Sistemas de geração distribuída conectados à rede devem atender as especificações técnicas de conexão no que tange à injeção de corrente harmônica na rede elétrica. No intuito de satisfazer tais requerimentos de rede, filtros passivos são utilizados para interfacear o inversor fotovoltaico e a rede. Essa dissertação compara a resposta característica do tradicional filtro indutivo (filtro L) com o filtro Indutivo-Capacitivo-Indutivo (filtro LCL). É mostrado que o aumento da indutância permite uma supressão suficiente do ripple de corrente proveniente da frequência de chaveamento do inversor. O filtro LCL no entanto, proporciona uma melhor atenuação harmônica, o que permite reduzir o tamanho do filtro. A grande desvantagem do filtro LCL é sua impedância, que é caracterizada por um pico de ressonância próximo da frequência de corte do filtro, a qual deve ser amortecida para evitar a instabilidade. Técnicas passivas e ativas podem ser utilizadas para amortecer a ressonância do filtro LCL. Para abordar estas questões, esta dissertação apresenta uma comparação do controle de corrente do inversor trifásico conectado à rede com filtro L e com filtro LCL, discutindo a utilização de amortecimento passivo e ativo para diferentes regiões de frequência de ressonância. A partir dos modelos matemáticos, desenvolveu-se uma metodologia de projeto dos controladores e o comportamento dinâmico do sistema operando em malha fechada foi investigado. Para validar os estudos desenvolvidos ao longo desse trabalho, resultados experimentais são apresentados utilizando uma plataforma experimental trifásica de 5kW. Os principais componentes e suas funções são discutidas no decorrer do trabalho. Resultados experimentais são obtidos para verificar as análises teóricas e ilustrar o desempenho do inversor trifásico fotovoltaico conectado à rede elétrica com filtro L e filtro LCL. É mostrado que a frequência de ressonância e a frequência de amostragem do sistema podem ser relacionadas de maneira a se calcular uma frequência crítica, abaixo da qual é essencial realizar o amortecimento do filtro LCL. Ainda, os resultados experimentais mostram que o amortecimento ativo por resistor virtual, embora apresente um desenvolvimento simples, é eficaz para amortecer a ressonância do filtro LCL e permitir que o sistema opere estável dentro dos parâmetros pré-determinados. / Distributed generation systems must fulfill standards specifications of current harmonics injected to the grid. In order to satisfy these grid requirements, passive filters are connected between inverter and grid. This work compares the characteristic response of the traditional inductive (L) filter with the inductive-capacitive-inductive (LCL) filter. It is shown that increasing the inductance L leads to a good ripple current suppression around the inverter switching frequency. The LCL filter provides better harmonic attenuation and reduces the filter size. The main drawback is the LCL filter impedance, which is characterized by a typical resonance peak, which must be damped to avoid instability. Passive or active techniques can be used to damp the LCL resonance. To address this issue, this dissertation presents a comparison of current control for PV grid-tied inverters with L filter and LCL filter and also discuss the use of active and passive damping for different regions of resonance frequency. From the mathematical models, a design methodology of the controllers was developed and the dynamic behavior of the system operating in closed loop was investigated. To validate the studies developed during this work, experimental results are presented using a three-phase 5kW experimental platform. The main components and their functions are discussed in this work. Experimental results are given to support the theoretical analysis and to illustrate the performance of grid-connected PV inverter system. It is shown that the resonant frequency of the system, and sampling frequency can be associated in order to calculate a critical frequency, below which is essential to perform the damping of the LCL filter. Also, the experimental results show that the active buffer per virtual resistor, although with a simple development, is effective to damp the resonance of the LCL filter and allow the system to operate stable within predetermined parameters.

