Reduced modified nodal approach to circuit analysis

Automatic symbolic analysis of SC networks using a modified nodal approach

This chapter introduces the analysis and design of linear circuits. It reviews basic direct‐current (DC) analysis using traditional circuits theorems with application to circuit analysis and design. Using node voltage instead of element voltages as circuit variables can greatly reduce the number of equations that must be treated simultaneously. The chapter treats the analysis and design of circuits containing active devices such as transistors or operational amplifiers (op amps). It also discusses alternating current (AC) circuits. Those ac circuits that are excited by a single frequency, for example, power systems, can be easily and effectively analyzed using sinusoidal steady‐state techniques. Linear circuits are often characterized by their behavior to sinusoids, in particular, how they process signals versus frequency. Audio, communication, instrumentation, and control systems all require signal processing that depends at least in part on their frequency response.

State variable method is a powerful tool for analyzing dynamic circuits, and the key to its application lies in the extraction of state equations. In this paper, an improved modified nodal approach (MNA) has been proposed to extract the state equations. Based on the basic principle of linear circuits, the hybrid equations which can deal with all kinds of linear elements have been established. The non-state variables in the hybrid equations are eliminated by elementary row transformation method, and the state equations with capacitance voltage and inductance current as state variables is obtained. Aiming at the problem that the order of the hybrid equations is too large, a reduced order method has been put forward, which can eliminate the voltage source current and some node voltage variables in the hybrid equations. Matrix dimension calculation and case analysis results showed that the reduced order method can reduce the amount of computations in the extraction of state equations and the new method is more efficient.

Метою даної роботи є побудова еквівалентних електричних схем оптоелектронного навантаження, яке живиться від фотоелемента та акумулятора. В роботі показано необхідність створення таких еквівалентних електричних схем, а саме при підключенні світлодіодів та напівпровідникових лазерів до сонячних фотоелементів, в якості джерела електричної енергії, та при використанні акумуляторів електроенергії. Показано, що еквівалентні електричні схеми витікають з фізичних явищ в напівпровідникових пристроях і рівнянь, які описують явища перетворення електричної енергії в світлову. Викладено різні еквівалентні схеми оптоелектронного навантаження. Показано, як просту так і найбільш узагальнену еквівалентні електричні схеми. Зокрема, показано еквівалентну схему акумулятора і спрощені схеми фотоелемента та оптоелектронного випромінювача світла, де в якості навантаження виступає світлодіод. Зазначено, що розвитком даної моделі є більш узагальнена еквівалентна електрична схема, де в якості оптоелектронного навантаження виступає напівпровідниковий інжекційний лазер. Розписані їх параметри та викладені рівняння для струмів та напруг. Також показано існування пасивних паразитних елементів в таких електричних схемах. Також показано, що в якості схеми заміщення фотоелемента, в спрощеній моделі, використано ідеальне джерело напруги та резистор з конденсатором. В подальшому, в узагальненій моделі, для більш широкого моделювання роботи фотоелемента, в якості схеми заміщення було використано ідеальне джерело струму та нелінійні пасивні елементи. Тобто, в результаті, було отримано узагальнену еквівалентну електричну схему акумулятора, підключеного до фотоелемента та оптоелектронного навантаження. Побудовано рівняння для струмів та напруг в отриманої схеми заміщення. Зроблено висновок. Бібл. 7, рис. 5.

The paper presents an improvement of sensitivity analysis methods of analog lumped circuits. A practical and reliable approach has been developed and implemented in a computation program intended for linear and/or piecewise-linear approximation of the nonlinear RLCM circuits containing any type of passive elements, independent and controlled sources. A powerful modified nodal approach to build the mathematical model combined with some symbolic computation strategies has been exploited, in order to reduce the computational effort and to minimize the numerical errors. The developed software tool is conceived as a useful and valuable support for research and design engineers.

A circuit simulator has been developed on basis of Unified Nodal Analysis (UNA). It outperforms simulators with Modified Nodal Approach and Tableau formulation in that the initial-state and steady-state responses are generated from the UNA equations without transient analysis and transient simulations can be carried out from the UNA equations even for circuits with capacitor loops and inductor cutsets that cause singularity in the MNA equations. UNA's efficiency and accuracy are illustrated with an example circuit that fails most of the existing circuit simulators.

A methodology was developed for the prediction of the electrical properties of carbon nanotube-polymer nanocomposites via Monte Carlo computational simulations. A two-dimensional microstructure that takes into account waviness, fiber length and diameter distributions is used as a representative volume element. Fiber interactions in the microstructure are identified and then modeled as an equivalent electrical circuit, assuming one-third metallic and two-thirds semiconductor nanotubes. Tunneling paths in the microstructure are also modeled as electrical resistors, and crossing fibers are accounted for by assuming a contact resistance associated with them. The equivalent resistor network is then converted into a set of linear equations using nodal voltage analysis, which is then solved by means of the Gauss–Jordan elimination method. Nodal voltages are obtained for the microstructure, from which the percolation probability, equivalent resistance and conductivity are calculated. Percolation probability curves and electrical conductivity values are compared to those found in the literature.

