What are S-parameters?
S-parameters are the electrical characteristics of a signal in a complex network. It is also known as scattering parameters and mostly used in RF network and applications. Vector Network Analyzer is used to measure and analyze signal behavior of S-parameters. The signal behavior can be observed as gain, return loss, VSWR, reflection coefficient and group delay etc.
Modern VNAs are capable of performing multiple tasks other than just measuring S-parameters. Basic VNA will have two ports and will be expandable up to 24 ports depending on the model and applications.
We will take a bandpass filter as an example for this analysis. Bandpass filters are tuned to a particular bandwidth, which is called the passband. It gives maximum suppression to lower and higher frequencies (outside the passband).
Let’s take a look at each format of VNA (vector network analyzer) and find out what are the uses of each format.
A. Cartesian Display formats (rectangular display formats)
The cartesian diagram is the most common rectangular diagram to represent transmission and reflection parameters of S-parameters. Linearly scaled stimulus data will be displayed on the X-axis and measured value on the Y-axis. It is further subdivided into other formats.
1. Logarithmic Magnitude (Log Mag /dB Mag)
In Log Mag format, magnitude is displayed on the Y-axis, and frequency is displayed on the X-axis. Log mag format is suitable to analyze below parameters:
- Gain
- Insertion loss
- Return loss
- Isolation
2. Phase angle
It displays the phase deviation of the signal related to the reference calibration line. Phase is displayed on the Y-axis, and frequency is on the X-axis.
- Phase
3. Group Delay
Group delay is used to display the propagation time delay of the signals in the network. Group delay is frequency-dependent and has different delay times for transmission (at different frequencies). Delay time will be displayed on the Y-axis (in seconds) and frequency on the X-axis.
- Group delay
- Propagation delay analysis
4. Linear Magnitude
Linear magnitude displays the positive values of the magnitude measurement. Normalized measurement is displayed on Y-axis, and frequency on X axis.
- Reflection coefficient
- Transmission coefficient
- Time domain transfer function
5. Voltage Standing Wave Ration (VSWR) 
VSWR format displays the reflection coefficient parameters determined by the formula VSWR = (1 + |Γ|)/(1 – |Γ|)where Γ is the reflection coefficient.
- Standing wave ratio
6. Real Format 
Real format only displays the real part of the complex measurement data.
- Time domain measurements
7. Imaginary Format
Imaginary format only displays an imaginary part of the complex data.
- Impedance analysis
B. Smith chart format 
Smith chart format is a representation of the real (r) and imaginary part (r+jX) of the complex measurement. A horizontal line in the middle separates the inductive and capacitive regions.
The center of the Smith chart is a perfect 50-ohm impedance.
Moving towards the left side of the horizontal line reaches zero impedance which represents a perfect short condition.
Towards the right side of the horizontal line, impedance gets higher and higher until infinity represents a perfect open condition.
- Impedance Matching and analysis
An inverted Smith chart is used to display admittance (Y-chart).
C. Polar Format
The polar format displays both the magnitude and phase angle of the reflection coefficient of parameters S11 and S22 etc. It represents linear magnitude or logarithmic magnitude (dB Mag) and phase angle in degree.
- Magnitude
- Phase angle
Conclusion
S-parameters are one of the significant information for engineers to design, analyze, and simulate complex networks and resolve an issue. Modern network analyzers can be configured to perform even complicated real-time small signal and large signal analyses with sophisticated analysis software. The scope of RF has been widening with technology advancements, and it demands efficiency improvements.
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