Sistemas de geração distribuída conectados à rede devem atender as especificações técnicas de conexão no que tange à injeção de corrente harmônica na rede elétrica. No intuito de satisfazer tais requerimentos de rede, filtros passivos são utilizados para interfacear o inversor fotovoltaico e a rede. Essa dissertação compara a resposta característica do tradicional filtro indutivo (filtro L) com o filtro Indutivo-Capacitivo-Indutivo (filtro LCL). É mostrado que o aumento da indutância permite uma supressão suficiente do ripple de corrente proveniente da frequência de chaveamento do inversor. O filtro LCL no entanto, proporciona uma melhor atenuação harmônica, o que permite reduzir o tamanho do filtro. A grande desvantagem do filtro LCL é sua impedância, que é caracterizada por um pico de ressonância próximo da frequência de corte do filtro, a qual deve ser amortecida para evitar a instabilidade. Técnicas passivas e ativas podem ser utilizadas para amortecer a ressonância do filtro LCL. Para abordar estas questões, esta dissertação apresenta uma comparação do controle de corrente do inversor trifásico conectado à rede com filtro L e com filtro LCL, discutindo a utilização de amortecimento passivo e ativo para diferentes regiões de frequência de ressonância. A partir dos modelos matemáticos, desenvolveu-se uma metodologia de projeto dos controladores e o comportamento dinâmico do sistema operando em malha fechada foi investigado. Para validar os estudos desenvolvidos ao longo desse trabalho, resultados experimentais são apresentados utilizando uma plataforma experimental trifásica de 5kW. Os principais componentes e suas funções são discutidas no decorrer do trabalho. Resultados experimentais são obtidos para verificar as análises teóricas e ilustrar o desempenho do inversor trifásico fotovoltaico conectado à rede elétrica com filtro L e filtro LCL. É mostrado que a frequência de ressonância e a frequência de amostragem do sistema podem ser relacionadas de maneira a se calcular uma frequência crítica, abaixo da qual é essencial realizar o amortecimento do filtro LCL. Ainda, os resultados experimentais mostram que o amortecimento ativo por resistor virtual, embora apresente um desenvolvimento simples, é eficaz para amortecer a ressonância do filtro LCL e permitir que o sistema opere estável dentro dos parâmetros pré-determinados. / Distributed generation systems must fulfill standards specifications of current harmonics injected to the grid. In order to satisfy these grid requirements, passive filters are connected between inverter and grid. This work compares the characteristic response of the traditional inductive (L) filter with the inductive-capacitive-inductive (LCL) filter. It is shown that increasing the inductance L leads to a good ripple current suppression around the inverter switching frequency. The LCL filter provides better harmonic attenuation and reduces the filter size. The main drawback is the LCL filter impedance, which is characterized by a typical resonance peak, which must be damped to avoid instability. Passive or active techniques can be used to damp the LCL resonance. To address this issue, this dissertation presents a comparison of current control for PV grid-tied inverters with L filter and LCL filter and also discuss the use of active and passive damping for different regions of resonance frequency. From the mathematical models, a design methodology of the controllers was developed and the dynamic behavior of the system operating in closed loop was investigated. To validate the studies developed during this work, experimental results are presented using a three-phase 5kW experimental platform. The main components and their functions are discussed in this work. Experimental results are given to support the theoretical analysis and to illustrate the performance of grid-connected PV inverter system. It is shown that the resonant frequency of the system, and sampling frequency can be associated in order to calculate a critical frequency, below which is essential to perform the damping of the LCL filter. Also, the experimental results show that the active buffer per virtual resistor, although with a simple development, is effective to damp the resonance of the LCL filter and allow the system to operate stable within predetermined parameters.

Orientador: Ernesto Ruppert Filho / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-19T04:10:37Z (GMT). No. of bitstreams: 1 Nogueira_ViniciusdeFreitasGomes_M.pdf: 1151425 bytes, checksum: 25421deb7c7d0073c31744365ccb6e53 (MD5) Previous issue date: 2011 / Resumo: Os geradores síncronos trifásicos são atualmente os mais utilizados em geração de energia elétrica em grande escala no mundo todo. Na geração de energia elétrica em pequena escala, geralmente como geração distribuída, ligada à rede de distribuição em média tensão ou até mesmo em baixa tensão, eles tem sido muito usados devido à sua principal qualidade que é a de operar em velocidade constante. Entre as suas aplicações em geração distribuída destacam-se aquelas que usam energias renováveis como em médios e pequenos aproveitamentos hidráulicos, em aproveitamentos da biomassa e nos