Non linear analysis of circuits

[rassouly]

It would be great if we could also simulate P1dB, IIP3 and other non linear behavior of circuits under large probe signals. What would it take to implement this functionality?

[kpobrien]

That functionality already exists. hbnlsolve can simulate the response of the circuit for multiple large tones (and you could for example, consider one to be the pump and one to be the large probe). See the 2 pump JPA example. You can also compute the linearized response of the system (eg. a weak probe in addition to the other two tones) with the pump and large probe by calling hbsolve or hbnlsolve then hblinsolve. One thing to be careful about is the currents and node fluxes are the amplitudes in the frequency domain (the RFFT of the time domain signal). This may result in factors of 2 you need to consider if you care about the amplitudes of the tones. For a single strong tone, the frequencies are a 1d vector with all positive frequencies while two strong tones results in a 2d matrix with some negative frequencies.

using JosephsonCircuits
@variables wp1
w = (wp1,);
freq =  JosephsonCircuits.calcfreqsrdft((3,));
JosephsonCircuits.visualizefreqs(w,freq)

4-element Vector{Num}:
    0
  wp1
 2wp1
 3wp1

using JosephsonCircuits
@variables wp1,wp2
w = (wp1,wp2);
freq =  JosephsonCircuits.calcfreqsrdft((3,3));
JosephsonCircuits.visualizefreqs(w,freq)

4×7 Matrix{Num}:
    0         wp2         2wp2         3wp2        -3wp2        -2wp2        -wp2
  wp1   wp1 + wp2   wp1 + 2wp2   wp1 + 3wp2   wp1 - 3wp2   wp1 - 2wp2   wp1 - wp2
 2wp1  2wp1 + wp2  2wp1 + 2wp2  2wp1 + 3wp2  2wp1 - 3wp2  2wp1 - 2wp2  2wp1 - wp2
 3wp1  3wp1 + wp2  3wp1 + 2wp2  3wp1 + 3wp2  3wp1 - 3wp2  3wp1 - 2wp2  3wp1 - wp2

I'll make an example to illustrate this functionality when I get a chance. If you make such an example first and want to share, I'd welcome that contribution!

[rassouly]

Thank you very much for your answer! After posting this, I also realized that I could probably use a pump to simulate my strong signal.
I was looking for a way to change the probe amplitude in hbsolve (like I would do in real life on a VNA) but I realized that the linearization of the circuit entails that we are essentially probing at 0 power.
I'll try to write an example if I get this to work.

[kpobrien]

Exactly right! There is no probe power option in hbsolve because linearization implies it is infinitesimally small. I'd recommend running hbnlsolve in a loop similar to flux tunable JPA example.