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**What you will learn:**

- What are S-parameters?
- The multiple types of S-parameters beyond the small-signal variety.

Scatter parameters (S-parameters), which describe the fundamental characteristics of RF networks, come in many forms, including small-signal, large-signal, pulsed, cold, and mixed modes. They quantify how RF energy travels 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 single-ended network, which can be used to represent many standard RF components such as RF amplifiers, filters, or attenuators, to name a few.

The wave magnitudes, represented schematically in *Figure** **1*, are complex amplitudes of the voltage waves incident on ports 1 and 2 of the device. If we stimulate one port at a time with the corresponding wave quantity a_{1} or one_{2} when the other port terminates in the matched load, we can define the forward and reverse responses of the device in terms of b-wave quantities. These quantities represent the voltage waves reflected and transmitted by the network ports.

If we take the ratio of the resulting complex responses and the initial stimulus quantities, the S-parameters of a two-port component can be defined as shown in Equation 1:

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

The matrix S can be defined in a similar way for an arbitrary N port RF component.^{1.2}

### Types of S-parameters

*Small Signal*

Unless explicitly stated otherwise, the term “S-parameters” generally refers to 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 mode of operation. 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 .

*big signal *

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

The S-parameters of small and large signals are typically measured using continuous wave (CW) stimulation signals and applying narrowband response sensing. However, many RF components are designed to work with pulsed signals, which have a wide response in the frequency domain. It is therefore difficult to accurately characterize an RF component using the standard narrowband detection method.

*pulsed*

Therefore, for the characterization of devices in pulsed mode, the so-called pulsed S-parameters are generally used. These scattering parameters are obtained using special impulse response measurement techniques.^{3}

*Cold*

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

*Mixed mode*

So far we have defined S-parameters for a typical 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 S-parameters in mixed mode. *Figure 2* shows an example of the mixed-mode scattering parameters grouped into an extended S-matrix representing a typical two-port balanced component.

The indices of the mixed-mode S-parameters in this matrix use the naming convention b-mode, a-mode, b-port, and a-port. The first two describe the modes of the response port (mode b) and the stimulus port (mode a), and the last two specify the index numbers of these ports, where port b is the response and port a to the Port stimulus.

In our example, the port modes are defined by either the index 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 matrix S will also have additional elements with subscripts s describing the obtained quantities for unbalanced ports.

Mixed mode broadcast parameters allow us to determine basic parameters of an RF component such as return loss or gain. In addition, they help determine the key factors of merit used to characterize the performance of differential circuits, such as common mode rejection ratio (CMRR), amplitude imbalance, and phase imbalance.

### Conclusion

This article presented the basic definitions and briefly discussed the main types of broadcast parameters. S-parameters can be used to describe the fundamental characteristics of RF components at different frequencies and for different signal power levels.

The development of RF applications relies on the use of S-parameter data describing the integral structures and constituent components of RF designs. RF engineers measure or rely on already existing S-parameter data, which is usually stored in standard text files called Touchstone or SnP files. These files are often provided free of charge for the most popular RF components available on the market today.

### References

1.David Pozar, *microwave engineering*, Fourth Edition. Willey, 2011.

2. Michael Hiebel, *Fundamentals of** **Vector network analysis*. Rohde & Schwarz, 2007.

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