Documentation

# stabilityk

Stability factor K of 2-port network

## Syntax

[k,b1,b2,delta] = stabilityk(s_params)
[k,b1,b2,delta] = stabilityk(hs)

## Description

[k,b1,b2,delta] = stabilityk(s_params) calculates and returns the stability factor, k, and the conditions b1, b2, and delta for the 2-port network. The input s_params is a complex 2-by-2-by-M array, representing M 2-port S-parameters.

[k,b1,b2,delta] = stabilityk(hs) calculates and returns the stability factor and stability conditions for the 2-port network represented by the S-parameter object hs.

## Examples

collapse all

Examine the stability of network data from a file. Calculate stability factor and conditions

s_params = ckt.NetworkData.Data;
freq = ckt.NetworkData.Freq;
[k,b1,b2,delta] = stabilityk(s_params);

Check stability criteria

stability_index = (k>1)&(abs(delta)<1);
is_stable = all(stability_index)
is_stable = logical
1

List frequencies with unstable S-parameters

freq_unstable = freq(~stability_index)
freq_unstable =

0x1 empty double column vector

## Algorithms

Necessary and sufficient conditions for stability are k>1 and abs(delta)<1. stabilityk calculates the outputs using the equations

$\begin{array}{c}K=\frac{1-{|{S}_{11}|}^{2}-{|{S}_{22}|}^{2}+{|\Delta |}^{2}}{2|{S}_{12}{S}_{21}|}\\ {B}_{1}=1+{|{S}_{11}|}^{2}-{|{S}_{22}|}^{2}-{|\Delta |}^{2}\\ {B}_{2}=1-{|{S}_{11}|}^{2}+{|{S}_{22}|}^{2}-{|\Delta |}^{2}\end{array}$

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:

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

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

## References

Gonzalez, Guillermo, Microwave Transistor Amplifiers: Analysis and Design, 2nd edition. Prentice-Hall, 1997, pp. 217–228.