The thesis proposes a hybrid broadband equivalent model extraction method, and our goal is to combine via structure and irregular transmission line in print circuit board for extraction of broadband SPICE-compatible model by using the time domain algorithm and full wave simulation in frequency domain, respectively. We can construct broadband SPICE-compatible macro-model scalable library with two kind of different extraction methods, tow kind of extraction of equivalent model can construct the circuit structure for designer demand. Every modules of the broadband macro model of the two extraction models are represented by the optimum pole-residue forms. Using a systematic lumped-model extraction technique, all the optimum pole-residue rational functions can be transfered into a corresponding lumped circuit model. The accuracy of Extraction of Broadband Equivalent Models is demonstrated in frequency -domain responses compared with the 3D-FDTD or HFSS simulation. In addition, the extraction model can simulate in commercial tools effectively, ex: Hspice¡BADS. Even the model can simulate signal integrality and power integrality in Hspice or ADS.

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2013. / Submitted by Alaíde Gonçalves dos Santos (alaide@unb.br) on 2014-05-09T10:17:57Z No. of bitstreams: 1 2013_TitoRicardoVazdaCosta.pdf: 1644763 bytes, checksum: 9fa433c622de5e79882143d10503dbd9 (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2014-07-02T13:56:30Z (GMT) No. of bitstreams: 1 2013_TitoRicardoVazdaCosta.pdf: 1644763 bytes, checksum: 9fa433c622de5e79882143d10503dbd9 (MD5) / Made available in DSpace on 2014-07-02T13:56:31Z (GMT). No. of bitstreams: 1 2013_TitoRicardoVazdaCosta.pdf: 1644763 bytes, checksum: 9fa433c622de5e79882143d10503dbd9 (MD5) / A presente dissertação propõe o cálculo de um modelo de equivalente dinâmico para sistemas de potência trifásicos, com quatro terminais, sendo três referentes às fases e um de referência. A técnica é apropriada para a obtenção de redes elétricas com o propósito de substituir uma determinada parte do sistema elétrico (rede externa), a qual admite-se ser de menor impacto para a área específica de estudos (rede interna). Para determinação do equivalente trifásico, são necessárias apenas duas impedâncias, pois estas são os parâmetros básicos de um circuito trifásico acoplado. O interesse nesse equivalente é somente no cálculo de impedâncias, pois a finalidade do estudo é avaliar o impacto da geração de harmônicos na área do sistema considerada interna, onde há a fonte. Uma impedância própria e uma mútua são obtidas por meio de ajuste de grandezas medidas na barra de fronteira que separa a área interna da externa. O ajuste no domínio da frequência é baseado na técnica Vector Fitting. Para validação dos resultados, são realizadas simulações em regime permanente e comparadas as tensões nas três fases da barra de fronteira. O resultado também é comprovado a partir de curvas de resposta em frequência das tensões na barra de fronteira. Em ambos os casos, obtiveram-se resultados satisfatórios com desvio quadrado médio entre os resultados considerando o sistema completo e com o equivalente. Resultados satisfatórios também foram observados em simulações com o sistema submetido a desequilíbrio de corrente entre as fases. Os testes para avaliação do desempenho da técnica foram realizados em um sistema de 9 barras, das quais duas delas integram a área interna. _______________________________________________________________________________________ ABSTRACT / This master thesis proposes the computation of a three-phase power system dynamic equivalent which has four terminals. Three of these ports are related to phases and one is the reference. The technique is appropriated for obtaining an electrical network for replacing a part of a given power system (known as external network). This part of the system has a level of importance less than a specific electrical network (internal area), since this latter one is the target of the studies. For determining the three-phase equivalent two impedances are calculated named as self and mutual impedances. These parameters are used to form a coupled circuit. The equivalent replaces an external full network connected to an internal network through a border bus. The self and mutual impedance terms are obtained by setting vector quantities measured on the boundary of the system bus. For setting we make use of the methodology based on Vector Fitting. Results are validated by performing time simulations at steady state and by comparing the voltages at the three phase border bus. Also, the results are confirmed through simulations considering frequency response data. In both cases, the performance for computing the dynamic equivalent is considered satisfactory. This is justified by verifying the very low mean square deviation between results for the complete and equivalent system. All experiments were carried out by considering a 9-bus power system which has two bus inside the study zone.

This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page. / October 2005

This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page.

This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page.

