MixedModeConverter

class pmrf.models.components.ideal.MixedModeConverter(*, name: str | None = None, metadata: Any = None)

Bases: Model

(experimental) An ideal, lossless, frequency-independent 4-port mixed-mode converter.

This component converts a pair of equal-impedance physical (single-ended) ports into a differential-mode and a common-mode port, using the AWR voltage/current convention

\[V_d = V_p - V_n, \qquad V_c = \frac{V_p + V_n}{2},\]

with the corresponding modal currents, taken as flowing into the converter alongside the physical currents,

\[I_d = \frac{I_n - I_p}{2}, \qquad I_c = -(I_p + I_n).\]

Port ordering:

  • Port 1: differential mode of ports 3 and 4

  • Port 2: common mode of ports 3 and 4

  • Port 3: physical (single-ended) positive port p

  • Port 4: physical (single-ended) negative port n

With every port referenced to the same impedance \(Z_0\), this gives the signed scattering matrix

\[\begin{split}S = \frac{1}{3} \begin{bmatrix} 1 & 0 & 2 & -2 \\ 0 & -1 & 2 & 2 \\ 2 & 2 & 0 & 1 \\ -2 & 2 & 1 & 0 \end{bmatrix},\end{split}\]

which is real, symmetric (reciprocal) and orthogonal (lossless).

Unlike a power-normalized converter, the modal ports here carry the physical modal impedances: the differential port presents \(Z_d = 2 Z_0\) and the common port \(Z_c = Z_0 / 2\), which for 50 Ohm physical ports are 100 Ohm and 25 Ohm. This is visible in the diagonal, where \(S_{11} = 1/3\) and \(S_{22} = -1/3\) are the reflections of \(2 Z_0\) and \(Z_0 / 2\) in \(Z_0\). Modal loads may therefore be connected to the modal ports directly, at their physical impedances and with no external factor-of-two scaling.

The S-parameters are constant across all frequencies, and independent of the value of the reference impedance, provided every port shares the same one. This is validated on evaluation.

Raises:

equinox.EquinoxRuntimeError – At runtime, if the four reference impedances passed to s() are not all equal.