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S parameters or Scattering Parameters

As we know measurement of voltage and current is difficult at microwave frequencies unless properly defined pair of terminals are available. In coaxial cable and twin wire transmission line having TEM mode of propagation, terminal pair is available. In waveguide having non TEM mode of propagation, it is not available.

V,I equation in terms of E and H

Above Equation defines voltage and current w.r.t. E and H field. At microwave frequencies we talk in terms of E and H fields as V and I has no significance at such higher frequencies. At RF and microwave range of frequencies, measurements of current (I) and voltage (V) become very complex. At higher frequency we measure power and not current or voltage. At high microwave frequencies, it is difficult to implement short circuit and open circuit for the AC signals over the broad bandwidth. To overcome this problem, S parameters are used at microwave range. These S parameters are defined in terms of incident and reflected travelling waves.

S parameters are simple to use in analysis. As it is very easy to measure S parameters using network analyzers the popularity of the use of such parameters have been increased.

We will see S parameters(scattering parameters) which include S11/S22(Reflection coefficient),S12(Isolation) and S21(Insertion loss).

S parameters are popular in RF/Microwave circuit design and testing. Following are Scattering parameters used for measuring/characterizing the RF device.

S parameters or Scattering parameters

From the figure, following two equations are derived:
b1= S11 *a1 + S12 *a2
b2= S21 * a1 + S22 *a2
S11 - Reflection coefficient at Port1
S22 - Reflection coefficient at Port2
S12 - Isolation (Reverse)
S21 - Insertion loss (passive device case)

S-parameters are vector entities whch are derived from vector based measurements(magnitude, phase). Following scalar measurements are derived from S-parameters.

Following are the measurements related to reflection and incident waves:
Input SWR, Return Loss, VSWR, Input/output impedance, reflection coefficient, S parameters-S11,S22.

Following are the measurements related to transmission and incident waves:
Gain/Insertion Loss, Isolation, Insertion phase, Group delay, transmission coefficient, S parameters-S21, S12

Measurements of S-parameters

The S-parameters are measured by Vector Network Analyzer (VNA). Refer SNA vs VNA which describes basics of Scalar Network Analyzer and Vector Network Analyzer.
Refer VNA tutorial➤ for more information.

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