aproveitamentos eólicos. Neste trabalho estuda-se a modelagem do gerador síncrono, estabilidade transitória utilizando os diferentes modelos de representação do gerador síncrono e o seu desempenho dinâmico em algumas situações de operação em geração distribuída com cargas lineares e com cargas não lineares, com e sem o uso de filtragem ativa / Abstract: The three-phase synchronous generators are currently the most used in generating electricity on a large scale worldwide. In generating electricity on a small scale, usually as distributed generation, connected to the distribution network or even medium voltage low voltage, they have been widely used due to its main quality is to operate at constant speed. Among its applications in distributed generation to include those using renewable energy as in medium and small hydroelectric plants, biomass and hydroelectric in the Windmill. This paper studies the modeling of the synchronous generator, transient stability using different models of representation of the synchronous generator and its dynamic performance in some situations of operation distributed generation with linear loads and nonlinear loads, with and without the use of filtering active / Mestrado / Energia Eletrica / Mestre em Engenharia Elétrica

Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch. / ENGLISH ABSTRACT: This dissertation presents a synthesis method for broadband high-power absorptive microwave lters by cascading a wide stop-band wa e-iron lter with an absorptive harmonic pad. The classical image impedance synthesis methods for wa e-iron lters are updated to allow for non-uniform boss patterns, which enable control over both the stop-band attenuation and pass-band re ection of the lter. By optimising an accurate circuit model equivalent, computationally intensive numerical EM optimisation are avoided. The nonuniform wa e-iron lter achieves the same electrical speci cation as similar lters in literature, but in a smaller form factor. The prototype presented displays less than -21 dB in-band re ection over 8.5 - 10.5 GHz, with stop-band attenuation in excess of 50 dB over the harmonic bands 17 - 31.5 GHz and 30 dB over the 34 - 42 GHz. The prototype is designed to handling 4 kW peak power incident in the transmitted band, and is 130 mm in length. Minimal full-wave tuning is required post-synthesis, and good agreement is found between synthesised and measured responses. Additionally, a completely novel oblique wa e-iron boss pattern is proposed. For the absorptive harmonic pad, transversal broadwall slots in rectangular waveguide, coupling to an absorptive auxiliary guide, are investigated in the presence of standing wave surface current distributions. An accurate circuit model description of the cascaded structure is developed, and optimised to provide a required level of input match in the presence of an arbitrary re ective lter. Using numerical port parameter data of the wa eiron lter, a harmonic pad is developed that provides -12.5 dB input re ection match across the band 17 - 21 GHz with up to 1 kW peak incident power handling capability, yet is only 33 mm in length. Again, good agreement is found between synthesised and measured responses of the cascaded structure. / AFRIKAANSE OPSOMMING: Hierdie proefskrif stel 'n sintesetegniek voor vir wyeband, ho edrywing absorberende mikrogol lters deur 'n kaskade kombinasie van 'n verlieslose wafelyster lter met 'n wye stopband, en 'n absorberende harmoniekdemper. Die klassieke sintesemetodes vir wafelyster lters word aangepas om nie-uniforme tandpatrone toe te laat, wat beheer oor beide die lter se stopband attenuasie en deurlaatband weerkaatsing moontlik maak. Deur die optimering van 'n akkurate stroombaanmodel van die lter kan berekeningsintensiewe numeriese EM optimering vermy word. Die nieuniforme wafelyster lter behaal dieselfde spesi kasies as soortgelyke gepubliseerde lters, maar is meer kompak. Die vervaardigingsprototipe handhaaf minder as -21 dB intreeweerkaatsing oor die deurlaatband van 8.5 - 10.5 GHz, asook attenuasie van meer as 50 dB oor die stopband 17 - 31.5 GHz en 30 dB oor 34 - 42 GHz. Die prototipe is ontwerp om 4 kW intree kruindrywing te hanteer in die deurlaatband, en is 130 mm lank. Die metode vereis minimale verstellings tydens volgolf simulasie, en die meetresultate stem goed ooreen met die gesintetiseerde gedrag. 'n Nuwe skuinstandpatroon word ook voorgestel vir wafelyster lters. Vir die harmoniekdemper word transversale bre ewandgleuwe in reghoekige gol eier wat koppel na 'n absorberende newegol eier ondersoek in die teenwoordigheid van staandegolfpatrone in oppervlakstroom. 'n Akkurate stroombaanmodel van 'n gleufkaskade word ontwikkel, en geoptimeer om 'n vereiste intreeweerkaatsing te bewerkstellig in samewerking met 'n arbitr^ere weerkaatsende lter. Deur gebruik te maak van poortparameterdata van die wafelyster lter word 'n 33 mm lange hamoniekdemper ontwikkel wat 'n maksimum intreeweerkaatsing van -12.5 dB oor die band 17 - 21 GHz handhaaf vir kruindrywingsvlakke van tot 1 kW. Goeie ooreenstemming tussen gesintetiseerde en gemete resultate word weereens waargeneem vir die volledige saamgestelde struktuur.

