The objective of this thesis was to model the Fuzz Face , a transistor-based guitar distortion effect, digitally at the circuit level, and explore how changes in the discrete analog components change the digital model. The circuit was first simulated using SPICE simulation software. Typically outputs and how they changed based on transistor gains were documented. A test circuit was then constructed in lab to determine true transistor gains. An analog Fuzz Face circuit was then constructed, and physical parameters were recorded. A digital model was then created using MATLAB. Capacitive filtering effects were found to be negligible in terms of the guitar signal and were not modeled. The transistors were modeled using the Ebers-Moll equations. A MATLAB algorithm was written to produce Fuzz Face type distortion given an input guitar signal. The algorithm used numerical techniques to solve the nonlinear equations and stored them in a look-up table. This table was used to process the input clips. The sound of the Fuzz Face was not perfectly modeled, but the equations were found to provide a reasonable approximation of the circuit. Further study is needed to determine a more complete modeling equation for the circuit.

In this master thesis, a 2D device simulator run on a hybrid classical-quantum computer was developed. The simulator was developed to treat statistical quantum effects such as quantum tunneling and quantum confinement in nanoscale transistors. The simulation scheme is based on a self-consistent solution of the coupled non-linear 2D SchrödingerPoisson equations. The Open Boundary Condition (OBC) of the Schrödinger equation, which allows for electrons to pass through the device between the leads (source and drain), are modeled with the QuantumTransmitting Boundary Method (QTBM). The differential equations are discretized with the finite-element method, using rectangular mesh elements. The self-consistent loop is a very time-consuming process, mainly due to the solution of the discretized OBC Schrödinger equation. To accelerate the solution time of the Schrödinger equation, a quantum assisted domain decomposition method is implemented. The domain decomposition method of choice is the Block Cyclic Reduction (BCR) method. The BCR method is at least 15 times faster (CPU time) than solving the whole linear system of equations with the Python solver numpy.linalg.solve, based on the LAPACK routine _gesv. In the project, we also propose an alternative approach of the BCR method called the "extra layer BCR" that shows an improved accuracy for certain types of solutions. In a quantum assisted version, the matrix inverse solver as a step in the BCR method was computed on the D-Wave quantum annealer chip ADVANTAGE_SYSTEM4.1 [4]. Two alternative methods to solve the matrix inverses on a quantum annealer were compared. One is called the "unit vector" approach, based on work by Rogers and Singleton [5], and the other is called the "whole matrix" approach which was developed in the thesis. Because of the limited amount of qubits available on the quantum annealer, the "unit vector" approach was more suitable for adaption in the BCR method. Comparing the quantum annealer to the Python inverse solver numpy.linalg.inv, also based on LAPACK, it was found that an accurate solution can be achieved, but the simulation time (CPU time) is at best 500 times slower than numpy.linalg.inv.

The design of power amplifiers within a circuit simulator requires a good non-linear model that accurately predicts the electormagnetic behaviour of the power transistor. In recent years, a certain class of large signal frequency-dependent black-box behavioural modeling techniques known as Poly-Harmonic Distortion (PHD) models has been devised to mimic the non-linear unmatched RF transistor. These models promise a good prediction of the device behaviour under multi-harmonic periodic continuous wave inputs. This thesis describes the capabilities of the PHD modeling framework and the theoretical type of behaviour that it is capable of predicting. Specifically, the PHD framework cannot necessarily predict the response of a broadband aperiodic signal. This analysis will be performed by deriving the PHD modeling framework as a simplification of the Volterra series kernel functions under the assumption that the power transistor is operating under continuous periodic multi-harmonic voltage and current signals in a stable circuit. A PHD model will be seen as a set of describing functions that predict the response of the Device Under Test (DUT) for any given non-linear periodic continuous-wave inputs that have a specific fundamental frequency. Two popular implementations of PHD models that can be found in the literature are the X-parameter and Cardiff models. Each model formulates the describing functions of the general PHD model differently. The mathematical formulation of the X-parameter and Cardiff models will be discussed in order to provide a theoretical ground for comparing their robustness. The X-parameter model will be seen as the first-order Taylor series approximation of the PHD model describing functions around a Large Signal Operating Point (LSOP) of the device under test. The Cardiff large-signal model uses Fourier series coefficient functions that vary with the magnitude of the large signal(s) as the PHD model describing functions. This thesis will provide a breakdown of the measurement procedure required for the extraction of these models, the challenges involved in the measurement, as well as the mathematical extraction of the model coe cients from measurement data. As each of these models contain have extended versions that enhance the predictive capability of the model under stronger nonlinear modes of operation, a comparison is used to represent the cost of increasing model accuracy as a function of the increasing model complexity for each model. The order of complexity of each model can manifest itself in terms of the mathematical formulation, the number of parameters required and the measurement time that is required to extract each model for a given DUT. This comparison will fairly assess the relative strengths and weaknesses of each model.

