Passivity metric for a multi-port network.

A metric which is proportional to the amount of power lost in a multiport network, depending on the excitation port. Specifically, this returns a matrix who’s diagonals are equal to the total power received at all ports, normalized to the power at a single excitement port.

mathematically, this is a test for unitary-ness of the s-parameter matrix [1].

for two port this is

\[\sqrt( |S_{11}|^2 + |S_{21}|^2 \, , \, |S_{22}|^2+|S_{12}|^2)\]

in general it is

\[\sqrt( S^H \cdot S)\]

where \(H\) is conjugate transpose of S, and \(\cdot\) is dot product.


The total amount of power dissipated in a network depends on the port matches. For example, given a matched attenuator, this metric will yield the attenuation value. However, if the attenuator is cascaded with a mismatch, the power dissipated will not be equivalent to the attenuator value, nor equal for each excitation port.



Return type:

numpy.ndarray of shape fxnxn


s (ndarray) –