_constraint_s

pmrf.models.components.ideal._constraint_s(currents: Array | ndarray | bool | number | bool | int | float | complex, npoints: int) → Array

The S-parameters of an ideal, lossless constraint network.

An ideal transformer has no dynamics of its own: it only constrains the terminal voltages and currents. Since such a network neither stores nor dissipates energy, every allowed voltage vector is orthogonal to every allowed current vector, and the two subspaces are orthogonal complements. Writing the allowed currents as the range of \(X\), the scattering matrix is then the reflection

\[S = I - 2 X (X^T X)^{-1} X^T.\]

The result is real, symmetric and orthogonal, i.e. reciprocal and lossless, and it is independent of both frequency and the reference impedance.

Parameters:

• currents (ArrayLike) – An (n, r) matrix whose columns span the allowed terminal currents of the n-terminal network.

• npoints (int) – The number of frequency points to broadcast the result across.

Returns:

S-parameter matrix with shape (npoints, n, n).

Return type:

jnp.ndarray