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//define the S-paramters of the transistor at resonance frequency
s11=1.1*exp(%i*(170)/180*%pi);
s12=0.4*exp(%i*(-98)/180*%pi);
s21=1.5*exp(%i*(-163)/180*%pi);
s22=0.9*exp(%i*(-170)/180*%pi);
s=[s11,s12;s21,s22];
//define oscillation frequency
f0=8e9;
w0=2*%pi*f0;
//define parameters of the dielectric resonator
Z0=50;
beta=7;
R=beta*2*Z0;
Qu=5e3;
//compute equivalent L and C
L=R/(Qu*w0);
C=1/(L*w0^2);
//find output reflection coefficient of the DR
Gout_abs=beta/(1+beta);
Gout_angle=-atan(imag(s11),real(s11))/%pi*180;
//compute electrical length of the transmission line for the DR
theta0=-1/2*Gout_angle
Gout=Gout_abs*exp(%i*Gout_angle*%pi/180);
//find the output impedance of the DR
Zout=Z0*(1+Gout)/(1-Gout)
// find the equivalent capacitance (it will be necessary for the computation of the oscillator without DR)
CC=-1/(w0*imag(Zout))
Rs=50;
//define the frequency for the plot
delta_f=0.05e9; //frequency range
f=f0-delta_f/2 : delta_f/100 : f0+delta_f/2;
w=2*%pi*f;
if theta0<0
theta0=360+theta0;
end;
theta=theta0*f/f0/180*%pi;
//repeat the same computations as above, but for specified frequency range
Gs=(Rs-Z0)/(Rs+Z0);
G1=Gs*exp(-%i*2*theta);
R1=Z0*(1+G1)./(1-G1);
Zd=1./(1/R+1./(%i*w*L+%i*w*C));
R1d=R1+Zd;
G1d=(R1d-Z0)./(R1d+Z0);
G2=G1d.*exp(-%i*2*theta);
//compute the output reflection coefficient (we have oscillations if |Gout|>1)
Gout=s22+s12*s21*G2./(1-s11*G2);
figure;
plot(f/1e9,abs(Gout),'b','linewidth',2);
title('Output reflection coefficient of the oscillator with DR');
xlabel('Frequency f, GHz');
ylabel('Output reflection coefficient |\Gamma_{out}|');
mtlb_axis([7.975 8.025 0 14]);
//Redefine the frequency range (we have to increase it in order to be able to observe any variations in the response
delta_f=5e9;
f=f0-delta_f/2 : delta_f/100 : f0+delta_f/2;
w=2*%pi*f;
//Compute the output reflection coefficient of the oscillator but with DR replaced by a series combination of resistance and capacitance
ZZ2=real(Zout)+1./(%i*w*CC);
GG2=(ZZ2-Z0)./(ZZ2+Z0);
GG=s22+s12*s21*GG2./(1-s11*GG2);
figure;
plot(f/1e9,abs(GG),'r','linewidth',2);
title('Output reflection coefficient of the oscillator without DR');
xlabel('Frequency f, GHz');
ylabel('Output reflection coefficient |\Gamma_{out}|');
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