stabilityk

Stability factor K of two-port network

Description

example

[k,b1,b2,delta] = stabilityk(s_params) calculates and returns the stability factor, k, and the conditions b1, b2, and delta for the two-port network.

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

Examples

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Examine the stability of network data from a file by first calculating the stability factor.

S = sparameters('passive.s2p');
s_params = S.Parameters;
[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 = S.Frequencies;
freq_unstable = freq(~stability_index)
freq_unstable =

0x1 empty double column vector

Create a S-parameters object from a specified file. .

s_params = sparameters('passive.s2p');

Calculate the stability using stabilityk function.

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

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

0x1 empty double column vector

Input Arguments

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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

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

Data Types: function_handle

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.

 Gonzalez, Guillermo. Microwave Transistor Amplifiers: Analysis and Design. 2nd ed. Upper Saddle River, N.J: Prentice Hall, 1997.