Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance.

Today’s advances in communication systems and VLSI circuits increases the performance requirements and complexity of circuits. The performance of RF and mixed-signal circuits is normally limited by the nonlinear behavior of the transistors used in the design. This makes simulation of nonlinear circuits more important. Volterra series is a method used for simulation of mildly nonlinear circuits. Using Volterra series the response of the nonlinear circuit is converted into a sum of multiple linear circuit responses. Thus, using Volterra series, simulation of nonlinear circuits in frequency-domain analysis becomes possible. However, Volterra series is not able to simulate strongly nonlinear circuits such as saturated Power Amplifiers. In this thesis, a new time-varying Volterra analysis is presented. The time-varying Volterra analysis is the generalization of conventional Volterra analysis where instead of using a DC expansion point a time-varying waveform has been used. Employing a time-varying expansion waveform for Volterra analysis, time-varying Volterra achieves better accuracy than conventional Volterra. The time-varying expansion waveforms are derived using a fast pre-analysis of the circuit. Using numerical examples, it has been shown that the time-varying Volterra is capable of simulating nonlinear circuits with better accuracy than conventional Volterra analysis. The time-varying Volterra analysis in both time and frequency domains are discussed in this thesis. The time-varying Volterra analysis has been used to simulate a saturated Class-F Power Amplifier in frequency-domain. The simulation results show good agreement with ELDO® steady-state and Harmonic Balance simulation results. The proposed method manages to simulate nonlinear circuits, such as saturated Power Amplifier, mixers and nonlinear microwave circuits, with good accuracy. Also, this method can be used to simulate circuit with large number of nonlinear elements without the convergence issues of Harmonic Balance.

In this paper we present an approach to the nonlinear model reduction based on representing the nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a 'training input'. Computational results and performance data are presented for a nonlinear circuit and a micromachined fixed-fixed beam example. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques. Finally, it is shown tat the proposed technique is computationally inexpensive, and that the models can be constructed 'on-the-fly', to accelerate simulation of the system response. / Singapore-MIT Alliance (SMA)

We consider a type of forced "Van Der Pol" oscillator where the forced function is periodic and oscillatory around the t-axis. This problem derived from an electrical model. The important issues here is that this circuits presents the spiking phenomena over a one time period and it has important applications in signal processing and digital communication. The three most important problems that we addressed here in this thesis are to compute the number of spikes a solution completes in one time period (it can be used to transform the analog signal into digital information), how the dynamics of the number of spikes change with respect to the parameters amplitude (k) and frequency (w), and when the coupled circuits synchronize (i.e., the driver and the respond are on synchronous). Sophisticated mathematical and numerical analysis has been developed that enable us to give a complete study of the problems above described.

[pt] As técnicas de otimização multicritérios, que tiveram sua origem na área econômica, são necessárias na busca de soluções em qualquer ambiente onde existam objetivos competindo entre si. Nestes ambientes pode não existir uma solução ótima para determinado problema e sim soluções de compromisso entre os vários objetivos conflitantes. Uma das muitas áreas onde múltiplos objetivos coexistem é a área de Projetos de Circuitos Eletrônicos, onde desde um compromisso entre ganho e banda passante até compromissos bem mais complexos são freqüentemente encontrados. Para circuitos com alguma complexidade, processos analíticos são virtualmente inviáveis, tornando-se assim indispensável a utilização do computador como instrumento de projeto. Foi desenvolvido, então, um pacote em FORTRAN com aproximadamente 3.000 linhas de instrução para projetar nominalmente circuitos eletrônicos não lineares. Este pacote, respeitando a topologia fornecida para o circuito, atribui valores aos parâmetros de projeto, no caso valores de resistores, capacitores e indutores, de forma a atingir as especificações solicitadas. As opções existentes de projeto que foram implementadas são as seguintes: especificação das tensões nodais DC e/ou polarização de transistores e/ou faixa dinâmica e/ou impedância de entrada e/ou impedância de saída nas freqüências desejadas, além de poder ser escolhida a faixa de variação dos parâmetros de projeto. Estão contidos também, modelos globais (DC/AC) dos dispositivos eletrônicos mais comuns que podem ser solicitados pelo usuário, conforme sua necessidade ao descrever o circuito. Os modelos disponíveis são os seguintes: diodo de junção, transistores bipolares npn e pnp e amplificador operacional com entrada bipolar. / [en] Multiple criterion optimization techniques must be used in environments which competing objetives. In such environments no optimal solution is attained, but only compromise solutions among all the competing objectives. One of these environments is the Designs of Electronic Circuits, whose design compromises generally range from gain and bandwith to much more complex ones. For somewhat complex circuits, analitical processes are virtually unfeasible, so a digital computer has to be used as an instrument for calculus. Thus, a FORTRAN package was written to design nominally non-linear electronic circuits. This package, maintaining the circuit topology unchanged, gives values to resisters, capacitors and inductores so that it may meet the design requirements. The design options provided by the package are: specification of the node voltages and/or total biasing bipolar transistors (Vce - Ic) and/or total power comsumption and/or frequency response and/or input impedance and/or output impedance and/or dynamic range. All these options can be requested limiting the range of variation in the design parameters (resistors, capacitors and inductors) The package still provides global models for semiconductor devides which are: junction diode, bipolar npn/pnp transistors and an operational amplifier macro-model. The design options offered and the general purpose structure of the package provide a favorable environment for the application of the multiple criterion optimization techniques.

