Nonideal RF coupler model, admittance matrix in QUCS simulation

Question

I'm trying to simulate a nonideal directional coupler in QUCS. Unfortunately, the only model available is the ideal one without taking into account the isolation or insertion loss values.

Initially, I tried to model these effects with attenuators, but comparing the results from different simulators (which have the nonideal models) I can see some crucial differences in the final circuit attenuation plot. Probably my equivalent circuit is wrong.

Schematic of the circuit with my coupler model:

I'm starting to think that the right way to model the nonideal coupler is only by modifying the source code of the component. I already considered this, and the parameters are easily accessible. This is for example the admittance matrix for AC analysis:

void coupler::initAC (void) {
  setVoltageSources (0);
  allocMatrixMNA ();
  nr_double_t k = getPropertyDouble ("k"); //coupling factor i.e. 0.707
  nr_double_t z = getPropertyDouble ("Z"); // reference impedance i.e. 50 Ohm
  nr_double_t p = deg2rad (getPropertyDouble ("phi")); //coupler phase shift i.e. 90 deg. 
  nr_double_t b = 2 * std::sqrt (1 - k * k);
  nr_complex_t a = k * k * (qucs::polar (1.0, 2 * p) + 1.0);
  nr_complex_t c = qucs::polar (2 * k, p);
  nr_complex_t d = z * (a * a - c * c);
  nr_complex_t y;
  y = a * (2.0 - a) / d;
  setY (NODE_1, NODE_1, y); setY (NODE_2, NODE_2, y);
  setY (NODE_3, NODE_3, y); setY (NODE_4, NODE_4, y);
  y = -a * b / d;
  setY (NODE_1, NODE_2, y); setY (NODE_2, NODE_1, y);
  setY (NODE_3, NODE_4, y); setY (NODE_4, NODE_3, y);
  y = c * (a - 2.0) / d;
  setY (NODE_1, NODE_3, y); setY (NODE_3, NODE_1, y);
  setY (NODE_2, NODE_4, y); setY (NODE_4, NODE_2, y);
  y = b * c / d;
  setY (NODE_1, NODE_4, y); setY (NODE_4, NODE_1, y);
  setY (NODE_2, NODE_3, y); setY (NODE_3, NODE_2, y);
}

The problem is that I don't know which values to modify or what to add. I have not derived this admittance matrix and after searching the literature (Pozar) I couldn't find any example similar to this.

Do I really need to modify this admittance matrix (in AC and then S-params model) or there is a different equivalent circuit to model the nonideal isolation in coupler? If I really need to modify the matrix could You suggest some steps?

Edit:

The directional coupler in my circuit is discrete "Ultra Low Profile 0805 3 dB, 90° Hybrid Coupler" (https://cdn.ttm.com/repository/products/wireless-xinger/3db-hybrid-couplers/C2327J5003AHF/C2327J5003AHF_Datasheet(Rev_I).pdf) I have revisited the Annaren site which was changed to TTM Technologies and found the S-parameter files to be easily accessible now (must have missed it before or something changed on the website) The S-parameter model is all I need. Before, I checked for the s4p file and didn't find it so I tried to model it with this nonideal discrete approach or by trying to modify the admittance matrix.

Answer 1

You have given us very little information about the coupler you are trying to model, apart from the fact that it is not ideal. If you know enough about it to jump in and modify the y-matrix directly, you probably know enough about it to use one of QUCS standard models.

If you have measured parameters, then use a .s2p file for the four port.

If you know enough about it to generate a .s2p file, then that is probably easier than modifying the source.

Why can't you improve your model? If it is a backward-wave coupler - use a pair of coupled transmission lines. If it is a lumped element coupler - model it as it is. If it is a branch-line hybrid, model it as it is, etc..

Note - I'm not a QUCS user, but I'm sure that you can use the available features of the program to significantly improve your model.