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Copy pathGenetic_optimization_simulation_ESRR_SRR2_varactor_periodic.m
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Genetic_optimization_simulation_ESRR_SRR2_varactor_periodic.m
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%%% this is a program that use simulated scattering parameters of a periodic array of metaunits in a parallel plate waveguide to generate sideband signals by mimiking a time-varying modulation. Genetic algorithm is used to optimze the modulation signal.
clear;
clc
ep0 = 8.854418e-15; %%%%%%%% unit: C/(V*mm)
u0 = 4*pi*1e-10; %%%%%%%% unit: V*s/(A*mm)
c=(ep0*u0)^(-0.5); %%%%%% unit: mm/s
s21fin1=fopen('s21_ESRR+SRRin1_period_px10py15.5_RO3.54.txt');
s21phfin1=fopen('s21phase_ESRR+SRRin1_period_px10py15.5_RO3.54.txt');
s11fin1=fopen('s11_ESRR+SRRin1_period_px10py15.5_RO3.54.txt');
s11phfin1=fopen('s11phase_ESRR+SRRin1_period_px10py15.5_RO3.54.txt');
s21fout1=fopen('s21_out1.txt','w');
s21phfout1=fopen('s21phase_out1.txt','w');
s11fout1=fopen('s11_out1.txt','w');
s11phfout1=fopen('s11phase_out1.txt','w');
while ~feof(s21fin1)
line1 = fgetl(s21fin1);
line2 = fgetl(s11fin1);
line3 = fgetl(s21phfin1);
line4 = fgetl(s11phfin1);
if ~isempty(line1)
if (line1(9)== 'F')||(line1(1)== '-');
status=fseek(s21fin1,0,0);
status=fseek(s11fin1,0,0);
status=fseek(s21phfin1,0,0);
status=fseek(s11phfin1,0,0);
else fprintf(s21fout1,'%s\r\n', line1);
fprintf(s11fout1,'%s\r\n', line2);
fprintf(s21phfout1,'%s\r\n', line3);
fprintf(s11phfout1,'%s\r\n', line4);
end
else continue
end
%end
end
fclose('all');
s21f=load('s21_out1.txt');
s21phf=load('s21phase_out1.txt');
s11f=load('s11_out1.txt');
s11phf=load('s11phase_out1.txt');
%%
npar1=55;npar=npar1*npar1;
F=s21f(1:1001,1);
s21=reshape(s21f(:,2),1001,npar);
s21ph=reshape(s21phf(:,2),1001,npar);
s11=reshape(s11f(:,2),1001,npar);
s11ph=reshape(s11phf(:,2),1001,npar);
s21n=zeros(1001,npar);
s21phn=zeros(1001,npar);
s11n=zeros(1001,npar);
s11phn=zeros(1001,npar);
sq=[1:1:npar];
s21n(:,1:npar)=s21(:,sq);
s21phn(:,1:npar)=s21ph(:,sq);
s11n(:,1:npar)=s11(:,sq);
s11phn(:,1:npar)=s11ph(:,sq);
s21_cc(:,:,:)=reshape(s21n,1001,npar1,npar1);
s21ph_cc(:,:,:)=reshape(s21phn,1001,npar1,npar1);
s11_cc(:,:,:)=reshape(s11n,1001,npar1,npar1);
s11ph_cc(:,:,:)=reshape(s11phn,1001,npar1,npar1);
V1=-0.8:0.2:10;
V2=-0.8:0.2:10;
V1I=-0.8:0.02:10;
V2I=-0.8:0.02:10;
% here we flip the phase from CST simulation so that it follows the convention of exp(-iwt)
S21_cc=s21_cc.*exp(-1i.*s21ph_cc.*pi/180);
S11_cc=s11_cc.*exp(-1i.*s11ph_cc.*pi/180);
%%
ff=4.00;
[dd,fi]=min(abs(F-ff));
Rs21c(:,:)=real(S21_cc(fi,:,:));
Is21c(:,:)=imag(S21_cc(fi,:,:));
Rs11c(:,:)=real(S11_cc(fi,:,:));
Is11c(:,:)=imag(S11_cc(fi,:,:));
s21_C(:,:)=S21_cc(fi,:,:);
s11_C(:,:)=S11_cc(fi,:,:);
for j=1:length(V2I)
for k=1:length(V1)
Rs21c_I(k,:)=interp1(V2,Rs21c(k,:),V2I,'spline');
Is21c_I(k,:)=interp1(V2,Is21c(k,:),V2I,'spline');
Rs11c_I(k,:)=interp1(V2,Rs11c(k,:),V2I,'spline');
