# Trying to solve a four variable equation for a range of values

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Freddie Hoare on 6 Apr 2021 at 14:43
Commented: Freddie Hoare on 29 Apr 2021 at 22:24
Hello, I am trying to solve a noise parameter equation:
eqn1 = F == Fmin + ((4*Rn)/Z0)*((abs(gammas-gammaopt))^2/(abs(1+gammaopt)^2*(1-abs(gammas)^2)));
I have values for Fmin, Rn, gammas and gammopt (with Z0 being a constant).
My question is, how do I input a range of values for these variables and output a range of values for F?
Sorry if this is a relatively easy question, but I am quite new with Matlab and have been spending most of my time trying to input a range of values from ADS.
Freddie Hoare on 29 Apr 2021 at 22:24
syms gammas Z0 Fmin Rn gammaopt gammasreal gammasimag gammaoptreal gammaoptimag
F=sym ('F', [1 11])
gammaoptreal = [-0.605, -0.646,-0.682 ,-0.713,-0.736,-0.756,-0.774 ,-0.789,-0.802,-0.814,-0.825];
gammaoptimag= [0.489,0.462,0.439,0.417,0.394,0.375,0.357,0.340,0.325,0.311,0.298];
gammasreal= [-0.819,-0.820,-0.820,-0.821,-0.822,-0.822,-0.822,-0.822,-0.823,-0.823,-0.823];
gammasimag=[-0.406,-0.407,-0.408,-0.409,-0.409,-0.410,-0.410,-0.411,-0.411,-0.411,-0.412];
Z0 = [50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100];
Fmin = [3.922, 3.901,3.973 ,4.057,4.018,3.991,3.973,3.960,3.951,3.945,3.941];
Rn = [21.801, 21.847, 22.880, 23.992, 23.609, 23.336,23.155 , 23.026, 22.937,22.876 ,22.842];
gammas=complex(gammasreal, gammasimag)
gammaopt = complex(gammaoptreal, gammaoptimag)
solveF=F == Fmin + ((4*Rn)/Z0)*((abs(gammas-gammaopt).*abs(gammas-gammaopt)) /(abs(1+gammaopt).*abs(1+gammaopt) .*(1-abs(gammas).*abs(gammas) )));
% gammas = s_11 F = noise factor gammaopt = sopt Rn == noise
% resistance
Hi there, sorry I have taken so long to respond. Hope you are still available to help with this!
The values are all 1*11 arrays.

David Hill on 6 Apr 2021 at 15:22
If you want all possible combinations, then use ndgrid.
Z0=1.5;
Fmin=0:10;
Rn=1:20;
gammas=-10:1;
gammopt=13:.1:20;%I have no idea what these values are, just examples
[Fmin,Rn,gammas,gammopt]=ndgrid(Fmin,Rn,gammas,gammopt);%creates all possible combinations
F = Fmin(:) + (4*Rn(:)/Z0.*(gammas(:)-gammaopt(:)).^2)./((1+gammaopt(:)).^2.*(1-gammas(:).^2));
F=reshape(F,size(Fmin));%shapes F to same size as other matrices

R2020b

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