# RF Demystified: S-Parameters and Their Types

### Вопрос:

What are S-parameters and their main types?

### Ответ:

S-parameters describe the fundamental characteristics of RF networks, and their main types include small signal, large signal, pulsed, cold, and mixed-mode S-parameters.

### Introduction

This article continues a series of short discourses written to solve much of the RF mystery for non-RF engineers. Some of these RF articles are: “RF Demystified—Understanding Wave Reflections,” which discusses wave reflections, and “How to Easily Select the Right Frequency Generation Component,” which reviews the main types of frequency generation components that fulfill functions in the RF signal chain.

This time we will talk about the most basic term one needs to know to describe any RF component—the scattering parameters (or S-parameters). However, unlike many other articles on this topic, this one will not only focus on the basic definitions of S-parameters but will also give a concise overview of their key types commonly used in RF engineering.

### Fundamental Definitions

S-parameters quantify how RF energy propagates through a system and thus contain information about its fundamental characteristics. Using S-parameters, we can represent even the most complex RF device as a simple N-port network. Figure 1 shows an example of a two-port unbalanced network, which can be used to represent many standard RF components such as RF amplifiers, filters, or attenuators, just to name a few

The wave quantities a, schematically shown in Figure 1, are complex amplitudes of the voltage waves incident on Port 1 and Port 2 of the device. If we stimulate one port at a time with the corresponding wave quantity a1 or a2 when the other port is terminated into the matched load, we can define the forward and reverse responses of the device in terms of the wave quantities b. These quantities represent voltage waves reflected from and transmitted through the ports of the network. If we take the ratio of the resulting complex responses and the initial stimulus quantities, we can define the S-parameters of a two-port component as shown in Equation 1:

The intrinsic response of the network can then be expressed by grouping S-parameters together into a scattering matrix (S-matrix), which relates the complex wave quantities at all its ports. For the two-port unbalanced network, the stimulus-response relation will obtain the form in Equation 2:

The S-matrix can be defined in a similar manner for an arbitrary N-port RF component.1,2

### Types of S-Parameters

If not explicitly stated otherwise, the term “S-parameters” usually refers to the small signal S-parameters. They represent an RF network response to a small signal stimulus quantifying its reflection and transmission characteristics over frequency in a linear operational mode. Using small signal S-parameters, we can determine basic RF characteristics including voltage standing wave ratio (VSWR), return loss, insertion loss, or gain at given frequencies.

However, if we continuously increase the power level of a signal that is passing through an RF device, it will often result in more pronounced nonlinear effects. These effects can be quantified using another type of scattering parameters called large signal S-parameters. They vary not only across different frequencies but also across different power levels of a stimulus signal. This type of scattering parameter can be used to determine nonlinear characteristics of a device such as its compression parameters.

Both small and larger signal S-parameters are usually measured using continuous-wave (CW) stimulus signals and applying a narrow-band response detection. However, many RF components are designed to be operated with pulsed signals, which have a broad frequency-domain response. This makes it challenging to accurately characterize an RF component using the standard narrow-band detection method. Therefore, for the characterization of devices in a pulsed mode, the so-called pulsed S-parameters are typically utilized. These scattering parameters are obtained using special pulse-response-measurement techniques.3

Another particular type of S-parameters, which is rarely talked about, but which might sometimes become important to consider, is cold S-parameters. The term “cold” means that the scattering parameters are obtained for an active device in a nonactive mode (that is, when all its active elements are inactive, for example, transistor junctions are reverse or zero biased and no transfer currents flow). This type of S-parameters can be used for instance to improve matching of the signal chain segments with off-state components that cause high reflections in the signal path.

Up until now, we have defined S-parameters for a typical example of a single-ended component when the stimulus and response signals are referenced to ground. However, for balanced components that have differential ports, this definition is not sufficient. Balanced networks require a broader characterization approach, which must be able to fully describe their differential-mode and common-mode responses. This can be achieved by using mixed-mode S-parameters. Figure 2 shows an example of the mixed-mode scattering parameters grouped together into an extended S-matrix representing a typical two-port balanced component.

Subscripts of the mixed-mode S-parameters in this matrix use the naming convention b-mode, a-mode, b-port, and a-port, where the former two describe the modes of the response port (b-mode) and stimulus port (a-mode), and the latter two specify index numbers of these ports, where b-port corresponds to the response and a-port to the stimulus port. In our example, the port modes are defined either by the subscript d—differential—or c—common mode. However, in a more general case of a component that has both balanced and unbalanced ports, a mixed-mode S-matrix will also have additional elements with subscript s describing the quantities obtained for the single-ended ports. The mixed-mode scattering parameters allow us to determine not only the basic parameters of an RF component such as return loss or gain but also the key figures of merit used to characterize performance of the differential circuits such as common-mode rejection ratio (CMRR), magnitude imbalance, and phase imbalance.

### Conclusion

This article has presented basic definitions and briefly discussed the key types of scattering parameters. The S-parameters can be used to describe fundamental characteristics of RF components at different frequencies and for different power levels of a signal. The development of RF applications highly relies on the use of S-parameter data describing integral structures and constituent components of RF designs. RF engineers measure or rely on already existing S-parameter data, which is typically stored in standard text files known as Touchstone or SnP files. These files are often freely provided for the most popular RF components available on the market today.

Analog Devices provides the broadest portfolio of integrated RF components in the industry addressing the most demanding requirements across a wide variety of applications. In order to support RF engineers and ease the development process of the target applications, ADI offers the entire ecosystem around RF technologies including scattering parameters for a wide range of RF products, design tools, simulation models, reference designs, rapid prototyping platforms, and a discussion forum.

### References

1David Pozar. Microwave Engineering, Fourth Edition. Wiley, 2011.

2Michael Hiebel. Fundamentals of Vector Network Analysis. Rohde & Schwarz, 2007.

3Pulsed Measurements Using Narrowband Detection and a Standard PNA Series Network Analyzer.” Keysight Technologies, December 2017.