Understanding S-Parameters: S11, S22, S12, and S21

This article delves into the fundamental measurements of S-parameters, namely S11, S12, S22, and S21. We’ll explore the setup used for these measurements and what these parameters reveal about a device under test (DUT).

What are S-Parameters?

A vector signal contains both amplitude and phase information. When such a signal passes through a device (our DUT), its characteristics change. The output signal’s amplitude and phase will differ from the input. S-parameters capture these changes, providing insights into both amplitude and phase shifts.

Essentially, S-parameters are a complex matrix used to analyze the reflection and transmission characteristics of a device in the frequency domain. Amplitude variations tell us about insertion loss, while phase variations reveal phase shift.

Types of S-Parameters

For a two-port device, there are four S-parameters. The naming convention is “S” followed by two digits. The first digit indicates the output port, and the second indicates the input port. For instance, S21 means the output is measured at Port 2, with the input signal applied at Port 1.

S-parameter measurements can be categorized as:

• Transmission measurements: S21 and S12
• Reflection measurements: S11 and S22

What S11 and S22 Tell Us:

These parameters provide information about:

• Return loss or reflection coefficient
• Impedance and admittance
• Voltage Standing Wave Ratio (VSWR) of the input and output ports

What S21 and S12 Tell Us:

These parameters provide information about:

• Gain/Loss (insertion loss)
• Phase and group delay (delay time)

S-Parameter Measurement Setup

A Vector Network Analyzer (VNA) is the tool used to measure S-parameters.

The VNA internally measures both amplitude and phase using four receivers (R1, R2, A, and B).

How Each S-Parameter is Measured

Here’s how each S-parameter is derived:

• S11 (Input Reflection Coefficient): Measured as the ratio of A and R1.
• S22 (Output Reflection Coefficient): Measured as the ratio of B and R2.
• S21 (Transmission Insertion Loss): Measured as the ratio of B and R1 (output at Port 2, input at Port 1).
• S12 (Transmission Isolation): Measured as the ratio of A and R2 (output at Port 1, input at Port 2).

In essence, S-parameters give us a complete picture of how a signal behaves when it interacts with a device, which is crucial in RF and microwave engineering.