stabilityk

Stability factor K of two-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 two-port network.

example

[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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Stability of Network

Open Live Script

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

Examine Stability of Network Using S-Parameters Object

Open Live Script

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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`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

Algorithms

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

$\begin{matrix} K = \frac{1 - {| S_{11} |}^{2} - {| S_{22} |}^{2} + {| Δ |}^{2}}{2 | S_{12} S_{21} |} \\ B_{1} = 1 + {| S_{11} |}^{2} - {| S_{22} |}^{2} - {| Δ |}^{2} \\ B_{2} = 1 - {| S_{11} |}^{2} + {| S_{22} |}^{2} - {| Δ |}^{2} \end{matrix}$

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:

$Δ = S_{11} S_{22} - S_{12} S_{21}$

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

References

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

Version History

Introduced before R2006a