The design of power amplifiers within a circuit simulator requires a good non-linear model that accurately predicts the electormagnetic behaviour of the power transistor. In recent years, a certain class of large signal frequency-dependent black-box behavioural modeling techniques known as Poly-Harmonic Distortion (PHD) models has been devised to mimic the non-linear unmatched RF transistor. These models promise a good prediction of the device behaviour under multi-harmonic periodic continuous wave inputs. This thesis describes the capabilities of the PHD modeling framework and the theoretical type of behaviour that it is capable of predicting. Specifically, the PHD framework cannot necessarily predict the response of a broadband aperiodic signal. This analysis will be performed by deriving the PHD modeling framework as a simplification of the Volterra series kernel functions under the assumption that the power transistor is operating under continuous periodic multi-harmonic voltage and current signals in a stable circuit. A PHD model will be seen as a set of describing functions that predict the response of the Device Under Test (DUT) for any given non-linear periodic continuous-wave inputs that have a specific fundamental frequency. Two popular implementations of PHD models that can be found in the literature are the X-parameter and Cardiff models. Each model formulates the describing functions of the general PHD model differently. The mathematical formulation of the X-parameter and Cardiff models will be discussed in order to provide a theoretical ground for comparing their robustness. The X-parameter model will be seen as the first-order Taylor series approximation of the PHD model describing functions around a Large Signal Operating Point (LSOP) of the device under test. The Cardiff large-signal model uses Fourier series coefficient functions that vary with the magnitude of the large signal(s) as the PHD model describing functions. This thesis will provide a breakdown of the measurement procedure required for the extraction of these models, the challenges involved in the measurement, as well as the mathematical extraction of the model coe cients from measurement data. As each of these models contain have extended versions that enhance the predictive capability of the model under stronger nonlinear modes of operation, a comparison is used to represent the cost of increasing model accuracy as a function of the increasing model complexity for each model. The order of complexity of each model can manifest itself in terms of the mathematical formulation, the number of parameters required and the measurement time that is required to extract each model for a given DUT. This comparison will fairly assess the relative strengths and weaknesses of each model.

Next generation mobile communication systems require the use of linear RF power amplifier for higher data transmission rates. However, linear RF power amplifiers are inherently inefficient and usually require additional circuits or further system adjustments for better efficiency. This dissertation focuses on the development of new efficiency enhancement schemes for linear RF power amplifiers. The multistage Doherty amplifier technique is proposed to improve the performance of linear RF power amplifiers operated in a low power level. This technique advances the original Doherty amplifier scheme by improving the efficiency at much lower power level. The proposed technique is supported by a new approach in device periphery calculation to reduce AM/AM distortion and a further improvement of linearity by the bias adaptation concept. The device periphery adjustment technique for efficiency enhancement of power amplifier integrated circuits is also proposed in this work. The concept is clearly explained together with its implementation on CMOS and SiGe RF power amplifier designs. Furthermore, linearity improvement technique using the cancellation of nonlinear terms is proposed for the CMOS power amplifier in combination with the efficiency enhancement technique. In addition to the efficiency enhancement of power amplifiers, a scalable large-signal MOSFET model using the modified BSIM3v3 approach is proposed. A new scalable substrate network model is developed to enhance the accuracy of the BSIM3v3 model in RF and microwave applications. The proposed model simplifies the modeling of substrate coupling effects in MOS transistor and provides great accuracy in both small-signal and large-signal performances.