Neste trabalho são descritos e avaliados diferentes modelos de linhas aéreas de transmissão, considerando a variação dos parâmetros da linha com a frequência. Em geral os modelos apresentados são baseados no uso da matriz de admitâncias nodais, com algumas análises complementares empregando o método das características. São testados casos de circuito-aberto, curto-circuito, linha em carga e manobras com chaves. Os resultados de cálculo são comparados com as respostas simuladas nos programas ATP e PSCAD. Também são apresentadas as formulações para o cálculo de parâmetros da linha de transmissão, considerando o efeito pelicular e a resistividade do solo São avaliadas as respostas no domínio do tempo para diferentes modelos equivalentes de linha de transmissão, obtidos do modelo polo-resíduo com passividade da matriz de admitâncias nodais, sendo empregados: i) transformação do modelo racional para uma representação em espaço de estados, ii) construção de uma rede elétrica equivalente com resistências, indutores e capacitores e iii) representação por meio de um equivalente de Norton. Também é analisado o equivalente de Norton obtido dos modelos polo-resíduo com passividade de uma linha equivalente dobrada nas condições em curto-circuito e circuito-aberto. Foi analisada a solução de redes elétricas no domínio da frequência usando uma formulação nodal e sem a necessidade de ajustes intermediários da matriz de admitâncias nodais. As respostas de tensão e corrente são antitransformadas para o domínio do tempo por meio de diferentes formulações baseadas na transformada inversa de Fourier, levando em conta os métodos que mitigam erros de truncamento e discretização. As seguintes formulações foram avaliadas: i) transformada modificada de Fourier, ii) transformada inversa rápida de Fourier e iii) transformada inversa de Fourier com integração semianalítica. É também apresentado um modelo para linhas de transmissão em paralelo, baseado no domínio modal usando uma matriz de transformação constante, juntamente com a aplicação do método de ajuste Vector Fitting com o objetivo de modelar com precisão o efeito de acoplamento mútuo entre linhas. / In this work different overhead transmission lines models are described and evaluated, considering the frequency dependence of parameters. In general, the models are based on the nodal admittance matrix, with some complementary analysis using the method of characteristics. Cases of open-circuit, short-circuit, line connected to a load and switching maneuvers are tested. The calculation results are compared with the simulated responses obtained with the ATP and PSCAD. The formulations for the transmission line parameters are also presented, taking into account the skin effect and the ground return. The time-domain responses for different transmission line models are evaluated. These models are obtained from the passive pole-residue model of the nodal admittance matrix. The equivalent models are: i) state-space representation, ii) electrical network composed of resistors, inductors and capacitors, iii) the Norton\'s equivalent. In addition, an evaluation is performed for the Norton\'s equivalent obtained from the pole-residue models for the open-circuit and short-circuit conditions of a folded line equivalent. On the other hand, the network is solved completely in frequency-domain using a nodal formulation, without the fitting of the nodal admittance matrix. The voltage and current responses are transformed back to the time-domain by different formulations based on the inverse Fourier transform, taking into account methods to minimize errors by truncation and discretization. The formulations investigated are: i) modified Fourier transform, ii) fast Fourier transform, iii) inverse Fourier transform with semianalytic integration. The model for parallel transmission lines is also evaluated, based on modal domain using a constant transformation matrix and the application of the vector fitting method, with emphasis on accurate representation of mutual coupling effects.

