exercise 5.21

Cheby_Ztransformer.m

​

function [g,Zr]=Cheby_Ztransformer(Z0in,ZLin,SWR,N)
% single freq chebyshev impedance transformer with N ;lambda/4 ideal transmission line sections
% Zr: characteristic impedance of each section of transformer
% g reflection input of each section
% script author: John Bofarull Guix

% Z0in=50;ZLin=100  % test inputs
% SWR=1.25              % max SWR
% N=4;                         % N amount lambda/4 sections to insert between Z0 and ZL

%%% Input Checks %%%%%%%%%%%%%%%%
if numel(ZLin)>1 || numel(Z0in)>1                                % ZLin Z0in scalars only
       sprintf('ZLin Z0in scalars only.\n');return;
end

if Z0in==ZLin                                                                       % input check:ZLin,Z0in!=0
    sprintf('ZLin Z0in must be different.\n');return;
end

if imag(ZLin)~=0 || imag(Z0in)~=0                                 % input check: imag ZLin,Z0in =0
    sprintf('ZLin Z) reals only. \n');return;
end

if ZLin>Z0in                                 % the table generated following POZAR pg 260 only applies to ZL>Z0
    Z0=Z0in;ZL=ZLin;
    reverse=0;                                                                  % reverse=0  ZL/Z0>1
else
    Z0=ZLin;ZL=Z0in;
    reverse=1;                                                                     % reverse=1 ZL/Z0<1
end
%%%%%%%%%%%%%

ZL_ov_Z0=ZL/Z0;                                                             % ZL/Z0>0 only

syms x y;
tn=chebyshevT(N,x)
tn_coeffs=coeffs(tn,'All');tn_coeffs=double(tn_coeffs([end:-1:1])) % most significant poly term is 1
tn_coeffs=tn_coeffs([end:-1:1]);                                                            % least significant poly term is 1
tn_coeffs=nonzeros(tn_coeffs)';                                                           % cosine power expansion either take all even or all odd terms only
fplot(tn,'b');axis([-1.2 1.2 -1.2 5]);grid on
hold all;plot([-1 1 1 -1 -1],[-1 -1 1 1 -1],'r')                                            % band pass red rectangle

gamma_L=(ZL-Z0)/(ZL+Z0)                            % reflection that would be without impedance transformer
gamma_m=(SWR-1)/(SWR+1)                                            % worst allowed reflection within pass band

A=gamma_m                                 % Cheby polys always catch max reflection at both edges of band
% BLm=asec(cosh(1/N*acosh(1/gamma_m*abs(gamma_L))))
BLm=asec(cosh(1/N*acosh(abs(log(ZL/Z0)/(2*gamma_m)))))
BLm_degree=BLm*180/pi
a=sec(BLm)                                                                                         % = sec(theta_m)

remN2=rem(N,2);k=1;p={}            % generating matrix p to equate cheby coeffs to cos power expansions
for N0=[N:-2:0]
    switch remN2
        case 0
            n=N0/2;
            K1=[0:1:n-1];  N1=N0*ones(1,numel(K1));        
            p=[p; tn_coeffs(k)*[1/2^(N0-1)*arrayfun(@(a,b) nchoosek(a,b),N1,K1)  1/2^N0*nchoosek(N0,n) ]]
            k=k+1;
        otherwise
            n=(N0-1)/2;
            K1=[0:1:n]; N1=N0*ones(1,numel(K1));        
            p=[p; 1/4^n*tn_coeffs(k)*[ arrayfun(@(a,b) nchoosek(a,b),N1,K1) ]]
            k=k+1;
    end
end
p2=zeros(max(size(p)))
for k=1:1:max(size(p))
    L=p{k}
    p2([numel(L):-1:1],k)=L;
end
 p2=flip(p2)
 
g=sum(repmat(A/2*a.^[N:-2:0],max(size(p)),1).*p2,2)'   % generating 1st half reflection coefficients

if mod(numel(g),2)~=0    % correcting DC for even exponent, ene N cos power expansions with DC term
    g(end)=2*g(end);
end

gplot=g;   % use exact method for SWR plot

% g3=[zeros(1,N+1-numel(g)) flip(g)]                    % generating remaining reflection coefficients
g3=[zeros(1,N+1-numel(g)) g]    
g3([1:N+1-numel(g)])=g([1:N+1-numel(g)])
g=g3;

Zr=zeros(1,numel(g))                
if (~reverse)                                 % exact calculation
    Zr(1)=ZL;
    for k=2:1:numel(g)
         Zr(k)=Zr(k-1)/((1+g(k-1))/(1-g(k-1)));
    end
     Zr=flip(Zr)
    elseif (reverse) % reverse=0
        Zr(1)=ZL;
        for k=2:1:numel(g)
            Zr(k)=Zr(k-1)*(1+g(k-1))/(1-g(k-1));
        end
         Zr=flip(Zr)
end

% if (~reverse)                                % approximate
%     Zr(1)=ZL;
%     for k=2:1:numel(g)
%          Zr(k)=exp(log(Zr(k-1))-2*g(k-1));
%     end
%       Zr=flip(Zr)
%     elseif (reverse)       %  ZL<Z0
%         Zr(1)=ZL;
%         for k=2:1:numel(g)
%             Zr(k)=exp(log(Zr(k-1))+2*g(k-1));
%         end
%           Zr=flip(Zr)
% end

Zr
Zr/Z0

k2=1;                                                                       % generating variables for reflection coefficients of transformer
for s=0:1:size(g,2)-1
    str1=['g' num2str(s) '=' num2str(g(k2)) ];
    evalin('base',str1);
    k2=k2+1;
end
for s=1:1:size(Zr,2)                          % generating variables for characteristic impedances of transformer
    str1=['Z' num2str(s-1) '=' num2str(Zr(s)) ];
    evalin('base',str1);
%     k2=k2+1;
end

end