Is11c_I(k,:)=interp1(V2,Is11c(k,:),V2I,'spline');
end
Rs21_CI(:,j)=interp1(V1,Rs21c_I(:,j),V1I,'spline');
Is21_CI(:,j)=interp1(V1,Is21c_I(:,j),V1I,'spline');
Rs11_CI(:,j)=interp1(V1,Rs11c_I(:,j),V1I,'spline');
Is11_CI(:,j)=interp1(V1,Is11c_I(:,j),V1I,'spline');
end
%
dz=0;
s11_CI=(Rs11_CI+1i.*Is11_CI).*exp(1i.*ff.*1e9*2*pi/c*dz);
s21_CI=(Rs21_CI+1i.*Is21_CI).*exp(1i.*ff.*1e9*2*pi/c*dz); %%% forward scattering needs substract incident wave
%
figure(190)
subplot(2,2,1)
sf=contour(V1I,V2I,abs(s11_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('|S11|, ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
subplot(2,2,2)
sf=contour(V1I,V2I,abs(s21_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s21');
view([0,90])
tt=horzcat('|S21|, ','Freq=',num2str(ff),' GHz');
colorbar;hold off
title(tt)
subplot(2,2,3)
sf=mesh(V1I,V2I,angle(s11_CI));
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S11), ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
subplot(2,2,4)
sf=mesh(V1I,V2I,angle(s21_CI));
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S21), ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
%%
figure(112)
subplot(2,2,1)
sf=contour(V1,V2,abs(s11_C),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('|S11|, ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
subplot(2,2,2)
sf=contour(V1,V2,abs(s21_C),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s21');
view([0,90])
tt=horzcat('|S21|, ','Freq=',num2str(ff),' GHz');
colorbar;hold off
title(tt)
subplot(2,2,3)
sf=mesh(V1,V2,angle(s11_C));
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S11), ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
subplot(2,2,4)
sf=mesh(V1,V2,angle(s21_C));
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S21), ','Freq=',num2str(ff),' GHz');
colorbar;hold off;
title(tt)
%%
%%%%% remove the additional phase accumulated along the waveguide
dz=0;
s11_CI=(Rs11_CI+1i.*Is11_CI).*exp(1i.*ff.*1e9*2*pi/c*dz);
s21_CI=(Rs21_CI+1i.*Is21_CI).*exp(1i.*ff.*1e9*2*pi/c*dz); %%% forward scattering needs substract incident wave
%%s21_CI=1-s11_CI;
Om=0.5e6; %%%% Hz, frequency of modulation
t=-1.0/Om:1e-3/Om:1.0/Om;
phi1=0.*pi/180; %%%% relative phase of capaciance modulation
phi2=0.*pi/180;
%%
AM=2;
Om=0.5e6; %%%% Hz, frequency of modulation
t=-1.0/Om:1e-3/Om:1.0/Om;
V1_0=2; %%% center of biased voltage
V2_0=2;
deltaV1=2;deltaV2=2; %%% amplitude of biased voltage
V1_t=V1_0+deltaV1.*cos(2.*pi.*Om.*t+phi1);
V2_t=V2_0+deltaV2.*cos(2.*pi.*Om.*t+phi2); %
phi1=0.*pi/180; %%%% relative phase of capaciance modulation
phi2=0.*pi/180;
a1=1;a2=0.0;a3=0.0;
for na=1:length(AM)
am=AM(na);
dc1=0.063*am; %%%% amplitude of capaciance modulation
dc2=0.03*am;
Omg=2.*pi.*Om;
V1_t=V1_0+deltaV1.*(a1*cos(Omg.*t+phi1)+a2*cos(2*Omg.*t+2*phi1)+a3*cos(3*Omg.*t+3*phi1));
V2_t=V2_0+deltaV2.*(a1*cos(Omg.*t+phi2)+a2*cos(2*Omg.*t+2*phi2)+a3*cos(3*Omg.*t+3*phi2));
for nt=1:length(t)
[V1a,nV1_a]=min(abs(V1_t(nt)-V1I));
