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S-Parameters: Advantages and Disadvantages of S-Matrix

s parameters rf s matrix network analysis scattering parameters

This page covers the advantages and disadvantages of S Parameters (S-Matrix). It mentions S Parameters advantages or benefits and S Parameters disadvantages or drawbacks. S Parameters are derived from S-Matrix.

What is S-matrix?

  • S-matrix is composed of S-parameters or scattering parameters.
  • It is known as scattering matrix.
  • It describes the electrical behavior of linear electrical networks when subjected to steady-state stimuli using electrical signals.
  • They do not use open circuit and short circuit conditions.
  • They use matched loads to characterize linear electrical networks due to ease at higher frequencies compared to short/open circuit terminations.

Following figure depicts a 2-port network with s-parameters. A set of linear equations are written to describe network in terms of injected and transmitted waves.

S-matrix two port network

  • Sij = bi/aj = [(Power measured at port-i)/(Power injected at port-j)] 0.5

Where:

  • Sii = ratio of reflected power to injected power at port-i

  • Sij = ratio of power measured at port-j to power injected at port-i

  • An electrical circuit or network is composed of inductors, capacitors, or resistors in its basic form. Some of their parameters such as return loss, insertion loss, gain, VSWR, and reflection coefficients are represented by S-parameters.

  • S-parameters are similar to other parameters such as Z-parameters, Y-parameters, H-parameters, T-parameters, and abcd-parameters etc.

  • Following equations are used to derive various S-parameters such as S11, S12, S21 and S22.

S Parameters

Benefits or Advantages of S Parameters | S-Matrix

Following are the benefits or advantages of S Parameters:

  • It helps in ease of measurement at high frequencies compared to open/short current and voltage measurements.
  • S-parameters are used to extract transmission line parameters such as R, L, C, G, TD, and Z0.
  • The return loss, insertion loss, gain, VSWR, reflection coefficients, and transmission coefficients of the network are derived using S-parameters.
  • The behavior of S-parameters can be used to gain intuition of signal integrity problems.
  • It is easy to convert S-parameters of S-matrix to other parameters such as Z-parameters, Y-parameters, H-parameters, T-parameters and abcd-parameters.

Drawbacks or Disadvantages of S Parameters | S-Matrix

Following are the drawbacks or disadvantages of S Parameters:

  • It is useful in frequency domain analysis and not time domain analysis.
  • Most silicon loads are non-linear. Moreover, most digital circuits operate using voltage thresholds. These applications require time domain analysis which is not possible using S-parameters.
  • Conversion between time domain and frequency domain introduces errors.
  • Though it is possible to cascade S-parameters, it gets messy. Hence it is done in a better way using ABCD parameters.
  • It is not possible to describe a network in terms of both voltage and current waves using S-parameters. For this, ABCD parameters are used.