S-parameters are mathematical representation of energy propagation within a multiport electrical network. It is written as a complex matrix file also knows as scattering parameters. S-parameter file represents full combination of the reflection and transmission parameters in a multiport network with frequency component. It gives an idea of how the DUT behaves with a signal in both forward and reverse direction.
Let’s consider a two port network. In this case, a two port passive band pass filter as DUT and the measurement as two port s-matrix. Industrial standard of s-parameters are touchstone file format. It is also possible to record S-parameters as csv and matlab formats in most of the Vector Network Analyzers (VNA). VNAs are used to measure S-parameters.
S11 – Reflection coefficient at port 1. A signal sent from port one of VNA and received at port one
S12 – Reverse transmission (gain/loss). Signal sent from port 2 of VNA and received at port 1
S21 – Forward transmission (gain/loss). Signal sent from port one of VNA and received at port 2
S22 – Reflection coefficient at port2. Signal sent from port 2 of VNA and received at port 2.
S-parameters can be presented in many formats as below:
Reflection S11, S22: Return loss, Impedance, Admittance, VSWR.
Transmission S12, S21: Gain/Loss (IL – Insertion Loss), Phase and Group Delay.
N port S-matrix
If the number of ports in a network increases, the s-parameter will become complex according to the number of ports. Two port network has four parameters, three port will have nine parameter and so on. The parameters of any given s-matrix are represented as Snn where S is the parameter and n is the number or port.
Mix mode s-parameters
Mix mode s-parameters are representation of balanced circuits in a network. Two input or output ports can be combined into one balanced ports for combined measurement.
Touchstone file was originally introduced by EEsof and it was acquired by HP (now Keysight EEsof EDA). It became industrial standard and used worldwide. Standard touchstone file contains information about the type S, Y or Z parameters, format such as magnitude angle (DB), Real Imaginary and frequency component etc. It has file extension as .Snp where n is the number of ports.
Vector Network Analyzer
VNA is RF test equipment used by electrical and RF engineers to measure the electrical characteristic of a complex network. It has multiple transmitter and receiver combination to calculate the gain, loss, reflection, VSWR and impedance of a DUT. Modern network analyzers are capable of performing more complicated tasks.