Apresenta-se a evolução dos sitemas de comunicação, com ênfase especial nos sistemas com tecnologia óptica. Discute-se a necessidade contínua do aumento de capacidade de tais sistemas de comunicação, e a consequente repercussão sobre os futuros sistemas ópticos. Em vista da necessidade do aumento de capacidade dos futuros sistemas de comunicação óptica, apresentam-se em seguida duas propostas recentes da literatura, sendo uma referente à realização de um gerador de pulsos ópticos estreitos, e a outra referente à implementação de um extrator de relógio realizado com técnicas ópticas. Apresenta-se um breve resumo da teoria das malhas de sincronismo de fase, ou PLLs, mostrando como as duas propostas discutidas realizam funções típicas desses sistemas. Ressalta-se a necessidade dos PLLs de sistemas ópticos possuirem ganhos de malha (parâmetro K) elevados. Após a caracterização dos requisitos necessários para PLLs de futuros sistemas ópticos, e após um resumo de alguns conceitos necessários da teoria de redes e filtros elétricos, apresentam-se dois tipos de projeto de filtros para aqueles PLLs. As duas formas de projeto tem como objetivo viabilizar o uso de filtros de tipo e ordem arbitrários. Um tipo de projeto visa a realização da função de transferência do PLL com a curva de resposta igual à de um filtro escolhido. O outro tipo de projeto parte da realização do filtro de loop do PLL com as características de um tipo de filtro escolhido, e define métodos para ajustar a função de transferência resultante para esse PLL. Apresentam-se algoritmos para o cálculo de parâmetros importantes nos dois procedimentos. Após a discussão dos dois pontos de vista de projeto, apresentam-se exemplos de realização de PLLs de acordo com as técnicas apresentadas. Para cada exemplo, mostram-se as curvas de resposta em frequência tanto do PLL como do correspondente filtro de loop, bem como o lugar das raízes e a resposta de captura do PLL obtido. O processo de captura foi estudado por simulações que procuram reproduzir o mais fielmente possível as condições reais de implementação, sem entretanto considerar efeitos de ruído. Finalmente, mencionam-se brevemente possíveis linhas de pesquisa futuras, sendo o foco principal o uso de filtros com pólos e zeros finitos. / The evolution of communication systems is discussed, with emphasis on optical technology. Special consideration is given to the continuous need for increasing the capacity of such systems, and the impact over future optical communication. In view of the great demands imposed over the capacity of future optical systems, an overview is presented of two recent proposals found in the literature, one of such proposals being the implementation of a generator of short optical pulses, and the other being a clock extractor device realized through the use of optical techniques. A brief review is made of phase-locked loop (or PLL) theory, to show how the discussed proposals could be used to realize tipical functions found in these systems. The very high loop gains (the so-called parameter K) that must be used in PLLs of optical communication systems are emphasized. After discussion of the necessary characteristics for PLLs of future optical systems, and also after a review of some concepts of the theory of electrical networks and filters, two design procedures for filters to be used in such PLLs are presented. Both designs have the goal of allowing the use of loop filters with any type and order. The first type of design has the objective to realize a PLL transfer function that has a frequency response identical to the response of a chosen type of filter. The other design starts with a chosen type of filter for a PLL loop filter, arriving to an suitable PLL transfer function. Some algorithms for determination of important design parameters are also presented. After the discussion of the two types of design, some examples of PLLs obtained by such methods are presented. For each example, frequency response curves are presented for the PLL and the respective loop filter, as well as the root locus and the capture response for the PLL so obtained. The capture process was studied through the use of simulations with parameters intended to approximate real implementation conditions, although noise effects are not considered. Finally, some possible research lines are discussed, whose main focus is on filters with finite poles and zeros.

