example 5.5

ZIP with MATLAB scripts and note:

example 5.5 notes:

ideal transmission line: D*lambda =D*c/f and L=D*lambda, then beta*L=2*pi/lambda*D*lambda

D=L/lambda=L/c*f

when f=f0 then L= lambda0/4 =c/(f0*4) then D=c/(f0*4) *f/c=f/f0*D0 and D0=1/4

for a lambda/4 TL transformer: Zin=Z1^2/ZL, to match ZL=10 ohm Zin=Z0, Z1=(ZL*Z0)^.5

ZL=10;Z0=50;f0=3e9;SWR=1.5 % SWR=<1.5

Z1=(ZL*Z0)^.5

mod_refl=(SWR-1)/(SWR+1)

fractional bandwidth Df/f0

df_over_f0=2-4/pi*acos(mode_refl/(1-mod_refl^2)^.5*2*(Z0*ZL)^.5/abs(ZL-Z0))

Z1 = 22.360679774997898

mod_refl = 0.200000000000000

df_over_f0 = 0.293159219437866

POZAR suggests to simplify s11 ~ abs(ZL-Z0)/(2*(Z0*ZL)^.5)*abs(cos(q))

for q near pi/2 (pg 247) but with MATLAB there is no need:

Z0=50;ZL=Z0*[2 4 10];Z1=(ZL*Z0).^.5;

f0=2e9;df=1e5;f=[1e9:df:3e9];D0=1/4;

figure;hold all

for k=1:1:numel(ZL)

Zin=Z1(k)*(ZL(k)+1j*Z1(k)*tan(2*pi*f/f0*D0))./(Z1(k)+1j*ZL(k)*tan(2*pi*f/f0*D0));

s11=(Zin-Z0)./(Zin+Z0);

plot(f,abs(s11));grid on

end

this graph for 3 different loads is more accurate than figure 5.12 in pg 249