[V2a,nV2_a]=min(abs(V2_t(nt)-V2I));
Rs11_t(nt)=real(s11_CI(nV2_a,nV1_a));
Rs21_t(nt)=real(s21_CI(nV2_a,nV1_a));
Is11_t(nt)=imag(s11_CI(nV2_a,nV1_a));
Is21_t(nt)=imag(s21_CI(nV2_a,nV1_a));
V1IT(nt)=V1I(nV1_a);
V2IT(nt)=V2I(nV2_a);
end
[pl,rs]=polyfit(t,Rs11_t,40);
[Rs11_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Rs21_t,40);
[Rs21_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Is11_t,40);
[Is11_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Is21_t,40);
[Is21_tfit,delta]=polyval(pl,t,rs);
t0=-0.5/Om:1e-3/Om:0.5/Om-1e-3/Om;
s11_t=Rs11_t(501:1500)+1i.*Is11_t(501:1500);
s21_t=Rs21_t(501:1500)+1i.*Is21_t(501:1500);
s11_t=abs(s11_t).*exp(1i.*angle(s11_t));
s21_t=abs(s21_t).*exp(1i.*angle(s21_t));
%%% calculate the fourier spectrum
%%
t_ssb=exp(1i.*2*pi.*Om.*t0);% t_ssb is to test single side band
t_ssb=exp(1i.*(pi.*sin(2*pi*Om.*t0)));% t_ssb is to test single side band
nmax=8;
for n=0:1:nmax
fa=cos(2*pi.*Om.*n.*t0);
fb=sin(2*pi.*Om.*n.*t0);
dx=2*pi*Om.*(t0(2)-t0(1));
a_rf(n+1)=1/pi.*sum(s11_t.*fa)*dx;
b_rf(n+1)=1/pi.*sum(s11_t.*fb)*dx;
a_tr(n+1)=1/pi.*sum(s21_t.*fa)*dx;
b_tr(n+1)=1/pi.*sum(s21_t.*fb)*dx;
a_tr_ssb(n+1)=1/pi.*sum(t_ssb.*fa)*dx;
b_tr_ssb(n+1)=1/pi.*sum(t_ssb.*fb)*dx;
end
% note that for positive order, it means exp(-i\Omega t)=cos - i sin
s11_p=0.5*(a_rf-1i.*b_rf);
s11_n=0.5*(a_rf+1i.*b_rf);
s21_p=0.5*(a_tr-1i.*b_tr);
s21_n=0.5*(a_tr+1i.*b_tr);
s21_p_ssb=0.5*(a_tr_ssb-1i.*b_tr_ssb);
s21_n_ssb=0.5*(a_tr_ssb+1i.*b_tr_ssb);
As11=[fliplr(s11_p(2:end)),s11_n];
As21=[fliplr(s21_p(2:end)),s21_n];
As21_ssb=[fliplr(s21_p_ssb(2:end)),s21_n_ssb];
%AS11_AM(na,:)=As11;
%AS21_AM(na,:)=As21;
end
%%
N=-nmax:1:nmax;
figure(101)
%subplot(1,3,1)
stem(-nmax:1:nmax,abs(As21_ssb));hold on;
%stem(-nmax:1:nmax,abs(As21_ssb2));hold off;
%plot(AM,abs(AS21_AM(:,7:end)).^2);hold off;
figure(100)
subplot(1,3,1)
plot(t0,V1_t(501:1500));hold on
plot(t0,V2_t(501:1500),'r');hold off
legend('v1','v2')
subplot(1,3,2)
plot(t0,abs(s11_t));hold on;
plot(t0,abs(s21_t));hold off;
legend('s11','s21')
subplot(1,3,3)
plot(t0,phase(s11_t));hold on;
plot(t0,phase(s21_t));hold off;
legend('arg s11','arg s21')
%%%%%%%%%%%%%%%%%% voltage dependent capacitance
figure(200)
subplot(1,3,1)
sf=contour(V1I,V2I,abs(s11_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('|S11|, ','Freq=',num2str(ff),' GHz');
colorbar;hold on;
plot(V1_t,V2_t,'r');hold off
title(tt)
subplot(1,3,2)
sf=contour(V1I,V2I,abs(s21_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s21');
view([0,90])
tt=horzcat('|S21|, ','Freq=',num2str(ff),' GHz');
colorbar;hold on
title(tt)
plot(V1_t,V2_t,'r');hold off
subplot(1,3,3)
plot(t,V1_t);hold on;
plot(t,V2_t,'-.');hold off;
xlabel('t(s)');
ylabel('V1,V2(V)');
legend('V1','V2')
colorbar;hold on;
figure(201)
subplot(1,3,1)
sf=contour(V1I,V2I,angle(s11_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S11), ','Freq=',num2str(ff),' GHz');
colorbar;hold on;
plot(V1_t,V2_t,'r');hold off
title(tt)
subplot(1,3,2)
