% BINOMIAL MULTI SECTION MATCHING TRANSFORMER

% what does this program do ?
% 1. calculation of the values of all charachteristic Impedences of different sections.
% 2. plots the graph of VSWR vs. Frequency

% Done by Akhilesh Kumar Misra (991202) and Gaurav Singh (991210)

Z0=50;        % Characteristic Impedence
ZL=100;       % Load Impedence
FrBW=0.7;     % Fractional bandwidth
f0=100;       % central Frequency  
MaxSWR=1.1;   % Maximum Tolerable Impedence

Toue_m=(MaxSWR-1)/(MaxSWR+1); 
Toue_0=abs((ZL-Z0)/(ZL+Z0));         
Theta_m=(2-FrBW)*pi/4;
N=log10(abs(Toue_m/Toue_0))/log10(abs(cos(Theta_m))); % Number of Sections

if N<=0,
    N=1;
else N=ceil(N);
end

A=Toue_0*(2^(-1*N));

% we define an array Zn which contains characteristic impedences of each section
Zn=zeros([1 N+1]);

Zn(1)=Z0;

Bino_coeff=zeros([1 N]);
for i=0:N-1
    Bino_coeff(i+1)=factorial(N)/(factorial(i)*factorial(N-i));
end

for n=1:N,    
    temp=(1 + Bino_coeff(n)*A)/(1 - Bino_coeff(n)*A);
    Zn(n+1)=Zn(n)*temp;
end

% now here finding the value of VSWR

f=f0/3:f0/50:5*f0/3;
VSWR=zeros([1,length(f)]);

for i=1:length(f)
    Theta=pi*f(i)/(f0*2);
    T=abs( Toue_0 * ((cos(Theta))^N) );
    VSWR(i)=(1+abs(T))/(1-abs(T));
end

sprintf('The number of sections of transformer is %d.',N)
sprintf('The impedances of the sections from line to load %s',num2str(Zn(2:length(Zn))))
plot(f,VSWR);
title('Plot of VSWR vs f (binomial transformer)')
xlabel('fo->');
ylabel('VSWR->');