Stability factor *μ* of 2-port network

[mu,muprime] = stabilitymu(s_params)

`[mu,muprime] = stabilitymu(s_params)`

calculates and
returns the stability factors *μ* and *μ′* of a 2-port
network. The input `s_params`

is a complex 2-by-2-by-*M*
array, representing *M* 2-port S-parameters.

`[mu,muprime] = stabilitymu(hs)`

calculates and
returns the stability factors for the network represented by the S-parameter object
`hs`

.

The stability factor, *μ*, defines the minimum distance between the center
of the unit Smith chart and the unstable region in the load plane. The function assumes that
port 2 is the load.

The stability factor, *μ′*, defines the minimum distance between the
center of the unit Smith chart and the unstable region in the source plane. The function assumes
that port 1 is the source.

Having *μ* > 1 or *μ′* > 1 is
the necessary and sufficient condition for the 2-port linear network to be unconditionally
stable, as described by the S-parameters.

`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:

*S*,_{11}*S*,_{12}*S*, and_{21}*S*are S-parameters, from the input argument_{22}`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`

.

Edwards, Marion Lee, and Jeffrey H. Sinsky, “A New Criterion for Linear 2-Port
Stability Using a Single Geometrically Derived Parameter,” *IEEE Transactions on
Microwave Theory and Techniques*, Vol. 40, No. 12, pp. 2303-2311,
December 1992.