Elements of electromagnetic field theory and guided waves Modes of a circular cavity Dipole radiation – Thomson model Hertzian dipole and its far-zone field Radiated power and radiation resistance Magnetic dipole Linear antenna Antenna excitation of a rectangular WG

Circular resonator since Top view Usually d<2a Side view:

Thompson’s model of dipole radiation z (t<<t) r r r t: a, v(t ≥ t)=at t’=(t-r/c) rays Let the charge acquire (+a), then (-a) and return back, etc. Series of pulses! Wave fronts Oscillating dipole creates a spherical EM wave

Hertzian dipole H x z E t’=t-R/c → q R>>l IA ,VA l<<l w Thomson’s formula: E t’=t-R/c → q R>>l IA ,VA l<<l leff w For phasors it takes form: Linear charge density Continuity equation: Hertzian dipole moment H=Hf=Eq/h

Radiated power and radiation resistance of a short dipole R>>l IAleff

Magnetic dipole z Hq x Ef R>>l p÷Eq Duality: E H q m÷Hf=-Eq /h pwm0 m/c m=m0ISaz S I <<l 2 -

Linear antennas l~(0.25…0.75)l l~(0.5…1.5)l l<<l Hertzian dipole No radiation from here No radiation from here l~(0.25…0.75)l l<<l l~(0.5…1.5)l No radiation from here Hertzian dipole (without spheres) Dipole linear antenna Monopole linear antenna h (if kh<p) Imax IA I(z) Cable, ground plane, or 2d arm

Antenna excitation of WG y TE10 TM11 b l S0 VA d d z VA d≈b/2 Consider the monopole excitation Find Rrad and C10