exercise 5.15
ZIP with MATLAB scripts and note:
exercise 5.15 notes:
without a 3D electromagnetic simulator, the key parameters that answer the question can still be calculated as follows:
c0=2.998e8;
f0=1e10;
etha0=377; % open air
er=20;
L=1e-3; % 1mm
a=2.286e-2;
k0=2*pi*f0/c0
beta_a=(k0^2-(pi/a)^2)^.5 % air filled waveguide
Za=k0*etha0/beta_a
% dimensions of the matching section
ZL=etha0
Zm=(Za*ZL)^.5
% propagation constant beta_m
% from Zm=k0*etha0/beta_m
beta_m=k0*etha0/Zm
% relative permittivity
% from beta_m=(er*k0^2-(pi/a)^2)^.5
er=(beta_m^2+(pi/a)^2)/k0^2
% physical length of the matching section
% from L_match=lambda_g/4
L_match=2*pi/(4*beta_m)
k0 = 2.095792297258034e+02
beta_a = 1.582312729300044e+02
Za = 4.993410477180422e+02
ZL = 377
Zm = 4.338796780095859e+02
beta_m = 1.821043335541571e+02
er = 1.184977544175792
L_match = 0.008625804208705
