S Parameters or Scattering Parameters

Scattering parameters or S parameters are used to analyze the behavior of RF devices and their networks at any frequency.

S parameters are complex numbers that characterize a device. Since the response of electronic devices varies with frequency, the S parameters of the device will be frequency dependent too.

These parameters are usually used to characterize one port and two port devices.

1 port S Parameters

There are two types of 1 port devices - loads and sources.

A 1 port load is characterized by just one S parameter - S1. S1 corresponds to the voltage reflection coefficient of the device.

A 1 port source is characterized by one S parameter, S1, its reflection coefficient and also by its supply voltage.

2 Port S Parameters

A two port device is characterized by a 2 x 2 matrix of S parameters.

      |S11    S12|
S = |              |    
      |S21    S22|

where

• S11 is the reflection coefficient at port 1
  
• S22 is the reflection coeffieicnet at port 2
• S21 is the forward gain or the transmission coefficient from port 1 to port 2
• S12 is the transmission coefficient from port 2 to 1 or the backward gain

For a RF amplifier, S11 is the input impedance, S22 is the output impedance, S21 is the gain of the amplifier and S12 is close to 0.

S Parameters Measurement

S parameters can be measured by vector network analyzer or Time Domain Reflectometry.

S Parameter Conversion

Various formulae exist to convert from S parameters to Impedances, and convert S parameters to Y parameters.

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