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s2tf

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

Description

example

tf = s2tf(s_params) converts the scattering parameters of a 2-port network to 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(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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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 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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2-port S-parameters, specified as an RF Toolbox™ sparameters object.

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

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

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

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

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=VlVa

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

    Source voltage, source impedance, and load impedance in a circuit

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

    tf=(Zs+Zs*)Zs*S21(1+Γl)(1Γs)2(1S22Γl)(1ΓinΓs)

    where:

    Γl=ZlZoZl+ZoΓs=ZsZoZs+ZoΓin=S11+(S12S21Γl(1S22Γl))

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

    GT=|tf|2Re(Zl)|Zl|2|Zs|2Re(Zs)

    Notice that if Zl and ZS are real, GT=|tf|2ZsZl.

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

    tf=VlVs=S21(1+Γl)(1Γs)2(1S22Γl)(1ΓinΓs)

    You can use this option to compute the transfer function VLVin 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=bp2ap1=Re(Zl)Re(Zs)ZlS21(1+Γl)(1Γs)(1S22Γl)(1ΓinΓs)

Output Arguments

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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:

  • Vl is the output voltage across the load impedance.

  • Vs is the source voltage.

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

  • ap1 is the incident power wave, equal to Vs2Re(Zs).

  • bp2 is the transmitted power wave, equal to Re(Zl)ZlVl.

References

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

See Also

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Introduced in R2006b