Measurement-based modeling of vector network analyzer calibration standards and nonlinear microwave devices using artificial neural networks

This thesis is comprised of two parts. The first segment covers artificial neural network (ANN) modeling for improved vector network analyzer (VNA) calibrations. Specifically, measurement-based ANNs are applied to model a variety of on-wafer and coaxial vector network analyzer calibrations, including open-short-load-thru (OSLT) and line-reflect-match (LRM). A sensitivity analysis of the ANNs is performed by determining the training error as functions of the number of hidden neurons and the number of training points. The respective accuracies of these calibrations are then assessed using the ANN-modeled standards. As a major research result, this doctoral thesis shows that ANN models offer a number of advantages over using calibrated measurement data files or equivalent circuit models, namely: they do not require the numerous details and parameters of physical models; calibration times can be reduced because only a few training points are required to accurately model the standards; ANN model descriptions are much more compact than large measurement data files; ANN models, trained on only a few measurement points can be much more accurate than direct calibrations when limited calibration data are available; ANNs give an optimized estimate in the presence of noise; and ANN models are able to accurately model loads with measured DC resistances slightly outside of their training range.; In the second part of this thesis, new frequency-domain models and figures of merit for nonlinear microwave circuits are developed for sparse-tone inputs. This section begins with a method for preserving time-invariant phase relationships when ratios are taken between two harmonically related signals by introducing a third signal that is used as a phase reference. Then, as another major research result, this doctoral thesis introduces nonlinear large-signal scattering ($S$) parameters, a new type of frequency-domain mapping that relates incident and reflected signals. A general form of nonlinear large-signal $S$-parameters is presented. It is shown that they reduce to classic S-parameters in the absence of nonlinearities. Nonlinear large-signal impedance ($Z$) and admittance ($A$) parameters are also introduced, and equations relating the different representations are derived. Next, definitions of power gain, transducer gain, and available gain are expanded by taking harmonic content into account. An example is provided showing how the expanded definitions of gain and nonlinear large-signal $S$-parameters allow one to examine the behavior of a nonlinear model by simply performing a harmonic balance simulation. Next, this thesis illustrates how nonlinear large-signal $S$-parameters can be used as a tool in the design process of a nonlinear circuit, specifically a single-diode 1–2 GHz frequency-doubler. For the case where a nonlinear model is not readily available, a method of extracting nonlinear large-signal $S$-parameters is developed using ANN models trained with multiple measurements made by a nonlinear vector network analyzer equipped with two sources. Finally, nonlinear large-signal $S$-parameters are compared to another form of nonlinear mapping, known as nonlinear scattering functions. The nonlinear large-signal $S$-parameters are shown to be more general.