s2tf

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

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Syntax

tf = s2tf(s_params)

tf = s2tf(s_params,z0,zs,zl)

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

tf = s2tf(sparams_obj)

tf = s2tf(sparams_obj,zs,zl)

tf = s2tf(sparams_obj,zs,zl,option)

Description

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

example

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

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

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

Examples

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S-Parameters to Voltage or Power Transfer Function

Open Live Script

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

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

tf = 202×1 complex

   0.9964 - 0.0254i
   0.9960 - 0.0266i
   0.9956 - 0.0284i
   0.9961 - 0.0290i
   0.9960 - 0.0301i
   0.9953 - 0.0317i
   0.9953 - 0.0334i
   0.9952 - 0.0349i
   0.9949 - 0.0367i
   0.9946 - 0.0380i
      ⋮

Calculate Voltage Transfer Function of S-Parameters Object

Open Live Script

Calculate the voltage transfer function of a S-parameters object using s2tf function.

sparams = sparameters('passive.s2p');
tf = s2tf(sparams)

tf = 202×1 complex

   0.9964 - 0.0254i
   0.9960 - 0.0266i
   0.9956 - 0.0284i
   0.9961 - 0.0290i
   0.9960 - 0.0301i
   0.9953 - 0.0317i
   0.9953 - 0.0334i
   0.9952 - 0.0349i
   0.9949 - 0.0367i
   0.9946 - 0.0380i
      ⋮

Input Arguments

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`sparams_obj` — 2–port S-parameters
`sparameter` object

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

`s_params` — Scattering parameters
2-by-2-by-M array (default)

Scattering parameters, specified as a complex 2-by-2-by-M array where M represents the number of frequency points of the S-parameters.

`z0` — Reference impedance
`50` (default) | positive scalar

Reference impedance of S-parameters, specified as a positive scalar in ohms.

`zs` — Source impedance
`50` (default) | positive scalar | vector

Source impedance of S-parameters, specified as a positive scalar or vector of length equal to the number of frequencies in ohms.

`zl` — Load impedance
`50` (default) | positive scalar | vector

Load impedance of S-parameters, specified as a positive scalar or vector of length equal to the number of frequencies in ohms.

`option` — Transfer function type
`1` (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, V_a, to the output voltage for arbitrary source and load impedances:

$t f = \frac{V_{l}}{V_{a}}$
The following figure shows how to compute V_a from the source voltage V_s:

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

$t f = \frac{(Z_{s} + Z_{s}^{*})}{Z_{s}^{*}} \frac{S_{21} (1 + Γ_{l}) (1 - Γ_{s})}{2 (1 - S_{22} Γ_{l}) (1 - Γ_{i n} Γ_{s})}$
where:

$\begin{matrix} Γ_{l} = \frac{Z_{l} - Z_{o}}{Z_{l} + Z_{o}} \\ Γ_{s} = \frac{Z_{s} - Z_{o}}{Z_{s} + Z_{o}} \\ Γ_{i n} = S_{11} + (S_{12} S_{21} \frac{Γ_{l}}{(1 - S_{22} Γ_{l})}) \end{matrix}$
The following equation shows how the preceding transfer function is related to the transducer gain computed by the powergain function:

$G_{T} = {| t f |}^{2} \frac{Re (Z_{l})}{{| Z_{l} |}^{2}} \frac{{| Z_{s} |}^{2}}{Re (Z_{s})}$
Notice that if Z_l and Z_S are real, $G_{T} = {| t f |}^{2} \frac{Z_{s}}{Z_{l}}$ .
2 — The transfer function is the gain from the source voltage to the output voltage for arbitrary source and load impedances:

$t f = \frac{V_{l}}{V_{s}} = \frac{S_{21} (1 + Γ_{l}) (1 - Γ_{s})}{2 (1 - S_{22} Γ_{l}) (1 - Γ_{i n} Γ_{s})}$
You can use this option to compute the transfer function $\frac{V_{_{L}}}{V_{i n}}$ by setting zs to 0. This setting means that Γ_s = –1 and V_in = V_s.
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:
$t f = \frac{b_{p 2}}{a_{p 1}} = \frac{\sqrt{Re (Z_{l}) Re (Z_{s})}}{Z_{l}} \frac{S_{21} (1 + Γ_{l}) (1 - Γ_{s})}{(1 - S_{22} Γ_{l}) (1 - Γ_{i n} Γ_{s})}$

Output Arguments

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`tf` — Voltage transfer function
vector of doubles

Voltage transfer function, returned as a vector of doubles.

Complex Number Support: Yes

Algorithms

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

2-port network block diagram

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

V_l is the output voltage across the load impedance.
V_s is the source voltage.
V_in is the input voltage of the 2-port network.
$a_{p 1}$ is the incident power wave, equal to $\frac{V_{s}}{2 \sqrt{Re (Z_{s})}}$ .
$b_{p 2}$ is the transmitted power wave, equal to $\frac{\sqrt{Re (Z_{l})}}{Z_{l}} V_{l}$ .

References

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

Version History

Introduced in R2006b

s2tf

Syntax

Description

Examples

S-Parameters to Voltage or Power Transfer Function

Calculate Voltage Transfer Function of S-Parameters Object

Input Arguments

sparams_obj — 2–port S-parameters sparameter object

s_params — Scattering parameters 2-by-2-by-M array (default)

z0 — Reference impedance 50 (default) | positive scalar

zs — Source impedance 50 (default) | positive scalar | vector

zl — Load impedance 50 (default) | positive scalar | vector

option — Transfer function type 1 (default) | integer

Output Arguments

tf — Voltage transfer function vector of doubles

Algorithms

References

Version History

See Also

`sparams_obj` — 2–port S-parameters
`sparameter` object

`s_params` — Scattering parameters
2-by-2-by-M array (default)

`z0` — Reference impedance
`50` (default) | positive scalar

`zs` — Source impedance
`50` (default) | positive scalar | vector

`zl` — Load impedance
`50` (default) | positive scalar | vector

`option` — Transfer function type
`1` (default) | integer

`tf` — Voltage transfer function
vector of doubles