PoleResidueMatrix¶

class photonforge.PoleResidueMatrix(poles, residues, frequency_scaling=6.283185, ports=None, delays=None)¶

Pole-residue representation of an S matrix.

Each element $v$ is represented by a rational function of the form:

S_{v} = e^{i 2 π f d} \sum_{n = 0}^{N - 1} \frac{r_{v n}}{s - p_{n}} + r_{v N}

in which $p_{n}$ are the poles (shared by all elements) and $r_{v n}$ are the residues for matrix element $v$ , $d$ is the delay, $h$ is a frequency scaling factor, and $s = - i h f$ .

Parameters:

poles – Sequence of complex poles shared by all matrix elements.
residues – Dictionary of residues, one per matrix element. Each item is a sequence of complex residues used for that element.
frequency_scaling – Scaling applied to the frequencies in evaluation.
ports – Mapping from port names to ports or to None.
delays – Dictionary of explicit time delays (in seconds), one per matrix element. Missing elements have no time delay applied. If a single number is given, this is used as a global delay for all matrix elements.

Note

The number of residues for each element is 1 more that the number of poles because of the last term in the representation.

Including explicit delays in the model can reduce the number of poles required to obtain a good fit. However, if the delays are too large, it can be difficult to obtain a good stable fit.

Example

An SMatrix instance can be obtained by calling an instance of PoleResidueMatrix with the desired frequencies:

>>> pole_res = PoleResidueMatrix(
...     poles=[-C_0 / 1.0],
...     residues={("P0", "P0"): [2.0 * C_0, 0.0]},
... )
>>> s_matrix = pole_res(C_0 / 1.55)
>>> s_matrix.elements
{('P0', 'P0'): array([0.11473006+0.46507755j])}

Methods

`copy`()	Create a copy of this pole_residue_matrix.
`enforce_passivity`(frequencies[, ...])	Attempt to make the pole-residue matrix passive, while minimizing the perturbation at the specified frequencies.
`get_rms_error`(s_matrix)	Compute the error between this pole-residue matrix and another S matrix.
`is_passive`()	Check whether the pole-residue matrix is passive.

Attributes

`delays`	Dictionary of delays for each element, in seconds (read only).
`frequency_scaling`	Frequency scaling factor
`poles`	Poles for all elements (read only).
`ports`	Associated ports (read only).
`residues`	Dictionary of residues for each element (read only).

copy()¶

Create a copy of this pole_residue_matrix.

Returns:: New copy.

delays¶: Dictionary of delays for each element, in seconds (read only).

enforce_passivity(frequencies, max_iterations=20, real=False, feedthrough=False)¶

Attempt to make the pole-residue matrix passive, while minimizing the perturbation at the specified frequencies.

Parameters:

frequencies – List of frequencies at which the perturbation should be minimized. This is usually the frequencies of the S matrix data being fit.
max_iterations – Maximal number of passivity enforcement iterations.
real – Whether the poles come in conjugate pairs, representing a real-valued (non-baseband) system.
feedthrough – Whether to include a feedthrough (constant) term in the pole-residue model.

Returns:

Bool representing whether passivity enforcement succeeded.

frequency_scaling¶: Frequency scaling factor

get_rms_error(s_matrix)¶

Compute the error between this pole-residue matrix and another S matrix.

Parameters:: s_matrix – S matrix to compare and calculate the RMS error.
Returns:: The RMS error between matrices.

is_passive()¶

Check whether the pole-residue matrix is passive.

Returns:: Bool representing whether the pole-residue matrix is passive.

poles¶: Poles for all elements (read only).

ports¶: Associated ports (read only).

residues¶: Dictionary of residues for each element (read only).