% Statistical Variation on Shielded Pair

close all
clear all
clc

wire_diameter = 1 ; % wire diameter
wire_space = 1.5 ; % distance between wire centers
er = 4 ;
N = 376.73 ;

% Analytical Solution
d = wire_diameter ;
D = wire_space ;   
ZoA = N/pi/2/sqrt(er)*acosh((2*D^2-d^2)/d^2);

% Random Parameters
ss = 1000 ; % sample size
Zo = zeros(1,ss) ; % Characteristic Impedance matrix
DT = .001 ; % dimensional tolerance
    
for i=1:ss
    
    % Analytical Solution with Statistical Variation
    d = wire_diameter + (rand-.5)*2*DT ;
    D = wire_space + (rand-.5)*2*DT ;   
    Zo(i) = N/pi/2/sqrt(er)*acosh((2*D^2-d^2)/d^2) ;
    
end

figure
plot(Zo)
title('Z_0 in Statistically Varying Dimensions of Wire Pair')

% Sinusoidal Variation
% d = d*(DT*sin((1:ss)/(pi*ss/20))+1); % vary wire diameter sinusoidally
D = D*(DT*sin((1:ss)/(pi*ss/20))+1); % vary wire separation sinusoidally
% NOTE: When both diameter and separation are varied together, the effects
% cancel each other out.
Zos = N./pi./2./sqrt(er).*acosh((2.*D.^2-d.^2)./d.^2) ;

figure
plot(Zos)
title('Z_0 in Sinusoidally Varying Dimensions of Wire Pair')