Scattering parameters

[Lennart-Quantware]

Hello,

Would it be possible to specify a scattering parameter matrix between ports and include it in a harmonic balance simulation which includes junctions?

Lennart

[kpobrien]

Hi Lennart, good to hear from you. You can using frequency dependent resistors/impedances (they can be complex valued and have arbitrary frequency dependence). Search for @register_symbolic in this issue #7 . In brief, you would define the scattering parameter matrix in terms of impedances, define those functions, register them as symbolic functions, then add the symbolic variable as an argument in hbsolve. A few tricky parts: make sure you take the absolute value of the frequency (since the idlers will have negative frequencies in the simulation) and if the real part of the resistance is negative, that will break quantum efficiency calculation. The scattering parameters will still be correct.

Longer term, I'm working towards building a scattering parameter based harmonic balance solver which can directly operate on arbitrary scattering parameter matrices, but I don't know the timeline for that.

[Lennart-Quantware]

Great! Thank you so much, I'm now able to simulate a 2-port network with arbitrary transmission function by converting it to equivalent Z-parameters.

Would be nice indeed if arbitrary S-parameters are natively supported, but for now this will work fine.
I did run into a couple of issues, just wanted to share them in case you are going to work on this in the future.

1. Any element in the circuit as a function of w needs to be registered with @register_symbolic which in turns needs to be placed at the top level, so I can't put it easily into a neat function.
2. It seems to be incompatible with lossy elements, for example when adding a lossy capacitor with value 1e-12 * 1 / (1 + im * 1e-3) to the circuit dict, I need to update the type of the circuit dict from Tuple{String,String,String,Num} to Tuple{String,String,String,Complex{Num}} but then Symbolics is throwing an InexactError because it is trying to interpret a Complex value as a Real.

Lennart

[kpobrien]

Good! Regarding (1) and (2), if you post minimal examples of those I can take a look.