With the advances in the telecommunications industry, there is a need to solve the in-band full-duplex (IBFD) problem for antenna systems. One premise for solving the IBFD problem is to have strong isolation between transmitter and receiver antennas in an antenna system. To increase isolation, antenna engineers are dependent on simulation software to calculate the isolation between the antennas, i.e., the mutual coupling. Full-wave simulations that accurately calculate the mutual coupling between antennas are timeconsuming, and there is a need to reduce the required time. In this thesis, we investigate how implemented data-driven interpolation methods can be used to reduce the simulation times when applied to frequency domain solvers. Here, we benchmark the four different interpolation methods vector fitting, the Loewner framework, Cauchy interpolation, and a modified version of Nevanlinna-Pick interpolation. These four interpolation methods are benchmarked on seven different antenna frequency responses, to investigate their performance in terms of how many interpolation points they require to reach a certain root mean squared error (RMSE) tolerance. We also benchmark different frequency sampling algorithms together with the interpolation methods. Here, we have predetermined frequency sampling algorithms such as linear frequency sampling distribution, and Chebyshevbased frequency sampling distributions. We also benchmark two kinds of adaptive frequency sampling algorithms. The first type is compatible with all of the four interpolation methods, and it selects the next frequency sample by analyzing the dynamics of the previously generated interpolant. The second adaptive frequency sampling algorithm is solely for the modified NevanlinnaPick interpolation method, and it is based on the free parameter in NevanlinnaPick interpolation. From the benchmark results, two interpolation methods successfully decrease the RMSE as a function of the number of interpolation points used, namely, vector fitting and the Loewner framework. Here, the Loewner framework performs slightly better than vector fitting. The benchmark results also show that vector fitting is less dependent on which frequency sampling algorithm is used, while the Loewner framework is more dependent on the frequency sampling algorithm. For the Loewner framework, Chebyshev-based frequency sampling distributions proved to yield the best performance. / Med de snabba utvecklingarna i telekomindustrin så har det uppstått ett behov av att lösa det så kallad i-band full-duplex (IBFD) problemet. En premiss för att lösa IBFD-problemet är att framgångsrikt isolera transmissionsantennen från mottagarantennen inom ett antennsystem. För att öka isolationen mellan antennerna måste antenningenjörer använda sig av simulationsmjukvara för att beräkna isoleringen (den ömsesidiga kopplingen mellan antennerna). Full-wave-simuleringar som noggrant beräknar den ömsesidga kopplingen är tidskrävande. Det finns därför ett behov av att minska simulationstiderna. I denna avhandling kommer vi att undersöka hur våra implementerade och datadrivna interpoleringsmetoder kan vara till hjälp för att minska de tidskrävande simuleringstiderna, när de används på frekvensdomänslösare. Här prestandajämför vi de fyra interpoleringsmetoderna vector fitting, Loewner ramverket, Cauchy interpolering, och modifierad Nevanlinna-Pick interpolering. Dessa fyra interpoleringsmetoder är prestandajämförda på sju olika antennsystemsvar, med avseende på hur många interpoleringspunkter de behöver för att nå en viss root mean squared error (RMSE)-tolerans. Vi prestandajämför också olika frekvenssamplingsalgoritmer tillsammas med interpoleringsmetoderna. Här använder vi oss av förbestämda frekvenssamplingsdistributioner så som linjär samplingsdistribution och Chebyshevbaserade samplingsdistributioner. Vi använder oss också av två olika sorters adaptiv frekvenssamplingsalgoritmer. Den första sortens adaptiv frekvenssamplingsalgoritm är kompatibel med alla de fyra interpoleringsmetoderna, och den väljer nästa frekvenspunkt genom att analysera den föregående interpolantens dynamik. Den andra adaptiva frekvenssamplingsalgoritmen är enbart till den modifierade Nevanlinna-Pick interpoleringsalgoritmen, och den baserar sitt val av nästa frekvenspunkt genom att använda sig av den fria parametern i Nevanlinna-Pick interpolering. Från resultaten av prestandajämförelsen ser vi att två interpoleringsmetoder framgångsrikt lyckas minska medelvärdetsfelet som en funktion av antalet interpoleringspunkter som används. Dessa två metoder är vector fitting och Loewner ramverket. Här så presterar Loewner ramverket aningen bättre än vad vector fitting gör. Prestandajämförelsen visar också att vector fitting inte är lika beroende av vilken frekvenssamplingsalgoritm som används, medan Loewner ramverket är mer beroende på vilken frekvenssamplingsalgoritm som används. För Loewner ramverket så visade det sig att Chebyshev-baserade frekvenssamplingsalgoritmer presterade bättre.

Thesis (PhD (Electical and Electronic Engineering))--University of Stellenbosch, 2006. / Resonant frequencies and Q-factors of microwave ring resonators are predicted using interpolation- based modelling. A robust and efficient multivariate adaptive rational-multinomial combination interpolant is presented. The algorithm models multiple resonance frequencies of a microwave ring resonator simultaneously by solving an eigenmode problem. To ensure a feasible solution when using the Method of Moments, a frequency dependent scaling constant is applied to the output model. This, however, also induces a discontinuous solution space across the specific geometry and requires that the frequency dependence be addressed separately from other physical parameters. One-dimensional adaptive rational Vector Fitting is used to identify and classify resonance frequencies into modes. The geometrical parameter space then models the different mode frequencies using multivariate adaptive multinomial interpolation. The technique is illustrated and evaluated on both two- and three-dimensional input models. Statistical analysis results suggest that models are of a high accuracy even when some resonance frequencies are lost during the frequency identification procedure. A three-point rational interpolant function in the region of resonance is presented for the calculation of loaded quality factors. The technique utilises the already known interpolant coefficients of a Thiele-type continued fraction interpolant, modelling the S-parameter response of a resonator. By using only three of the interpolant coefficients at a time, the technique provides a direct fit and solution to the Q-factors without any additional computational electromagnetic effort. The modelling algorithm is tested and verified for both high- and low-Q resonators. The model is experimentally verified and comparative results to measurement predictions are shown. A disadvantage of the method is that the technique cannot be applied to noisy measurement data and that results become unreliable under low coupling conditions.