Apresenta-se a evolução dos sitemas de comunicação, com ênfase especial nos sistemas com tecnologia óptica. Discute-se a necessidade contínua do aumento de capacidade de tais sistemas de comunicação, e a consequente repercussão sobre os futuros sistemas ópticos. Em vista da necessidade do aumento de capacidade dos futuros sistemas de comunicação óptica, apresentam-se em seguida duas propostas recentes da literatura, sendo uma referente à realização de um gerador de pulsos ópticos estreitos, e a outra referente à implementação de um extrator de relógio realizado com técnicas ópticas. Apresenta-se um breve resumo da teoria das malhas de sincronismo de fase, ou PLLs, mostrando como as duas propostas discutidas realizam funções típicas desses sistemas. Ressalta-se a necessidade dos PLLs de sistemas ópticos possuirem ganhos de malha (parâmetro K) elevados. Após a caracterização dos requisitos necessários para PLLs de futuros sistemas ópticos, e após um resumo de alguns conceitos necessários da teoria de redes e filtros elétricos, apresentam-se dois tipos de projeto de filtros para aqueles PLLs. As duas formas de projeto tem como objetivo viabilizar o uso de filtros de tipo e ordem arbitrários. Um tipo de projeto visa a realização da função de transferência do PLL com a curva de resposta igual à de um filtro escolhido. O outro tipo de projeto parte da realização do filtro de loop do PLL com as características de um tipo de filtro escolhido, e define métodos para ajustar a função de transferência resultante para esse PLL. Apresentam-se algoritmos para o cálculo de parâmetros importantes nos dois procedimentos. Após a discussão dos dois pontos de vista de projeto, apresentam-se exemplos de realização de PLLs de acordo com as técnicas apresentadas. Para cada exemplo, mostram-se as curvas de resposta em frequência tanto do PLL como do correspondente filtro de loop, bem como o lugar das raízes e a resposta de captura do PLL obtido. O processo de captura foi estudado por simulações que procuram reproduzir o mais fielmente possível as condições reais de implementação, sem entretanto considerar efeitos de ruído. Finalmente, mencionam-se brevemente possíveis linhas de pesquisa futuras, sendo o foco principal o uso de filtros com pólos e zeros finitos. / The evolution of communication systems is discussed, with emphasis on optical technology. Special consideration is given to the continuous need for increasing the capacity of such systems, and the impact over future optical communication. In view of the great demands imposed over the capacity of future optical systems, an overview is presented of two recent proposals found in the literature, one of such proposals being the implementation of a generator of short optical pulses, and the other being a clock extractor device realized through the use of optical techniques. A brief review is made of phase-locked loop (or PLL) theory, to show how the discussed proposals could be used to realize tipical functions found in these systems. The very high loop gains (the so-called parameter K) that must be used in PLLs of optical communication systems are emphasized. After discussion of the necessary characteristics for PLLs of future optical systems, and also after a review of some concepts of the theory of electrical networks and filters, two design procedures for filters to be used in such PLLs are presented. Both designs have the goal of allowing the use of loop filters with any type and order. The first type of design has the objective to realize a PLL transfer function that has a frequency response identical to the response of a chosen type of filter. The other design starts with a chosen type of filter for a PLL loop filter, arriving to an suitable PLL transfer function. Some algorithms for determination of important design parameters are also presented. After the discussion of the two types of design, some examples of PLLs obtained by such methods are presented. For each example, frequency response curves are presented for the PLL and the respective loop filter, as well as the root locus and the capture response for the PLL so obtained. The capture process was studied through the use of simulations with parameters intended to approximate real implementation conditions, although noise effects are not considered. Finally, some possible research lines are discussed, whose main focus is on filters with finite poles and zeros.

The thesis covers a series of PC programs that we have written that will enable users to easily design FIR linear phase lowpass digital filters and multistage sampling rate conversion systems. The first program is a rewrite of the McClellanParks computer program with some slight modifications. The second program uses an algorithm proposed by Rabiner that determines the length of a lowpass digital filter. Rabiner used a formula proposed by Herrmann et al. to initially estimate the filter length in his algorithm. The formula, however, assumes unity gain. We present a modification to the formula so that the gain of the filter is normalized to accommodate filters that have a gain greater than one (as in the case of a lowpass filter used in an interpolator). We have also changed the input specifications from digital to analog. Thus, the user supplies the sampling rate, passband frequency, stopband frequency, gain, and the respective maximum band errors. The program converts the specifications to digital. Then, the program iteratively estimates the filter length and interacts with the McClellan-Parks Program to determine the actual filter length that minimizes the maximum band errors. Once the actual length is known, the filter is designed and the filter coefficients may be saved to a file. Another new finding that we present is the condition that determines when to add a lowpass filter to a multistage decimator in order to reduce the total number of filter taps required to implement the system. In a typical example, we achieved a 34% reduction in the total required number of filter taps. The third program is a new program that optimizes the design of a multistage sampling rate conversion system based upon the sum of weighted computational rates and storage requirements. It determines the optimum number of stages and the corresponding upsampling and downsampling factors of each stage of the design. It also determines the length of the required lowpass digital filters using the second program. Quantization of the filter coefficients may have a significant impact on the frequency response. Consequently, we have included a routine within our program that determines the effects of such quantization on the allowable error margins within the passband and stopband. Once the filter coefficients are calculated, they can be saved to files and used in an appropriate implementation. The only requirements of the user are the initial sampling rate, final sampling rate, passband frequency, stop band frequency, corresponding maximum errors for each band, and the weighting factors to determine the optimization factor. We also present another new program that implements a sampling rate conversion from CD (44.1 kHz) to DAT (48 kHz) for digital audio. Using the third program to design the filter coefficients, the fourth program converts an input sequence (either samples of a sine wave or a unit sample sequence) sampled at the lower rate to an output sequence sampled at the higher rate. The frequency response is then plotted and the output block may be saved to a file.

