Resonator profile

resonatorprofile(nu,nu0,Qu,beta,type)
out = resonatorprofile(nu,nu0,Qu,beta,type)
[nu,out] = resonatorprofile([],nu0,Qu,beta,type)

% Different output options
H = resonatorprofile(nu,nu0,Qu,beta,'transferfunction')
Gamma = resonatorprofile(nu,nu0,Qu,beta,'voltagereflection')
Prefl = resonatorprofile(nu,nu0,Qu,beta,'powerreflection')

This function computes the resonator profile and can return the transfer function, the voltage reflection coefficient or the power reflection coefficient. nu is the frequency range vector, in GHz, over which it is computed. If it is empty, an appropriate range is chose automatically. nu0 is the resonator resonance frequency in GHz. Qu is the unloaded Q-factor of the resonator. beta is the coupling coefficient: 1 for critical coupling (matched), less than 1 for undercoupling, and greater than 1 for overcoupling.

The loaded Q-factor is related to the unloaded Q-factor Qu and the coupling coefficient beta through:

The option type can be used to request either of the following:

• transferfunction - the resonator transfer function
  
• voltagereflection - the voltage reflection coefficient, i.e. the ratio of the E-fields of the reflected wave and the incoming wave
  
• powerreflection - the power reflection coefficient
  

If no output is requested, resonatorprofile plots the results.

Here is a simple example

nu = linspace(9.2,9.8,1001);   % GHz
nu0 = 9.5;                     % GHz
Qu = 1000;
beta = 1;
resonatorprofile(nu,nu0,Qu,beta,'voltagereflection');

To plot the power reflection coefficient on a logarithmic dB scale, use

P_refl = resonatorprofile(nu,nu0,Qu,beta,'powerreflection');
plot(nu,10*log10(P_refl));
xlabel('frequency (GHz)');
ylabel('reflected power (dB)');

resonator