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Antennas/Radiation Six 22 m antennas comprising the Australia Telescope Compact Array (ATCA) Why do moving charges radiate? http://www.cco.caltech.edu/~phys1/java/ phys1/MovingCharge/MovingCharge.html Hertzian Dipole Static charge Uniform velocity Sudden acceleration Uniform acceleration p = I0l/w Eq = m0 d2p/dt2 x sinqq/4pr = (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) Shortening Cerenkov Radiation 1/[1-vcosq/c] Source outruns wave Front falls behind, like the wake of a boat v < c/n v > c/n Why do moving charges radiate? Rest position of charge at t=0 Charge stops accelerating here at t=Dt Present position of charge uniformly moving at time t 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 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 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. Why do moving charges radiate? Optical “Shock Front” Kink Propagates outwards at speed of light Eq q q vt Er = q/4pe0r2 r=ct v=aDt Eq = Er (vtsinq/cDt) = (q/4pe0c2)(vsinq/Dt)(1/ct) Eq q q vt Er = q/4pe0r2 r=ct v=aDt Eq = (qm0/4p)asinq/r 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) 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 Disconnect between outside and inside Kinks/loops Eq ~ m0qasinq/4pr Hj ~ Eq/Z0 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’ From A to B ^ R^ Rq B = x A = ∂/∂R ∂/∂q AR RAq ^ Rsinqj 2sinq /R ∂/∂j RsinqAj 2 ^ = m0p0jwej(wt-bR)sinqj(1+jbR)/4pR From B to E ^ ^ R Rq m0e0jwE = x B = ∂/∂R ∂/∂q BR RBq ^ Rsinqj 2sinq /R ∂/∂j RsinqBj E has two parts ^ 3 ^ E1 = p0ej(wt-bR)(1+jbR)(2Rcosq+qsinq)/4pe R 0 Oscillatory dipolar field ^ E2 = (m0sinq/4pR)(d2p/dt2)q Transverse radiation field Hertzian Dipole p = I0l/w E = E1 + E2 E1 = p0[sin(wt-br) + br.cos(wt-br)] x [2cosqr + sinqq]/4pe0r3 Usual dipolar field, with oscillations E2 = m0w2p0sin(wt-br)sinqq/4pr = m0 d2p/dt2 x sinqq/4pr = (qm0/4p)asinqq/r Transverse radiation field Radiation Patterns Transverse radiation field completes loops Dipole field Flipped Dipole field from oscillation term cos(wt-bR) Oscillatory term has a node Half-wave antenna I = I0ejwtsin(2pz/l) = I0ejwtsin(bz) L = l/2 Half-wave antenna Many small dipoles, for each of which dEq ~ m0wI(z)dzsinqej(wt-bR’)/4pR’ dz z q R Far field: Eq ~ jI0c2ej(wt-bR) F(q)/4pe0R F(q) = cos[(p/2)cosq]/sinq Half-wave antenna Far field: Eq ~ jI0c2ej(wt-bR) F(q)/4pe0R F(q) = cos[(p/2)cosq]/sinq Slightly tighter than point dipole L=l L = 1.5 l Parabolic Reflector (Dish Antenna) http://www.antenna-theory.com/antennas/dipole.php