sf=contour(V1I,V2I,angle(s21_CI),25);
%set(sf, 'EdgeColor', 'none');
xlabel('V1(V)');
ylabel('V2(V)');
axis([min(V1),max(V1),min(V2),max(V2)])
zlabel('s11');
view([0,90])
tt=horzcat('arg(S21), ','Freq=',num2str(ff),' GHz');
colorbar;hold on;
plot(V1_t,V2_t,'r');hold off
title(tt)
subplot(1,3,3)
plot(t,V1_t);hold on;
plot(t,V2_t,'-.');hold off;
xlabel('t(s)');
ylabel('V1,V2 ');
legend('V1','V2')
colorbar;hold on;
%% optimization
warning on;
optimiz=1;
fit=0;
% relative phase of capaciance modulation
phi1=0.*pi/180; phi2=0.*pi/180;
% voltage dependent capacitance
Vf=1.8;
V1_0=2;
V2_0=2;
deltaV1=1.5;deltaV2=1.5;
V1_t=V1_0+deltaV1.*cos(2.*pi.*Om.*t+phi1)/2;
V2_t=V2_0+deltaV2.*cos(2.*pi.*Om.*t+phi2)/2;
% initial input parameters of waveform
% amplitude of modulation (offset tuned manually)
am1=deltaV1; am2=deltaV2;
% relative phase
phi1=0.*pi/180;
phi2=0.*pi/180;
% offset
offs1=V1_0;offs2=V2_0;
%%% degree of mutation in bias offset, amplitude and phases
% mutation in waveform coefficients
mutco=0.05;
% mutation in relative phase
mutph=5*pi/180;
% mutation in bias offset
mutof=0.10;
% mutation in voltage amplitude
mutam=0.10;
% when flag_sym=0, the sidebands coefficients have central symmetry
flag_sym=1;
% when iden_waveform=1, v1 and v2 have the same waveform
iden_waveform=0;
n_od=8; %%% number of orders in modulation
N_GR=50; %%% number of generation
N_Geno=50; %%% number of genos
nmax=15; %%%% number of orders of harmonics for HB analysis
n_objhm=nmax;
n_round=50; %%% number of rounds of optimization
BestOBJ_allpass=zeros(n_round,1);
AS21_best_allpass=zeros(n_round,nmax*2+1);
AS11_best_allpass=zeros(n_round,nmax*2+1);
A_best_allpass=zeros(n_round,2*n_od-1);
BestOBJ_allpass=zeros(n_round,1);
AS21_best_allpass=zeros(n_round,nmax*2+1);
AS11_best_allpass=zeros(n_round,nmax*2+1);
A1_best_allpass=zeros(n_round,n_od);
A2_best_allpass=zeros(n_round,n_od);
B1_best_allpass=zeros(n_round,n_od);
B2_best_allpass=zeros(n_round,n_od);
PH1_best_allpass=zeros(n_round,1);
PH2_best_allpass=zeros(n_round,1);
AM1_best_allpass=zeros(n_round,1);
AM2_best_allpass=zeros(n_round,1);
OF1_best_allpass=zeros(n_round,1);
OF2_best_allpass=zeros(n_round,1);
%
for pn=1:n_round
%%%% NA: new amplitude for different orders of modulation for different
%%%% genos, it is generated by hybridiing the best 4 and sorting the
%%%% other genos based on performance
NA1=zeros(N_Geno,n_od);NA2=zeros(N_Geno,n_od);
NB1=zeros(N_Geno,n_od);NB2=zeros(N_Geno,n_od);
NPH1=zeros(N_Geno,1);NPH2=zeros(N_Geno,1);
NAM1=zeros(N_Geno,1);NAM2=zeros(N_Geno,1);
NOF1=zeros(N_Geno,1);NOF2=zeros(N_Geno,1);
%%%% the matrix of sorted different orders of amplitude of modulation for different genos
%%%% according to the objective function
SortA1=zeros(n_od,N_Geno);SortA2=zeros(n_od,N_Geno);
SortB1=zeros(n_od,N_Geno);SortB2=zeros(n_od,N_Geno);
SortPH1=zeros(1,N_Geno);SortPH2=zeros(1,N_Geno);
SortAM1=zeros(1,N_Geno);SortAM2=zeros(1,N_Geno);
SortOF1=zeros(1,N_Geno);SortOF2=zeros(1,N_Geno);
