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# s2tf

Convert S-parameters of 2-port network to voltage or power-wave transfer function

## Syntax

• tf = s2tf(s_params)
• tf = s2tf(s_params,z0,zs,zl)
• tf = s2tf(s_params,z0,zs,zl,option)
• tf = s2tf(hs)
• tf = s2tf(hs,zs,zl)
• tf = s2tf(hs,zs,zl,option)

## Description

tf = s2tf(s_params) converts the scattering parameters, s_params, of a 2-port network into the voltage transfer function of the network.

tf = s2tf(s_params,z0,zs,zl) calculates the voltage transfer function using the reference impedance z0, source impedance zs, and load impedance zl.

tf = s2tf(s_params,z0,zs,zl,option) calculates the voltage or power-wave transfer function using the method specified by option.

tf = s2tf(hs) converts the 2-port S-parameter object, hs, into the voltage transfer function of the network.

tf = s2tf(hs,zs,zl) calculates the voltage transfer function using the source impedance zs, and load impedance zl.

tf = s2tf(hs,zs,zl,option) calculates the voltage or power-wave transfer function using the method specified by option.

## Input Arguments

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### hs — 2–port s-parameterss-parameter object

2-port S-parameters, specified as an RF Toolbox™ S-parameter object.

### s_params — Scattering parameters2x2xM array (default)

Scattering parameters, specified as a complex 2-by-2-by-M array.

### z0 — Reference impedance50 ohms (default)

Reference impedance of S-parameters, specified in ohms.

### zs — Source impedance50 ohms (default)

Source impedance of S-parameters, specified in ohms.

### zl — Load impedance50 ohms (default)

Load impedance of S-parameters, specified in ohms.

### option — Transfer function type1 (default) | integer

Transfer function type, specified as an integer equal to 1, 2, or 3.

• 1 — The transfer function is the gain from the incident voltage, Va, to the output voltage for arbitrary source and load impedances:

$tf=\frac{{V}_{l}}{{V}_{a}}$

The following figure shows how to compute Va from the source voltage Vs:

For the S-parameters and impedance values, the transfer function is:

$tf=\frac{\left({Z}_{s}+{Z}_{s}^{*}\right)}{{Z}_{s}^{*}}\frac{{S}_{21}\left(1+{\Gamma }_{l}\right)\left(1-{\Gamma }_{s}\right)}{2\left(1-{S}_{22}{\Gamma }_{l}\right)\left(1-{\Gamma }_{in}{\Gamma }_{s}\right)}$

where:

$\begin{array}{c}{\Gamma }_{l}=\frac{{Z}_{l}-{Z}_{o}}{{Z}_{l}+{Z}_{o}}\\ {\Gamma }_{s}=\frac{{Z}_{s}-{Z}_{o}}{{Z}_{s}+{Z}_{o}}\\ {\Gamma }_{in}={S}_{11}+\left({S}_{12}{S}_{21}\frac{{\Gamma }_{l}}{\left(1-{S}_{22}{\Gamma }_{l}\right)}\right)\end{array}$

The following equation shows how the preceding transfer function is related to the transducer gain computed by the powergain function:

${G}_{T}={|tf|}^{2}\frac{\mathrm{Re}\left({Z}_{l}\right)}{{|{Z}_{l}|}^{2}}\frac{{|{Z}_{s}|}^{2}}{\mathrm{Re}\left({Z}_{s}\right)}$

Notice that if Zl and ZS are real, ${G}_{T}={|tf|}^{2}\frac{{Z}_{s}}{{Z}_{l}}$.

• 2 — The transfer function is the gain from the source voltage to the output voltage for arbitrary source and load impedances:

$tf=\frac{{V}_{l}}{{V}_{s}}=\frac{{S}_{21}\left(1+{\Gamma }_{l}\right)\left(1-{\Gamma }_{s}\right)}{2\left(1-{S}_{22}{\Gamma }_{l}\right)\left(1-{\Gamma }_{in}{\Gamma }_{s}\right)}$

You can use this option to compute the transfer function $\frac{{V}_{{}_{L}}}{{V}_{in}}$ by setting zs to 0. This setting means that Γs = –1 and Vin = Vs.

• 3 — The transfer function is the power-wave gain from the incident power wave at the first port to the transmitted power wave at the second port:

$tf=\frac{{b}_{p2}}{{a}_{p1}}=\frac{\sqrt{\mathrm{Re}\left({Z}_{l}\right)\mathrm{Re}\left({Z}_{s}\right)}}{{Z}_{l}}\frac{{S}_{21}\left(1+{\Gamma }_{l}\right)\left(1-{\Gamma }_{s}\right)}{\left(1-{S}_{22}{\Gamma }_{l}\right)\left(1-{\Gamma }_{in}{\Gamma }_{s}\right)}$

## Output Arguments

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### tf — Voltage transfer functionvector of doubles

Voltage transfer function, returned as a vector of doubles.

Complex Number Support: Yes

## Examples

Calculate the voltage transfer function of an S-parameter array:

```ckt = read(rfckt.passive,'passive.s2p');
sparams = ckt.NetworkData.Data;
tf = s2tf(sparams)```

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### Algorithms

The following figure shows the setup for computing the transfer function, along with the impedences, voltages, and the power waves used to determine the gain.

The function uses the following voltages and power waves for calculations:

• Vl is the output voltage across the load impedance.

• Vs is the source voltage.

• Vin is the input voltage of the 2-port network.

• ${a}_{p1}$ is the incident power wave, equal to $\frac{{V}_{s}}{2\sqrt{\mathrm{Re}\left({Z}_{s}\right)}}$.

• ${b}_{p2}$ is the transmitted power wave, equal to $\frac{\sqrt{\mathrm{Re}\left({Z}_{l}\right)}}{{Z}_{l}}{V}_{l}$.