Understanding S-Parameters (Scattering Parameters)

As we know, measuring voltage and current at microwave frequencies is difficult unless properly defined terminal pairs are available. In coaxial cable and twin-wire transmission lines having TEM mode propagation, a terminal pair is available. However, in waveguides having non-TEM mode propagation, it is not.

The equation above defines voltage and current with respect to the E and H fields. At microwave frequencies, we typically talk in terms of E and H fields because V and I don’t have the same significance at such higher frequencies.

At RF and microwave frequencies, measurements of current (I) and voltage (V) become very complex. At higher frequencies, we measure power, not current or voltage. Furthermore, at high microwave frequencies, it is difficult to implement short circuit and open circuit conditions for AC signals over a broad bandwidth.

To overcome these problems, S parameters are used at microwave frequencies. These S parameters are defined in terms of incident and reflected traveling waves. They are simple to use in analysis, and because they are easy to measure using network analyzers, their popularity has increased.

We will explore S parameters (scattering parameters) which include $S_{11}$/$S_{22}$ (Reflection coefficient), $S_{12}$ (Isolation), and $S_{21}$ (Insertion loss). S parameters are popular in RF/Microwave circuit design and testing.

The following are scattering parameters used for measuring/characterizing RF devices:

From the figure, the following two equations are derived:

$b_1 = S_{11} * a_1 + S_{12} * a_2$

$b_2 = S_{21} * a_1 + S_{22} * a_2$

Where:

• $S_{11}$ - Reflection coefficient at Port 1
• $S_{22}$ - Reflection coefficient at Port 2
• $S_{12}$ - Isolation (Reverse)
• $S_{21}$ - Insertion loss (passive device case)

S-parameters are vector entities which are derived from vector-based measurements (magnitude, phase).

The following scalar measurements are derived from S-parameters:

Measurements related to reflection and incident waves:

Input SWR, Return Loss, VSWR, Input/output impedance, reflection coefficient, S parameters - $S_{11}$, $S_{22}$.

Measurements related to transmission and incident waves:

Gain/Insertion Loss, Isolation, Insertion phase, Group delay, transmission coefficient, S parameters - $S_{21}$, $S_{12}$

Measurements of S-parameters

S-parameters are measured by a Vector Network Analyzer (VNA). Refer to resources comparing Scalar Network Analyzers (SNA) vs. Vector Network Analyzers (VNA) that describe the basics of each. For more detailed information, refer to VNA tutorials.