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

This article delves into the fundamental measurements of S-parameters, namely S11, S12, S22, and S21.

What are S-Parameters?

A vector signal consists of both amplitude and phase information. When a signal is passed from linear of non-linear device which we call it DUT (Device Under Test) in our discussion; the characteristics of signal will alter. The amplitude/phase of output signal is different compare to input signal. S-parameter convey both of these information i.e. amplitude and phase.

Amplitude variation information provides insertion loss while timing variation provides phase shift. S parameters are complex matrix which helps us analyzing reflection and transmission characteristics in the frequency domain.

It provides information concerning the performance of linear electrical networks, including RF circuits, amplifiers, and filters, whichs includes -

• Signal magnitude, phase, reflection, and attenuation
• Location of Signal losses, Impedance mismatches
• Transmission line parameters, notably R, L, C, G, TD, Z0

Types of S-Parameters

The S-parameter matrix can be used to determine reflection coefficients and transmission gains from both sides of a two port network. This concept can further be used to determine s-parameters of a multi port network.

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 measurement parameters viz. S11,S22
• Reflection measurement parameters viz. S21, S12

S11 and S22 provide us information on the following -

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

S21 and S12 provide us information on the following -

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

Setup Block diagram for Measuring S-Parameters

A Vector Network Analyzer (VNA) is the tool used to measure S-parameters. The following figure depicts internal block diagram of VNA.

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.