skrf.network.z2s

skrf.network.z2s(z, z0=50, s_def='power')

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

For power-waves, Eq.(18) from [3]:

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

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

For pseudo-waves, Eq.(73) from [4]:

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

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

Parameters:

• z (complex array-like) – impedance 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:

s – scattering parameters

Return type:

complex array-like

References

[1]

http://en.wikipedia.org/wiki/impedance_parameters

[2]

http://en.wikipedia.org/wiki/S-parameters

[3] (1,2)

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] (1,2)

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.