% correction calculations

clear


syms Gzo Gsc Goc Gm
% solution # 1 & 2

   delta = (Gzo-Gsc)/(Goc-Gzo);
   M0     = simple((1-delta)/(1+delta));
   T1    = simple((Gzo-Gsc)*(1+M0));
   T2    = simple((Goc-Gzo)*(1-M0));
   D     = Gzo;

   G1= (Gm-D)/(T1+(Gm-D)*M0);
   G2 = (Gm-D)/(T2+(Gm-D)*M0);

   G1 = simple(G1);
   G2 = simple(G2);
   
 % s
 
  clear Gzo Gsc Goc  D T M Gm G
 
 syms Gzo Gsc Goc T M G Gm
  

 %  Gm = D + T*G/(1-M*G)        % the fundamental equation 
 D   = Gzo;                     % measure Zo, G = 0; therefore D = Gzo
 Eq1 = D + T/(1-M) - Goc;       % measure open circuit,  G=+1;
 Eq2 = D - T/(1+M) - Gsc;       % measure short circuit, G=-1;
 
 
 s = solve(Eq1,Eq2, T, M);      % solve for T & M in terms of Goc, Gsc
 M=simple(s.M);              
 T=simple(s.T);
 Eq0 = D + T*G/(1-M*G) - Gm;   % fundamental equation rewritten
 G   = simple(solve(Eq0,G))    % solve E0 for G in terms of Gm, D,T,M,
                               % (which are now in terms of Gzo, Goc,Gsc)