[pt] Este trabalho trata dos efeitos das não-linearidades de transistores de efeito de campo utilizados em amplificadores de microondas. Para tanto, o transistor é modelado por um circuito não- linear equivalente, cujos elementos são determinados através da medição dos parâmetros espalhamento do mesmo, na faixa de 3 GHz a 9 GHz, e com o auxílio de um programa de otimização de circuitos e outro de ajuste de curvas. O método de análise utilizado é o da expansão em série de Volterra, para o qual foi desenvolvido um programa computacional que permite a determinação dos ganhos de transdução e das potências de saída na freqüência fundamental e no terceiro produto de intermodulação, bem como do ponto de 1dB de compressão de ganho, da taxa de distorção de intermodulação de terceira ordem. Esse programa permite, ainda, a verificação da influência das impedâncias de fechamento fora da faixa, nas características de distorção de intermodulação. Através dessa análise pôde-se verificar que as terminações fora da faixa exercem pouca ou nenhuma influência nas características de distorção de intermodulação, com exceção das terminações na freqüência diferença, (freqüência de diferença = freqüência 2 - freqüência 1), onde pôde-se constatar uma redução de até 8dB no nível do terceiro produto de intermodulação, para uma escolha apropriada das impedâncias de fechamento nessa freqüência. Esses resultados, contudo, não podem ser considerados definitivos, uma vez que o modelo adotado não levou em consideração o fato do FET utilizado ser pré-adaptado. Também, devido ao transistor ter-se danificado durante as medições de intermodulação, tais resultados não puderam ser comprovados experimentalmente. / [en] This work deals with the effects of non-linear ities of field-effect transistors used in microwave amplifiers. To do so, the transistor is modeled by a non-linear equivalent circuit, with its components determined through the measurement of its scattering parameters, in the range of 3 GHz to 9GHz, and with the aid of a circuit optimization program and another for curve fitting. The method of analysis used is the Volterra series expansion, for which a computer program was developed, permitting the determination of the transducer gains and output powers in the fundamental frequency, and in the third-order intermodulation product, as well as the 1 dB compression point, the third-order intermodulation distortion ratio, and the third-order intercept point. This program also allows for the verification of the influence of out-of-band terminating impedances on the intermodulation distortion characteristics. Through this analysis it was possible to verify that the out-of-band terminations have little or no influence on the intermodulation distortion characteristics, with the exception of the terminations in the difference frequency, (difference frequency = frequency 2 - frequency 1), for which it was found a decrease of up to 8 dB in the third- order intermodulation product level, for the appropriate choice of these impedances. These results, however, cannot be said to represent the real behavior of the FET since the model used did not account for the internal matching of the device. Also, due to the fact that the transistor was damaged during the intermodulation measurements, such results could not be verified experimentally.

