# Understanding Scattering Parameter Analysis of RF Networks

### Key Takeaways

• The scattering parameter (S-parameter) analysis of RF networks is a steady-state analysis that can be applied to any network at any frequency.

• S-parameter analysis analyzes the stability, input, and output reflection coefficients, power gains, and other parameters in a circuit.

• S-parameter analysis is particularly important for RF, microwave, and optical frequency regions of the electromagnetic spectrum. Network stability and the efficient transfer of power from source to load are requirements for RF and microwave circuit designs. The circuit must be designed so that it is stable under the worst-case conditions. The power flow from source to load in RF networks should be optimized so that the power losses are minimum at operating conditions. One way to measure the stability of an RF circuit is through scattering parameter (S-parameter) analysis.

Scattering parameter analysis of RF networks is a steady-state analysis that can be applied to any network at any frequency. S-parameter analysis analyzes the stability, input, and output reflection coefficients, power gains, and other parameters in a circuit. Let’s take a closer look at this type of analysis.

## Scattering Parameter Analysis of RF Networks

An RF circuit consists of several sources, guiding structures, active and passive multiport networks, and terminations. These circuits support electromagnetic fields and different modes of wave propagation. Each mode of propagation carries signals of different amplitudes with its own spatial field configuration, phase, and group velocities.

The modes of propagation in a single waveguide structure in an RF network can undergo multiple variations depending on the polarization of the transverse electric field. With the change in propagation mode, the characteristic impedance of the waveguide changes and so does the phase constant. Each element of the RF circuit is vulnerable to similar changes, and it is not appropriate to represent the circuit as an impedance or admittance matrix.

The advantage of scattering parameter analysis of RF networks is that the impedance value is not relevant in this type of analysis—scattering parameter analysis is majorly based on the reflection coefficients and power. The S-parameters give an idea about the relative wave amplitudes and relative power terms.

S-parameter analysis is a powerful tool for designing high-frequency RF and microwave circuits. S-parameter analysis can be utilized for high-frequency networks as well as low-frequency networks. However, low-frequency networks can be easily represented using other parameters such as impedance or admittance. It is not as essential to describe a circuit in S-parameters at low frequencies.

## Why Should You Use S-Parameter Analysis in High-Frequency Applications?

S-parameter analysis is particularly useful in RF, microwave, and optical frequency regions of the electromagnetic spectrum. At these frequency ranges, the circuit can be represented in terms of admittance and impedance parameters. However, S-parameter representation and analysis are more appropriate at RF and microwave frequencies for the following reasons:

1. It is impossible to define appropriate voltages and currents for an RF or microwave network in a unique manner.

2. It is difficult to measure the voltages and currents in some circuits, and this leads to the practical limitation of representing the circuit network in impedance and admittance parameters.

3. When measuring the impedance and admittance of an RF or microwave network, the measurements need to be conducted either at short-circuit or open circuit conditions. Measurements at high frequencies are not easy to achieve under short and open circuit conditions. If you do so, the circuit may undergo oscillations and become unstable. Also, active devices can self-destruct at short or open-circuit conditions.

## The Advantages of S-Parameter Analysis

At high frequencies, voltage and current measurements are not suitable for circuit analysis, as they are more like traveling waves. The S-parameter measures these traveling waves. The advantages of scattering parameter analysis on RF networks are:

1. There are well-established and familiar methods to measure RF and microwave quantities, such as the reflection coefficient, attenuation, power gains, and phase. S-parameter analysis makes it much easier to measure these quantities compared to voltages and currents.

2. The cascading of the S-parameter matrix is possible, making this type of analysis convenient. In the case of large RF networks, system performance can be calculated by cascading the individual component S-parameters.

3. The flow-graph representation in S-parameter analysis simplifies the complexity of any microwave system and it is easy to understand design requirement areas in the circuit.

Scattering parameter analysis of RF networks is a powerful tool that helps to build stable high-frequency circuits. Cadence’s software offers Cadence Spectre, which is useful in the advanced analysis of RF and microwave circuits.