl R e R e y j H jk jkr jkr ρ ρ π φ ( ) H j E E yh y y j E y φ ρ φ ωε ωε,

14 Septembe 9, 5 Self impedance nput impedance efeed to at the cuent maximum V m Rm + jx m nduced potential maximum V C dv C ( ' ) dv ( ) ( ) ( ) ' ' E ' C d'

15 Septembe 9, 5 Self impedance () nput impedance m efeed to at the cuent maximum m C sink l ' E ( ' ) d' C: integation contou on the suface of the dipole nput impedance i efeed to at the cuent at the input teminas i m sin kl ( )

16 Antenna poblems Septembe 9, 5 Poblem : Gandma s TV antenna Simple wie S: Antenna elements P: WLAN antenna design S: Antenna coupling

17 Septembe 9, 5 Mutual impedance Linea dipole adiating in the pesence of anothe element l / P l / li d

18 Mutual impedance () Septembe 9, 5 Antenna system two-pot netwok V V + + T-equivalent - - V, V

19 Septembe 9, 5 Mutual impedance Self impedance Mutual impedance (ecipocal netwoks) nput impedance (shot cicuit at pot ) V in V, V V, V V

20 Septembe 9, 5 Mutual impedance Mutual impedance efeed to at the input cuent of the antenna i sin V ( kl / ) sin( kl / ) i i i i C ( ' ) E ( ' ) C l sin k d' ' E ( ' ) C : integation contou on the suface of the antenna d'

21 Poblems Septembe 9, 5 Download the matlab scipt Calculate the self impedance of the antenna element as a function of l and λ the input impedance of the antenna element as a function of l and λ The adiation patten of the antenna system in the hoiontal plane as a function of l and d. Calculate the optimum combination of l,l and d fo a diective antenna system given λ