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 power-normalized common-mode and differential-mode port pair, using the orthogonal modal transform

\[\begin{split}U = \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}.\end{split}\]

Port ordering:

• Port 1: physical (single-ended) port p

• Port 2: physical (single-ended) port n

• Port 3: common mode of ports 1 and 2

• Port 4: differential mode of ports 1 and 2

Writing the incident and reflected waves of the physical pair as \(a_{12} = (a_1, a_2)^T\) and \(b_{12} = (b_1, b_2)^T\), and likewise \(a_{34} = (a_c, a_d)^T\) for the modal pair, the converter enforces \(b_{34} = U a_{12}\) and \(b_{12} = U a_{34}\), so that

\[\begin{split}S = \begin{bmatrix} 0 & U \\ U & 0 \end{bmatrix}.\end{split}\]

Since \(U\) is real, symmetric and orthogonal, S is symmetric (reciprocal) and unitary (lossless), and all four ports are perfectly matched. The transform is its own inverse, so cascading two converters back-to-back through the modal pair gives identity.

Because the modal waves are power-normalized, the modal ports carry the same wave normalization as the physical ports: the usual \(Z_0/2\) common-mode and \(2 Z_0\) differential-mode impedances are absorbed into the normalization. The S-parameters are therefore constant across frequency and independent of the reference impedance, provided every port shares the same reference impedance. This is validated on evaluation.

Raises:

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