Antennas/Radiation

1. Antennas/Radiation Six 22 m antennas comprising the Australia Telescope Compact Array (ATCA)

2. Why do moving charges radiate? http://www.cco.caltech.edu/~phys1/java/ phys1/MovingCharge/MovingCharge.html

3. Hertzian Dipole p = I0l/w Eq= m0 d2p/dt2 xsinqq/4pr Static charge Uniform velocity Sudden acceleration Uniform acceleration = (qm0/4p)a(t)sinqq/r • Need accelerating charges a(t) • Transverse field components are the ones to notice Eq • 1/r dependence (radiation fields propagate far away) • Angle dependence (radiate perp. to oscillation)  sinq (Remember Brewster angle. Also watch kinks)

4. Source outruns wave Front falls behind, like the wake of a boat Shortening  Cerenkov Radiation 1/[1-vcosq/c] v < c/n v > c/n

5. Rest position of charge at t=0 Charge stops accelerating here at t=Dt Present position of charge uniformly moving at time t Why do moving charges radiate? First (larger) sphere launched at t=0 (left red dot) Second (smaller) launched at t=Dt (middle one) Both have evolved to their current sizes at t when charge is at the rt. dot

6. Why do moving charges radiate? Inside smaller sphere: see present uniformly moving charge and its radial field Outside larger sphere: See original static charge and its radial field Shaded area: created during acceleration 0 < t < Dt Here fields bend to connect the two other radial fields

7. Why do moving charges radiate? The kinks in this “sphere of influence” propagate as radiation fields. Note that they are angle-dependent and don’t decrease as fast with radius.

8. Why do moving charges radiate?

9. Optical “Shock Front” Kink Propagates outwards at speed of light

13. Er = q/4pe0r2 Eq vtsinq cDt vt cDt q q r=ct v=aDt Eq= Er (vtsinq/cDt) = (q/4pe0c2)(vsinq/Dt)(1/ct)

14. Er = q/4pe0r2 Eq vtsinq cDt vt cDt q q r=ct v=aDt Eq= (qm0/4p)asinq/r

15. Transverse E is radiated Eq(t) = (qm0/4p)[a(t’)]sin(q)/r Hf(t) = Eq/Z0 = (q/4pc)[a(t’)]sin(q)/r S = EqHf a2sin2(q)/r2 P ~ S.r2dW ~ constant (Larmor formula) t’ = t – r/c Electrostatics,∫E.dA independent of r (Flux field conserved) EM Radiation, ∫S.dA independent of r (Flux power conserved)

16. What about oscillating charges Kinks turn into loops http://www.falstad.com/emwave1/ http://www-antenna.ee.titech.ac.jp/~hira/hobby/edu/em/smalldipole/smalldipole.html

17. Kinks/loops Disconnect between outside and inside

18. Eq ~ m0qasinq/4pr Hj ~ Eq/Z0

19. Hertzian Dipole (far field) Delay effect A ~ m0Idej(wt-bR)/4pR = [m0wjpej(wt-bR)/4pR]z = [m0wjpej(wt-bR)/4pR](Rcosq-qsinq) Assume v << c so we ignore Doppler ‘shortening’ ^ ^ ^

20. R ∂/∂R AR Rq ∂/∂q RAq Rsinqj ∂/∂j RsinqAj /R2sinq  x A = From A to B ^ ^ ^ B = = m0p0jwej(wt-bR)sinqj(1+jbR)/4pR2 ^

21. R ∂/∂R BR Rq ∂/∂q RBq Rsinqj ∂/∂j RsinqBj /R2sinq  x B = From B to E ^ ^ ^ m0e0jw E =

22. E has two parts ^ ^ E1 = p0ej(wt-bR)(1+jbR)(2Rcosq+qsinq)/4pe0R3 Oscillatory dipolar field ^ E2 = (m0sinq/4pR)(d2p/dt2)q Transverse radiation field

23. Hertzian Dipole p = I0l/w E = E1 + E2 E1 = p0[sin(wt-br) + br.cos(wt-br)] x [2cosqr + sinqq]/4pe0r3 E2 = m0w2p0sin(wt-br)sinqq/4pr Usual dipolar field, with oscillations = m0 d2p/dt2 xsinqq/4pr = (qm0/4p)asinqq/r Transverse radiation field

24. Radiation Patterns Dipole field Transverse radiation field completes loops Flipped Dipole field from oscillation term cos(wt-bR) Oscillatory term has a node

25. Half-wave antenna I = I0ejwtsin(2pz/l) = I0ejwtsin(bz) L = l/2

26. Half-wave antenna Many small dipoles, for each of which dEq ~ m0wI(z)dzsinqej(wt-bR’)/4pR’ R’ = R-zcosq dz R z q Far field: Eq ~ jI0c2ej(wt-bR)F(q)/4pe0R F(q) = cos[(p/2)cosq]/sinq

27. Half-wave antenna Far field: Eq ~ jI0c2ej(wt-bR)F(q)/4pe0R F(q) = cos[(p/2)cosq]/sinq Slightly tighter than point dipole

28. L = l L = 1.5 l Parabolic Reflector (Dish Antenna) http://www.antenna-theory.com/antennas/dipole.php