%%% the objective function
BestOBJ=zeros(1,N_GR);
%%% the S parameters of different orders of harmonics for different genos
As21_Gn=zeros(N_Geno,nmax*2+1);
As11_Gn=zeros(N_Geno,nmax*2+1);
%%% S parameters for the best geno in each generation
Best_As21=zeros(N_GR,nmax*2+1);
Best_As11=zeros(N_GR,nmax*2+1);
%%% amplitude and phase for the best geno in each generation
Best_A1=zeros(n_od,N_GR);
Best_A2=zeros(n_od,N_GR);
Best_B1=zeros(n_od,N_GR);
Best_B2=zeros(n_od,N_GR);
Best_PH1=zeros(1,N_GR);
Best_PH2=zeros(1,N_GR);
Best_AM1=zeros(1,N_GR);
Best_AM2=zeros(1,N_GR);
Best_OF1=zeros(1,N_GR);
Best_OF2=zeros(1,N_GR);
%%% amplitude of modulation harmonics
A1=zeros(N_GR,n_od);B1=zeros(N_GR,n_od);PH1=zeros(N_GR,1);AM1=zeros(N_GR,1);OF1=zeros(N_GR,1);
A2=zeros(N_GR,n_od);B2=zeros(N_GR,n_od);PH2=zeros(N_GR,1);AM2=zeros(N_GR,1);OF2=zeros(N_GR,1);
%%% best four genos
BestA1=zeros(4,n_od);BestA2=zeros(4,n_od);
BestB1=zeros(4,n_od);BestB2=zeros(4,n_od);
BestPH1=zeros(4,1);BestPH2=zeros(4,1);
BestAM1=zeros(4,1);BestAM2=zeros(4,1);
BestOF1=zeros(4,1);BestOF2=zeros(4,1);
sign1_od=zeros(n_od,length(t));
sign2_od=zeros(n_od,length(t));
%%% define the coefficient of input waveform
% for channel 1
a1_0=[1,random('unif',-mutco,mutco,1,n_od-1)]; %%%% initial amplitude for different orders
b1_0=[1,random('unif',-mutco,mutco,1,n_od-1)]; %%%% initial amplitude for different orders
ph1_0=phi1+0.*random('unif',-mutph,mutph,1,1); %%%% initial phase for different orders
% for channel 2
a2_0=[1,random('unif',-mutco,mutco,1,n_od-1)]; %%%% initial amplitude for different orders
b2_0=[1,random('unif',-mutco,mutco,1,n_od-1)]; %%%% initial amplitude for different orders
ph2_0=phi2+random('unif',-mutph,mutph,1,1); %%%% initial phase for different orders
am1_0=am1.*(1+random('unif',-mutam,mutam,1,1));
am2_0=am2.*(1+random('unif',-mutam,mutam,1,1));
offs1_0=offs1.*(1+random('unif',-mutof,mutof,1,1))+random('unif',-mutof,mutof,1,1);
offs2_0=offs2.*(1+random('unif',-mutof,mutof,1,1))+random('unif',-mutof,mutof,1,1);
if am1_0+offs1>max(V1) am1_0=max(V1)-offs1;
end
if -am1_0+offs1<min(V1) am1_0=offs1-min(V1);
end
if am2_0+offs2>max(V2) am2_0=max(V2)-offs2;
end
if -am2_0+offs2<min(V2) am2_0=offs2-min(V2);
end
%%%%% Generation
for n_gr=1:1:N_GR
%%%%% Geno
for n_geno=1:1:N_Geno
%%% for the second generation use new genos formed based on the last
%%% generation
if n_gr>1
a1_0=NA1(n_geno,:); a2_0=NA2(n_geno,:);
b1_0=NB1(n_geno,:); b2_0=NB2(n_geno,:);
ph1_0=NPH1(n_geno,:); ph2_0=NPH2(n_geno,:);
am1_0=NAM1(n_geno,:);am2_0=NAM2(n_geno,:);
offs1_0=NOF1(n_geno,:);offs2_0=NOF2(n_geno,:);
end
%%% for geno number larger than 5, introduce mutation
if n_geno>4
a1=a1_0+random('unif',-mutco,mutco,1,n_od);
a2=a2_0+random('unif',-mutco,mutco,1,n_od);
b1=b1_0+random('unif',-mutco,mutco,1,n_od);
b2=b2_0+random('unif',-mutco,mutco,1,n_od);
ph1=ph1_0+0.*random('unif',-mutph,mutph,1,1);
ph2=ph2_0+random('unif',-mutph,mutph,1,1);
am1=am1_0.*(1+random('unif',-mutam,mutam,1,1));
