skrf.network.s2z

skrf.network.s2z(s: numpy.ndarray, z0: Union[numbers.Number, Sequence[numbers.Number], numpy.ndarray] = 50, s_def: str = 'power') → numpy.ndarray[source]

Convert scattering parameters [1] to impedance parameters [2]

For power-waves, Eq.(19) from [3]:

\[Z = F^{-1} (1 - S)^{-1} (S G + G^*) F\]

where \(G = diag([Z_0])\) and \(F = diag([1/2\sqrt{|Re(Z_0)|}])\)

For pseudo-waves, Eq.(74) from [4]:

\[Z = (1 - U^{-1} S U)^{-1} (1 + U^{-1} S U) G\]

where \(U = \sqrt{Re(Z_0)}/|Z_0|\)

Parameters:
  • s (complex array-like) – scattering parameters
  • z0 (complex array-like or number) – port impedances.
  • s_def (str -> s_def : can be: 'power', 'pseudo' or 'traveling') – Scattering parameter definition : ‘power’ for power-waves definition [3], ‘pseudo’ for pseudo-waves definition [4]. ‘traveling’ corresponds to the initial implementation. Default is ‘power’.
Returns:

z – impedance parameters

Return type:

complex array-like

References

[1]http://en.wikipedia.org/wiki/S-parameters
[2]http://en.wikipedia.org/wiki/impedance_parameters
[3]Kurokawa, Kaneyuki “Power waves and the scattering matrix”, IEEE Transactions on Microwave Theory and Techniques, vol.13, iss.2, pp. 194–202, March 1965.
[4]Marks, R. B. and Williams, D. F. “A general waveguide circuit theory”, Journal of Research of National Institute of Standard and Technology, vol.97, iss.5, pp. 533–562, 1992.