cascade_abcd

pmrf.rf.cascade_abcd(a_stacked: Array | ndarray | bool | number | bool | int | float | complex) → Array

Reduce a stack of ABCD-parameter matrices to a single cascaded network.

The ABCD representation cascades by matrix multiplication, so the reduction is the ordered product of the sections, at a single frequency point. Use jax.vmap to apply it across a frequency axis.

Mathematical Formulation

\[A_{cas} = A_{0} A_{1} \cdots A_{M-1}\]

Parameters:

a_stacked (ArrayLike) – ABCD-parameter matrices of the sections, shape (M, 2N, 2N), ordered from the input of the cascade to its output.

Returns:

ABCD-parameter matrix of the cascaded network, shape (2N, 2N).

Return type:

jnp.ndarray