The objective of this research is to develop, characterize, and demonstrate novel parametric architectures capable of wideband operation while maintaining high gain and stability. To begin the study, phase-incoherent upconverting parametric amplifiers will be explored by first developing a set of analytical models describing their achievable gain and efficiency. These models will provide a set of design tools to optimize and evaluate prototype circuit boards. The prototype boards will then be used to demonstrate their achievable gain, bandwidth, efficiency, and stability. Further investigation of the analytical models and data collected from the prototype boards will conclude bandwidth and gain limitations and end the investigation into phase-incoherent upconverting parametric amplifiers in lieu of negative-resistance parametric amplifiers. Traditionally, there were two versions of negative-resistance parametric amplifiers available: degenerate and non-degenerate. Both modes of operation are considered single-frequency amplifiers because both the input and output frequencies occur at the source frequency. Degenerate parametric amplifiers offer more power gain than their non-degenerate counterpart and do not require additional circuitry for idler currents. As a result, a phase-coherent degenerate parametric amplifier printed circuit board prototype will be built to investigate achievable gain, bandwidth, and stability. Analytical models will be developed to describe the gain and efficiency of phase-coherent degenerate parametric amplifiers. The presence of a negative resistance suggests the possibility of instability under certain operating conditions, therefore, an in-depth stability study of phase-coherent degenerate parametric amplifiers will be performed. The observation of upconversion gain in phase-coherent degenerate parametric amplifiers will spark investigation into a previously unknown parametric architecture: phase-coherent upconverting parametric amplifiers. Using the phase-coherent degenerate parametric amplifier prototype board, stable phase-coherent upconversion with gain will be demonstrated from the source input frequency to its third harmonic. An analytical model describing the large-signal transducer gain of phase-coherent upconverting parametric amplifiers from the first to the third harmonic of the source input will be derived and validated using the prototype board and simulations.

MOR (Model Order Reduction) est devenu un domaine très répondu dans la recherche grâce à l'intérêt qu'il peut apporter dans la réduction des systèmes, ce qui permet d'économiser du temps, de la mémoire et le coût de CPU pour les outils de CAO. Ce domaine contient principalement deux branches: linéaires et non linéaires. MOR linéaire est un domaine mature avec des techniques numériques bien établie et bien connus dans la domaine de la recherche, par contre le domaine non linéaire reste vague, et jusqu'à présent il n'a pas montré des bons résultats dans la simulation des circuits électriques. La recherche est toujours en cours dans ce domaine, en raison de l’intérêt qu'il peut fournir aux simulateurs contemporains, surtout avec la croissance des puces électroniques en termes de taille et de complexité, et les exigences industrielles vers l'intégration des systèmes sur la même puce.Une contribution significative, pour résoudre le problème de Harmonic Balance (Equilibrage Harmonique) en utilisant la technique MOR, a été proposé en 2002 par E. Gad et M. Nakhla. La technique a montré une réduction substantielle de la dimension du système, tout en préservant, en sortie, la précision de l'analyse en régime permanent. Cette méthode de MOR utilise la technique de projection par l'intermédiaire de Krylov, et il préserve la passivité du système. Cependant, il souffre de quelques limitations importantes dans la construction de la matrice “pre-conditioner“ qui permettrait de réduire le système. La limitation principale est la nécessité d'une factorisation explicite comme une suite numérique de l'équation des dispositifs non linéaires . cette limitation rend la technique difficile à appliquer dans les conditions générales d'un simulateur. Cette thèse examinera les aspects non linéaires du modèle de réduction pour les équations de bilan harmoniques, et il étudiera les solutions pour surmonter les limitations mentionnées ci-dessus, en particulier en utilisant des approches de dérivateur numériques. / MOR recently became a well-known research field, due to the interest that it shows in reducing the system, which saves time, memory, and CPU cost for CAD tools. This field contains two branches, linear and nonlinear MOR, the linear MOR is a mature domain with well-established theory and numerical techniques. Meanwhile, nonlinear MOR domain is still stammering, and so far it didn’t show good and successful results in electrical circuit simulation. Some improvements however started to pop-up recently, and research is still going on this field because of the help that it can give to the contemporary simulators, especially with the growth of the electronic chips in terms of size and complexity due to industrial demands towards integrating systems on the same chip. A significant contribution in the MOR technique of HB solution has been proposed a decade ago by E. Gad and M. Nakhla. The technique has shown to provide a substantial system dimension reduction while preserving the precision of the output in steady state analysis. This MOR method uses the technique of projection via Krylov, and it preserves the passivity of the system. However, it suffers a number of important limitations in the construction of the pre-conditioner matrix which is ought to reduce the system. The main limitation is the necessity for explicit factorization as a power series of the equation of the nonlinear devices. This makes the technique difficult to apply in general purpose simulator conditions. This thesis will review the aspects of the nonlinear model order reduction technique for harmonic balance equations, and it will study solutions to overcome the above mentioned limitations, in particular using numerical differentiation approaches.

Se presenta un estudio de las oscilaciones microondas en régimen de gran señal en dispositivos activos de estado sólido caracterizados por su función descriptiva sinusoidal. Para ello se han confeccionado programas de cálculo frecuencial no lineal que resuelven circuitos de microondas formados por una o varias no linealidades cargadas por cualquier circuito pasivo externo. Por último se hace un estudio experimental exhaustivo para comprobar la aplicabilidad de los métodos precedentemente descritos.

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.