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s2tf - Convert S-parameters of 2-port network to transfer function

Syntax

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

Description

tf = s2tf(s_params, z0, zs, zl,option) converts the scattering parameters, s_params, of a 2-port network into the voltage transfer function or power-wave transfer function of the network.

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:

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.
is the incident power wave, equal to .
is the transmitted power wave, equal to .

The impedances in the figure are optional arguments to the s2tf function which defines them as follows:

z0 is the reference impedance of the S-parameters.
zs is the source impedance.
zl is the load impedance.

The default value of these impedances is 50 ohms.

The optional option argument determines the definition of the transfer function. option can be:

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

The following figure shows how to compute V_a from the source voltage V_S:

In terms of S-parameters and impedance values, the transfer function is as follows:

where

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

Notice that if Z_l and Z_S are real, .
2 — The transfer function is the gain from the source voltage to the output voltage for arbitrary source and load impedances:

You can use this option to compute the transfer function by setting zs to 0. This setting means that and .
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: