example 5.8

c=3e8;Z0=50;ZL=100;

D0=4;

f0=2e9;lambda=c/f0;L=D0*lambda;

dz=L/10000;z1=[0:dz:L/2-dz];

z2=[L/2:dz:L];

 

% triangular taper

Z1=Z0*exp(2*(z1/L).^2*log(ZL/Z0));

Z2=Z0*exp((4*z2/L-2*z2.^2/L^2-1)*log(ZL/Z0));

z=[z1 z2];

Z_triang=[Z1 Z2];

figure(1);plot(z,Z_triang);grid on;hold all

 

% the constant Z doesn't give the expected result because

% Z varies along z, pg262 s11_triang~=(Z_triang-Z0)./(Z_triang+Z0)

 

dD=.001;D=[0:dD:D0];

gamma_triang_mod=.5*log(ZL/Z0)*((sin(pi*D))./(pi*D)).^2;

figure(2);plot(gamma_triang_mod);grid on;hold all

 

% exponential taper

a=1/z(end)*log(ZL/Z0);

Z_exp=Z0*exp(a*z);

figure(1);plot(z,Z_exp);

 

gamma_exp_mod=.5*log(ZL/Z0)*abs(sin(2*pi*D))./(2*pi*D);

figure(2);plot(gamma_exp_mod);

 

% Klopfenstein taper

 

gamma0=.5*log(ZL/Z0);

 

% requirement

gamma_m=.02;

 

A=acosh(gamma0/gamma_m);

 

gamma_klopfy=gamma0/cosh(A)*cos(((2*pi*D).^2-A^2).^.5);

figure(2);plot(abs(gamma_klopfy));ax2=gca;

 

legend('triang','exp','klopf');