Graduation date: 1996

This dissertation presents the research on several different projects. The first project is a via-less CPW RF probe pad to microstrip transition; The second, the third, and the fourth one are reconfigurable microwave circuits using RF MEMS switches: an X-band reconfigurable bandstop filter for wireless RF frontends, an X-band reconfigurable impedance tuner for a class-E high efficiency power amplifier using RF MEMS switches, and a reconfigurable self-similar antenna using RF MEMS switches. The first project was developed in order to facilitate the on-wafer measurement for the second and the third project, since both of them are microstrip transmission line based microwave circuits. A thorough study of the via-less CPW RF probe pad to microstrip transition on silicon substrates was performed and general design rules are derived to provide design guidelines. This research work is then expanded to W-band via-less transition up to 110 GHz. The second project is to develop a low power reconfigurable monolithic bandstop filter operating at 8, 10, 13, and 15 GHz with cantilever beam capacitive MEMS switches. The filter contains microstrip lines and radial stubs that provide different reactances at different frequencies. By electrically actuating different MEMS switches, the different reactances from different radial stubs connecting to these switches will be selected, thus, the filter will resonate at different frequencies. The third project is to develop a monolithic reconfigurable impedance tuner at 10 GHz with the cantilever DC contact MEMS switch. The impedance tuner is a two port network based on a 3bit-3bit digital design, and uses 6 radial shunt stubs that can be selected via integrated DC contact MEMS switches. By selecting different states of the switches, there will be a total of 2^6 = 64 states, which means 64 different impedances will be generated at the output port of the tuner. This will provide a sufficient tuning range for the output port of the power amplifier to maximize the power efficiency. The last project is to integrate the DC contact RF MEMS switches with self-similar planar antennas, to provide a reconfigurable antenna system that radiates with similar patterns over a wide range of frequencies.

Translinear circuits are circuits in which the exponential relationship between the output current and input voltage of a circuit element is exploited to realize various algebraic or differential equations. This thesis is concerned with a subclass of translinear circuits, in which the basic translinear element, called a multiple-input translinear element (MITE), has an output current that is exponentially related to a weighted sum of its input voltages. MITE networks can be used for the implementation of the same class of functions as traditional translinear circuits. The implementation of algebraic or (algebraic) differential equations using MITEs can be reduced to the implementation of the product-of-power-law (POPL) relationships, in which an output is given by the product of inputs raised to different powers. Hence, the synthesis of POPL relationships, and their optimization with respect to the relevant cost functions, is very important in the theory of MITE networks. In this thesis, different constraints on the topology of POPL networks that result in desirable system behavior are explored and different methods of synthesis, subject to these constraints, are developed. The constraints are usually conditions on certain matrices of the network, which characterize the weights in the relevant MITEs. Some of these constraints are related to the uniqueness of the operating point of the network and the stability of the network. Conditions that satisfy these constraints are developed in this work. The cost functions to be minimized are the number of MITEs and the number of input gates in each MITE. A complete solution to POPL network synthesis is presented here that minimizes the number of MITEs first and then minimizes the number of input gates to each MITE. A procedure for synthesizing POPL relationships optimally when the number of gates is minimal, i.e., 2, has also been developed here for the single--output case. A MITE structure that produces the maximum number of functions with minimal reconfigurability is developed for use in MITE field--programmable analog arrays. The extension of these constraints to the synthesis of linear filters is also explored, the constraint here being that the filter network should have a unique operating point in the presence of nonidealities. Synthesis examples presented here include nonlinear functions like the arctangent and the gaussian function which find application in analog implementations of particle filters. Synthesis of dynamical systems is presented here using the examples of a Lorenz system and a sinusoidal oscillator. The procedures developed here provide a structured way to automate the synthesis of nonlinear algebraic functions and differential equations using MITEs.