function Example_Simplex
%Simplex Optimizer Example:
%
% Say we have measured an input impedance to a circuit, and we want to
% match that input impedance to a circuit model. The network analysis
% routines combined with a Simplex optimizer is an efficient and accurate
% method to accomplish a matched circuit model.
%
% Here, Jean-Luc Dellis's simplex alogorithm is used. Search for
% "simplexe" on Matlab's File Exchange. The file is simplexe.m
% Match to circuit: R1 + C1 + (L1 || C2 || R2) (only optimize for L1, C2
% and R2) R1=100ohm, C1=150pF. We're shooting for the optimizer to find
% that L1=1uH, C2=100pF, and R2=50ohms
%
% The optimizer does great with this circuit as long as the resonance is
% fairly damped. Once it becomes "sharp" (or high Q), the optimizer gets
% the wrong answer. Try making R2=500 ohsm, and see that the answer is
% wrong. I believe this is due to a couple factors. First, the imaginary
% to real ratio large, which adds difficults, and second there are
% probably multiple minima, which makes the simplex optimizer go off on
% the wrong route.
f=transpose(linspace(100e3,50e6,1e3)); %Set up the frequency vector, make it a column vector
z=model([1e-6,100e-12,50],f); %This is the ideal circuit that we're going to try and optimize for
%z=model([1e-6,100e-12,500],f); %Uncomment this to make the optimizer fail, set R2=500ohms, and make the resonance sharp
z(:,1)=z(:,1).*(1+0.05*randn(size(z(:,1)))); % We'll add some noise to make it hard
z(:,2)=z(:,2).*(1+0.05*randn(size(z(:,2)))); % We'll add some noise to make it hard
p=[0.1e-6,300e-12,10]; %Here's our initial guess, p=[L1,C2,R2] (not very good guesses!)
p=simplexe(@model,p,f,z); %Now we'll have the simplex optimizer try and find the correct values for L1, C2 & R2
disp(sprintf('L= %0.3guH C= %0.3gpF R=%0.3gohms',p(1).*1e6,p(2).*1e12,p(3))); %Print the values.
Zopt=model(p,f); %This is the answer the optimizer found.
%Plot the results
figure(1)
subplot(2,1,1)
plot(f,z(:,1),'r',f,Zopt(:,1),'c');
legend('Original Z','Optimized Z')
ylabel('Real Input Impedance, ohms')
subplot(2,1,2)
plot(f,z(:,2),'r',f,Zopt(:,2),'c');
xlabel('Freq, Hz');
ylabel('Imaginary Input Impedance, ohms')
end
function z=model(p,f)
%Here's our model for the optimizer to use
n=1;
ABCD{n} = ser_r(f,100); n=n+1; %R1
ABCD{n} = ser_c(f,150e-12); n=n+1; %C1
ABCD{n} = par_l(f,p(1)); n=n+1; %L1
ABCD{n} = par_c(f,p(2)); n=n+1; %C2
ABCD{n} = par_r(f,p(3)); n=n+1; %R2
ZZ=ImpedanceIntoCell(ABCD,1);
z = [10.*real(ZZ),imag(ZZ)];
end
