stabilitymu

Stability factor μ of two-port network

Syntax

[mu,muprime] = stabilitymu(s_params)

[mu,muprime] = stabilitymu(hs)

Description

[mu,muprime] = stabilitymu(s_params) calculates and returns the stability factor, μ, and μ' for the two-port S-parameters

[mu,muprime] = stabilitymu(hs) calculates and returns the stability factor for the two-port network represented by the S-parameter object hs.

Examples

Stability Factor of Two-Port Network

Calculate the stability factor of network data from a file.

S = sparameters('passive.s2p');
s_params = S.Parameters;
[mu,muprime] = stabilitymu(s_params);

Check stability criteria.

stability_index = (mu>1)|(muprime>1);
is_stable = all(stability_index)

is_stable = logical
   1

List frequencies with unstable S-parameters.

freq = S.Frequencies;
freq_unstable = freq(~stability_index)

freq_unstable =

  0x1 empty double column vector

Examine Stability Factor Using S-Parameter Object

Create a sparameters object from the specified file.

s_params = sparameters('passive.s2p');

Calculate the stability factor using stabilitymu function.

[mu,muprime] = stabilitymu(s_params);

Check the stability criteria.

stability_index = (mu>1)|(muprime>1);
is_stable = all(stability_index)

is_stable = logical
   1

List frequencies with unstable S-parameters.

freq = s_params.Frequencies;
freq_unstable = freq(~stability_index)

freq_unstable =

  0x1 empty double column vector

Input Arguments

s_params — Two-port S-parameters

complex 2-by-2-by-M array

Two-port S-parameters, specified as a complex 2-by-2-by-M array. M is the number of two-port S-parameters.

Data Types: double

hs — Two-port network

S-parameter object

Two-port network, specified as an S-parameter object.

Data Types: function_handle

Output Arguments

mu — Minimum distance between center of unit Smith chart and unstable region in load plane

vector

Minimum distance between the center of the unit Smith chart and the unstable region in the load plane, returned as vector equal to the number of frequency or data points.

muprime — Minimum distance between center of unit Smith chart and unstable region in source plane

vector

Minimum distance between the center of the unit Smith chart and the unstable region in the source plane, returned as a vector equal to the number of frequency or data points.

Algorithms

stabilitymu calculates the stability factors using the equations

$$\begin{array}{c}\mu =\frac{1-{\left|S_{11}\right|}^2}{\left|S_{22}-S_{11}^{*}\Delta \right|+\left|S_{21}{S}_{12}\right|}\\ \mu \prime =\frac{1-{\left|S_{22}\right|}^2}{\left|S_{11}-S_{22}^{*}\Delta \right|+\left|S_{21}{S}_{12}\right|}\end{array}$$

where:

• S₁₁, S₁₂, S₂₁, and S₂₂ are S-parameters, from the input argument s_params.

• Δ is a vector whose members are the determinants of the M 2-port S-parameter matrices:

  $$\Delta =S_{11}{S}_{22}-S_{12}{S}_{21}$$

• S* is the complex conjugate of the corresponding S-parameter.

The function performs these calculations element-wise for each of the M S-parameter matrices in s_params.

References

[1] Edwards, M.L., and J.H. Sinsky. “A New Criterion for Linear 2-Port Stability Using a Single Geometrically Derived Parameter.” IEEE Transactions on Microwave Theory and Techniques 40, no. 12 (December 1992): 2303–11. https://doi.org/10.1109/22.179894.

Version History

Introduced before R2006a