am2=am2_0.*(1+random('unif',-mutam,mutam,1,1));
offs1=offs1_0.*(1+random('unif',-mutof,mutof,1,1))+random('unif',-mutof,mutof,1,1);
offs2=offs2_0.*(1+random('unif',-mutof,mutof,1,1))+random('unif',-mutof,mutof,1,1);
% limit the amplitude and offset within the bias
% voltage
if am1+offs1>max(V1) am1=max(V1)-offs1;
end
if -am1+offs1<min(V1) am1=offs1-min(V1);
end
if am2+offs2>max(V2) am2=max(V2)-offs2;
end
if -am2+offs2<min(V2) am2=offs2-min(V2);
end
% for geno number <4, use the hybrid geno without mutation
else
a1=a1_0;a2=a2_0;
b1=b1_0;b2=b2_0;
ph1=ph1_0;ph2=ph2_0;
am1=am1_0;am2=am2_0;
offs1=offs1_0;offs2=offs2_0;
end
% define the spectral component of modulation
for n=1:n_od
sign1_od(n,:)=flag_sym.*a1(n).*sin(n.*(2*pi.*Om.*t+ph1))+b1(n).*cos(n.*(2*pi.*Om.*t+ph1));
if iden_waveform==1
a2(n)=a1(n);b2(n)=b1(n);ph2=ph2;
end
sign2_od(n,:)=flag_sym.*a2(n).*sin(n.*(2*pi.*Om.*t+ph2))+b2(n).*cos(n.*(2*pi.*Om.*t+ph2));
end
% total signal
signal1=sum(sign1_od);
signal2=sum(sign2_od);
% normalized signal
signal_1n=signal1./max(abs(signal1));
signal_2n=signal2./max(abs(signal2));
%
V1_t=offs1+am1.*signal_1n;
V2_t=offs2+am2.*signal_2n;
%
%
for nt=1:length(t)
[V1a,nV1_a]=min(abs(V1_t(nt)-V1I));
[V2a,nV2_a]=min(abs(V2_t(nt)-V2I));
Rs11_t(nt)=real(s11_CI(nV2_a,nV1_a));
Rs21_t(nt)=real(s21_CI(nV2_a,nV1_a));
Is11_t(nt)=imag(s11_CI(nV2_a,nV1_a));
Is21_t(nt)=imag(s21_CI(nV2_a,nV1_a));
V1IT(nt)=V1I(nV1_a);
V2IT(nt)=V2I(nV2_a);
end
if fit==1
[pl,rs]=polyfit(t,Rs11_t,40);
[Rs11_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Rs21_t,40);
[Rs21_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Is11_t,40);
[Is11_tfit,delta]=polyval(pl,t,rs);
[pl,rs]=polyfit(t,Is21_t,40);
[Is21_tfit,delta]=polyval(pl,t,rs);
end
t0=-0.5/Om:1e-3/Om:0.5/Om-1e-3/Om;
if fit==1
s11_t=Rs11_tfit(501:1500)+1i.*Is11_tfit(501:1500);
s21_t=Rs21_tfit(501:1500)+1i.*Is21_tfit(501:1500);
s11_t=abs(s11_t).*exp(1i.*angle(s11_t));
s21_t=abs(s21_t).*exp(1i.*angle(s21_t));
else
s11_t=Rs11_t(501:1500)+1i.*Is11_t(501:1500);
s21_t=Rs21_t(501:1500)+1i.*Is21_t(501:1500);
s11_t=abs(s11_t).*exp(1i.*angle(s11_t));
s21_t=abs(s21_t).*exp(1i.*angle(s21_t));
end
% calculation of the Fourier components of S parameters
for n=0:1:nmax
fa=cos(2*pi.*Om.*n.*t0);
fb=sin(2*pi.*Om.*n.*t0);
dx=2*pi*Om.*(t0(2)-t0(1));
a_rf(n+1)=1/pi.*sum(s11_t.*fa)*dx;
b_rf(n+1)=1/pi.*sum(s11_t.*fb)*dx;
a_tr(n+1)=1/pi.*sum(s21_t.*fa)*dx;
b_tr(n+1)=1/pi.*sum(s21_t.*fb)*dx;
end
s11_p=0.5*(a_rf-1i.*b_rf);
s11_n=0.5*(a_rf+1i.*b_rf);
s21_p=0.5*(a_tr-1i.*b_tr);
s21_n=0.5*(a_tr+1i.*b_tr);
As11=[fliplr(s11_p(2:end)),s11_n];
As21=[fliplr(s21_p(2:end)),s21_n];
As21_linear=As21;
As11_linear=As11;
%figure(1)
%plot(spec);hold on;
%plot(peakposition,As21,'o');
%%%% objective function define the order of harmonic that requires maximum
%%%% efficiency. -As11_linear(nmax+1) is to substract 0
%%%% order if we only care single sideband
OBJ11(n_geno)=abs(As21_linear(n_objhm))./abs(As21_linear(n_objhm+2));
