Parameters S strong signal - Characterization of non-linear devices

The design of radio frequency and microwave circuits and systems in the frequency domain is based on linear and non-linear device models. Linear devices can be easily characterized by a vector network analyzer in terms of the S-parameters used as input variables for simulation software. The superposition principle is then applied to establish the linear relationships between incoming and outgoing waves at all ports of the device or system.

Non-linear devices such as transistors or amplifiers operating in the high-signal regime, on the other hand, cannot be described by S-parameters, as the superposition principle does not apply in this case. However, if we determine the operating conditions that define the non-linear characteristics of devices, the non-linear equations that translate this behavior, and the method for extracting the parameters to be used in these equations, we can use measured data directly, as is the case for S-parameters and linear devices.

The idea is to generalize the definition of S-parameters to enable the characterization of devices with non-linear behavior. Three main families of concepts have been developed and marketed under the names "X-parameters", "S-functions" and "Cardiff model". These models are all based on the linearization of the nonlinear response around a single harmonic component of the input signal, by default the fundamental input component, of large amplitude (strong signal). The non-linear behavior is then analyzed in the frequency domain by measuring the responses to low-amplitude incident waves (small signal) corresponding to the harmonic frequencies of the fundamental, applied in addition to the strong-signal fundamental.

In this article, the formulation of X parameters is retained for objective reasons such as the rich bibliography and the possibility of measuring them with a conventional network analyzer equipped simply with an ad hoc option (nonlinear vector network analyzer) and generating files directly usable with compatible simulation software.

In the first part, we review the S-parameters, which are conventional and indispensable in the design, production and characterization of radiofrequency and microwave devices. We also highlight their limitations, which have led to the development of a new concept for measuring non-linear devices.

In the second part, we pose the problem of the non-linear device or device with non-linear behavior. This behavior occurs, for example, when the device is subjected to a large amplitude or strong signal.

In the third part, we present the principle...