# skrf.network.passivity¶

skrf.network.passivity(s)[source]

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.

Note

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.

Returns

passivity

Return type

numpy.ndarray of shape fxnxn

Parameters

s (numpy.ndarray) –

References

1

http://en.wikipedia.org/wiki/Scattering_parameters#Lossless_networks