OBJ21(n_geno)=(abs(As21_linear(n_objhm))^2+1.*abs(As21_linear(n_objhm+2))^2)./(sum(abs(As21_linear).^2+abs(As11_linear).^2));
OBJ(n_geno)=min(OBJ11(n_geno),1/OBJ11(n_geno))*OBJ21(n_geno);
% Record the waveform parameters
A1(n_geno,:)=a1;B1(n_geno,:)=b1;PH1(n_geno,:)=ph1;AM1(n_geno,:)=am1;OF1(n_geno,:)=offs1;
A2(n_geno,:)=a2;B2(n_geno,:)=b2;PH2(n_geno,:)=ph2;AM2(n_geno,:)=am2;OF2(n_geno,:)=offs2;
% Record the spectrum
As21_Gn(n_geno,:)=As21;
As11_Gn(n_geno,:)=As11;
end
% sort the objective function
[Sobj,Cn]=sort(OBJ);
%%% Sort the parameter according the objective function achieved
SortA1(:,:)=A1(Cn,:).';
SortB1(:,:)=B1(Cn,:).';
SortPH1(:,:)=PH1(Cn,:).';
SortAM1(:,:)=AM1(Cn,:).';
SortOF1(:,:)=OF1(Cn,:).';
SortA2(:,:)=A2(Cn,:).';
SortB2(:,:)=B2(Cn,:).';
SortPH2(:,:)=PH2(Cn,:).';
SortAM2(:,:)=AM2(Cn,:).';
SortOF2(:,:)=OF2(Cn,:).';
% record the best spectrum for each generation
BestOBJ(n_gr)=Sobj(end);
Best_As21(n_gr,:)=As21_Gn(Cn(end),:);
Best_As11(n_gr,:)=As11_Gn(Cn(end),:);
% record the best parameter for each generation
Best_A1(:,n_gr)=SortA1(:,end);
Best_B1(:,n_gr)=SortB1(:,end);
Best_PH1(:,n_gr)=SortPH1(:,end);
Best_AM1(:,n_gr)=SortAM1(:,end);
Best_OF1(:,n_gr)=SortOF1(:,end);
Best_A2(:,n_gr)=SortA2(:,end);
Best_B2(:,n_gr)=SortB2(:,end);
Best_PH2(:,n_gr)=SortPH2(:,end);
Best_AM2(:,n_gr)=SortAM2(:,end);
Best_OF2(:,n_gr)=SortOF2(:,end);
%%% Choose the best four parameters for the current generation
BestA1(1:4,:)=SortA1(:,end-3:end).';
BestB1(1:4,:)=SortB1(:,end-3:end).';
BestPH1(1:4,:)=SortPH1(:,end-3:end).';
BestAM1(1:4,:)=SortAM1(:,end-3:end).';
BestOF1(1:4,:)=SortOF1(:,end-3:end).';
BestA2(1:4,:)=SortA2(:,end-3:end).';
BestB1(1:4,:)=SortB2(:,end-3:end).';
BestPH2(1:4,:)=SortPH2(:,end-3:end).';
BestAM2(1:4,:)=SortAM2(:,end-3:end).';
BestOF2(1:4,:)=SortOF2(:,end-3:end).';
%%% Generate new generation via hybridization
% waveform 1
NA1(1,:)=(BestA1(1,:)+BestA1(2,:))/2;NA1(2,:)=(BestA1(2,:)+BestA1(3,:))/2;
NA1(3,:)=(BestA1(3,:)+BestA1(4,:))/2;NA1(4,:)=(BestA1(4,:)+BestA1(1,:))/2;
NB1(1,:)=(BestB1(1,:)+BestB1(2,:))/2;NB1(2,:)=(BestB1(2,:)+BestB1(3,:))/2;
NB1(3,:)=(BestB1(3,:)+BestB1(4,:))/2;NB1(4,:)=(BestB1(4,:)+BestB1(1,:))/2;
NPH1(1,:)=(BestPH1(1,:)+BestPH1(2,:))/2;NPH1(2,:)=(BestPH1(2,:)+BestPH1(3,:))/2;
NPH1(3,:)=(BestPH1(3,:)+BestPH1(4,:))/2;NPH1(4,:)=(BestPH1(4,:)+BestPH1(1,:))/2;
NAM1(1,:)=(BestAM1(1,:)+BestAM1(2,:))/2;NAM1(2,:)=(BestAM1(2,:)+BestAM1(3,:))/2;
NAM1(3,:)=(BestAM1(3,:)+BestAM1(4,:))/2;NAM1(4,:)=(BestAM1(4,:)+BestAM1(1,:))/2;
NOF1(1,:)=(BestOF1(1,:)+BestOF1(2,:))/2;NOF1(2,:)=(BestOF1(2,:)+BestOF1(3,:))/2;
NOF1(3,:)=(BestOF1(3,:)+BestOF1(4,:))/2;NOF1(4,:)=(BestOF1(4,:)+BestOF1(1,:))/2;
NA1(5:end,:)=SortA1(:,5:end).';
NB1(5:end,:)=SortB1(:,5:end).';
NPH1(5:end,:)=SortPH1(:,5:end).';
NAM1(5:end,:)=SortAM1(:,5:end).';
NOF1(5:end,:)=SortOF1(:,5:end).';
% waveform 2
NA2(1,:)=(BestA2(1,:)+BestA2(2,:))/2;NA2(2,:)=(BestA2(2,:)+BestA2(3,:))/2;
NA2(3,:)=(BestA2(3,:)+BestA2(4,:))/2;NA2(4,:)=(BestA2(4,:)+BestA2(1,:))/2;
