ZIP with MATLAB scripts and note:
exercise 6.3
exercise 6.3 notes:
c0=2.998792586
er=1
f1=4e9;f2=6e9;f0=5e9
Nf=1e6 % amount frequency points between f1 f2
df=abs(f1-f2)/(Nf+1) % frequency resolution
f=[f1:df:f2];
delta_f=f-f0;
lambda1=c0/f1;lambda2=c0/f2;lambda0=c0/f0
dlambda=abs(lambda1-lambda2)/(Nf+1)
lambda=[lambda2:dlambda:lambda1];
L=lambda0/4
RLoad=1e9;Rgen=50;
ZL=RLoad; % load assumed constant resistance over all band
Z0=Rgen;
alpha=.1;beta=2*pi./lambda;
D=1/4
Zin_1=...
Z0*(ZL+Z0*tanh(alpha*D*c0./f+1j*2*pi*f/c0*L))./...
(Z0+ZL*tanh(alpha*D*c0./f+1j*2*pi*f/c0*L));
% lossy TL general expression
[min_absZin nf0]=min(abs(Zin_1))
f(nf0)
Zin_3=Z0./(alpha*L+1j*2*pi*delta_f*2*pi/(2*pi*f0));
% 2nd approximation
Zin_1_lossless=Z0*1j*cot(2*pi*f/c0*L); % lossless TL
min_absZin = 2.500056844268334e-04
nf0 = 500002
= 5.000000099999900e+09
even reducing the open circuit value and increasing alpha, Zin peak is quite sharp so the top graph of the plot on right hand side has been zoomed
figure(1); % lossy transmission line
subplot(2,1,1);plot(f,abs(Zin_1));
title('exact |Zin1|');grid on
subplot(2,1,2);plot(f,angle(Zin_1));
title('exact phase(Zin1)');grid on
figure(2); % lossy transmission line
subplot(2,1,1);
plot(f,real(Zin_1));title('exact real(Zin1)');grid on
subplot(2,1,2);plot(f,imag(Zin_1));
title('exact Im(Zin1)');grid on
figure(3); % lossless transmission line
plot(f,abs(Zin_1_lossless));title('ideal TL |Zin1|');grid on
figure(5); % 2nd approximation
subplot(2,1,1);hold all;
plot(f,real(Zin_3));
title('2nd approximation real(Zin3)');grid on
subplot(2,1,2);hold all;plot(f,imag(Zin_3));
title('2nd approximation Im(Zin3)');grid on
R=real(Zin_1);
X=imag(Zin_1./(delta_f));
figure(6);plot(f,X);grid on;title('L with exact Zin')
R=real(Zin_3);
X=imag(Zin_3./(2*delta_f));
figure(7);plot(f,X);grid on;title('L with approximate Zin')
C=-1/X(nf0)
R=R(nf0)
% unloaded Q
Q0=2*pi*f0*R*C
% or Q=pi*Z0/(Z0*alpha*length_TL)
pi/(alpha*lambda0)
% or Q=beta/(2*alpha)
beta(nf0)/(2*alpha)
C =
5.026538250561876e-07
R =
4.747528413972352e+04
Q0 =
7.496981465000001e+08
=
5.238095939439863e+10
=
5.236000596344180e+10