NB2(1,:)=(BestB2(1,:)+BestB2(2,:))/2;NB1(2,:)=(BestB2(2,:)+BestB2(3,:))/2;
NB2(3,:)=(BestB2(3,:)+BestB2(4,:))/2;NB1(4,:)=(BestB2(4,:)+BestB2(1,:))/2;
NPH2(1,:)=(BestPH2(1,:)+BestPH2(2,:))/2;NPH2(2,:)=(BestPH2(2,:)+BestPH2(3,:))/2;
NPH2(3,:)=(BestPH2(3,:)+BestPH2(4,:))/2;NPH2(4,:)=(BestPH2(4,:)+BestPH2(1,:))/2;
NAM2(1,:)=(BestAM2(1,:)+BestAM2(2,:))/2;NAM2(2,:)=(BestAM2(2,:)+BestAM2(3,:))/2;
NAM2(3,:)=(BestAM2(3,:)+BestAM2(4,:))/2;NAM2(4,:)=(BestAM2(4,:)+BestAM2(1,:))/2;
NA2(5:end,:)=SortA2(:,5:end).';
NB2(5:end,:)=SortB2(:,5:end).';
NPH2(5:end,:)=SortPH2(:,5:end).';
NAM2(5:end,:)=SortAM2(:,5:end).';
NOF2(5:end,:)=SortOF2(:,5:end).';
if n_gr>4
% sort all the best geno achieved in each generation so far
[S_bestobj,Cnbest]=sort(BestOBJ);
Bestsofar_A1=Best_A1(:,Cnbest);
Bestsofar_B1=Best_B1(:,Cnbest);
Bestsofar_PH1=Best_PH1(:,Cnbest);
Bestsofar_AM1=Best_AM1(:,Cnbest);
Bestsofar_OF1=Best_OF1(:,Cnbest);
Bestsofar_A2=Best_A2(:,Cnbest);
Bestsofar_B2=Best_B2(:,Cnbest);
Bestsofar_PH2=Best_PH2(:,Cnbest);
Bestsofar_AM2=Best_AM2(:,Cnbest);
Bestsofar_OF2=Best_OF2(:,Cnbest);
% choose the best 4 as source of mutation for the new
% generation, this can avoid degration if objective function
% becomes worse as the system evolves
NA1(5:8,:)= Bestsofar_A1(:,end-3:end).';
NB1(5:8,:)= Bestsofar_B1(:,end-3:end).';
NPH1(5:8,:)= Bestsofar_PH1(:,end-3:end).';
NAM1(5:8,:)= Bestsofar_AM1(:,end-3:end).';
NOF1(5:8,:)= Bestsofar_OF1(:,end-3:end).';
NA2(5:8,:)= Bestsofar_A2(:,end-3:end).';
NB2(5:8,:)= Bestsofar_B2(:,end-3:end).';
NPH2(5:8,:)= Bestsofar_PH2(:,end-3:end).';
NAM2(5:8,:)= Bestsofar_AM2(:,end-3:end).';
NOF2(5:8,:)= Bestsofar_OF2(:,end-3:end).';
end
if pn>1 && 9+pn-2<=N_Geno
NA1(9:9+pn-2,:)=A1_best_allpass(1:pn-1,:);
NB1(9:9+pn-2,:)=B1_best_allpass(1:pn-1,:);
NPH1(9:9+pn-2,:)=PH1_best_allpass(1:pn-1,:);
NAM1(9:9+pn-2,:)=AM1_best_allpass(1:pn-1,:);
NOF1(9:9+pn-2,:)=OF1_best_allpass(1:pn-1,:);
NA2(9:9+pn-2,:)=A2_best_allpass(1:pn-1,:);
NB2(9:9+pn-2,:)=B2_best_allpass(1:pn-1,:);
NPH2(9:9+pn-2,:)=PH2_best_allpass(1:pn-1,:);
NAM2(9:9+pn-2,:)=AM2_best_allpass(1:pn-1,:);
NOF2(9:9+pn-2,:)=OF2_best_allpass(1:pn-1,:);
elseif pn>1 && 9+pn-2>N_Geno
NA1(9:end,:)=A1_best_allpass(pn+8-N_Geno:pn-1,:);
NB1(9:end,:)=B1_best_allpass(pn+8-N_Geno:pn-1,:);
NPH1(9:end,:)=PH1_best_allpass(pn+8-N_Geno:pn-1,:);
NAM1(9:end,:)=AM1_best_allpass(pn+8-N_Geno:pn-1,:);
NOF1(9:end,:)=OF1_best_allpass(pn+8-N_Geno:pn-1,:);
NA2(9:end,:)=A2_best_allpass(pn+8-N_Geno:pn-1,:);
NB2(9:end,:)=B2_best_allpass(pn+8-N_Geno:pn-1,:);
NPH2(9:end,:)=PH2_best_allpass(pn+8-N_Geno:pn-1,:);
NAM2(9:end,:)=AM2_best_allpass(pn+8-N_Geno:pn-1,:);
NOF2(9:end,:)=OF2_best_allpass(pn+8-N_Geno:pn-1,:);
end
% draw the best waveform and spectrum
for n=1:n_od
sign1_best(n,:)=flag_sym.*Best_A1(n,n_gr).*sin(n.*(2*pi.*Om.*t+Best_PH1(n_gr)))+Best_B1(n,n_gr).*cos(n.*(2*pi.*Om.*t+Best_PH1(n_gr)));
if iden_waveform==1
Best_A2(n,n_gr)=Best_A1(n,n_gr);
Best_B2(n,n_gr)=Best_B1(n,n_gr);
Best_PH2(n_gr)=Best_PH2(n_gr);
end