The performance of a medium ring transmission line at steady state

This article proposes a novel hybrid finite-difference time-domain (FDTD) method to calculate the transient responses of the transmission line network based on the leapfrog alternating direction implicit FDTD (leapfrog ADI-FDTD) algorithm and the traditional FDTD method. The proposed hybrid method can be implemented by dividing the transmission line network into two parts that are the interconnects part in a printed circuit board solved by the leapfrog ADI-FDTD and the cable part solved by the traditional FDTD with different mesh sizes and the same time step, respectively. In addition, some boundary conditions should be introduced based on the modified nodal approach and Kirchhoff's law at the terminals of the transmission line network. The numerical results show that the proposed hybrid method is in good agreement with HSPICE. Especially, it is more efficient and applicative for the multiscale transmission line network problems due to the use of the implicit FDTD solver with unconditional stability compared with the traditional FDTD method.

The influence of the PANI structure on the conductive mechanism and on the electrical equivalent circuit analysis

Recently, progress in the high‐density wiring technique on a printed circuit board (PCB) has been remarkable. Thus the problem of malfunctions due to crosstalk noise occurring on the signal line must be addressed. The authors have been developing the noise estimation system for PCB named NESSY and a program to calculate the capacitance of multiconductor system (CALCAP). In NESSY, the wiring pattern is divided into small segments, which comprise the equivalent element circuit. The partial capacitance of the printed pattern is calculated by solving the integral equation and using the image method in CALCAP. The crosstalk analysis of equivalent circuit was made by the circuit simulation program.Among the results of this analysis, crosstalk noise using the partial element equivalent circuit (PEEC) agrees quite well with the measurement. The crosstalk noise should be anticipated by the close coupling theory in the case of frequently used wiring (both the width of signal line and line spacing are less than 1 mm). The crosstalk noise voltage was relatively large in the case of impedance mismatching. The far end crosstalk noise, previously neglected in most cases, becomes especially large.

Although the Spice program is very useful in many applications for standard circuit analysis, it has limited capability for R?? and microwave circuits analysis. This is because those circuits are usually described in terms of power-wave variables and defined by S-parameters, while the Spice program copes with standard circuit variables: node voltages and branch currents. However, if we introduce a simple mapping between incident power-wave and node voltage from one side and between reflected power-wave and branch current o i.e. bp!) = (I (n , and bp@) = ap(m). For legal connection of S-blocks into the network N it is required to blfil this interconnecting condition. According to the adopted mapping this condition can be easily iklfilled by a pair of VCVS with unit coupling coefficient at every internal port. Other types of connection between S-blocks can be transformed into cascaded connection using an additional S-block that is described by S-parameters with real coefficients. Therefore we get the equivalent S-parameters of the entire network using the same set-up circuit that is suitable for the y-parameter determination by Spice. The results obtained with our method are compared with results obtained by Touchstone program and no considerable discrepancies are observed.

The paper proposes an analysis method of nonlinear microwave circuits referred to as the frequency-domain-continuation intermodulation balance method (FDCIBM). This technique introduces a generalised complex matrix to represent (in the frequency domain) the steady-state variables of the nonlinear circuit with multifrequency large-signal excitation. In terms of this generalised complex matrix and a generalised complex-matrix convolution operator defined here, the frequencydomain- balance equation of the nonlinear circuit is a system of complex-variable nonlinear algebraic equations, that is solved using the continuation method. As an example, the intermodulation analysis of a GaAs MESFET amplifier is given.

Wireless sympathetic connection systems are proposed which employ a single resonator located between two electrically small non-resonant antennas. Symmetric configurations consisting of two equal transmitting and receiving antennas and a resonator are characterized by the equivalent reactive circuits with two inductors and one capacitor in the case of closed path type antennas and with two capacitors and one inductor in the case of open path type antennas. The equivalent circuit constants are identified by the series and parallel resonance frequencies for the even mode excitation and by the low frequency inductance or capacitance for the odd mode excitation. The power transfer efficiency evaluated by the equivalent circuit analysis agrees well with the full wave analysis result, and is 100 percent when the port impedances are matched to the image impedance and the structures are assumed to be lossless. Asymmetric cases of unequal transmitting and receiving antennas are treated, and the theory is applied to the simplified design of HF-RFID systems, where the reader/writer port impedance is 50Ω and the tag port impedance is 3 KΩ. The power transfer efficiency is evaluated in case the antennas and the resonator are made of cupper. It keeps the efficiency larger than −10 dB when the tag antenna moves from the home position by 15 cm horizontally or vertically.

En este trabajo se presenta un estudio comparativo de la impedancia de un electrodo vertical enterrado en un suelo homogéneo donde los parámetros eléctricos (resistividad y permisibilidad) son dependientes de la frecuencia en relación a los mismos con parámetros constantes. Para su cálculo, es llevado en consideración que el electrodo vertical se puede interpretar como una línea de transmisión (LT) cuyos los parámetros eléctricos son distribuidos por unidad de longitud. Así, la impedancia del electrodo es computada como siendo la impedancia harmónica de LT en función de la frecuencia. Una vez obtenidas las impedancias de aterramiento del electrodo, y empleando una técnica de mínimos cuadrados, se las representan por circuitos eléctricos directamente en el dominio del tiempo. La ventaja de usar este tipo de representación es que el modelo puede insertarse fácilmente en software del tipo EMTP para el análisis de los transitorios electromagnéticos. Así, se calculan las elevaciones de potencial en el aterramiento para una descarga atmosférica incidente en el electrodo. Adicionalmente, una descarga atmosférica es inyectada en el topo de una torre de transmisión aterrada por un electrodo vertical, para evaluar las tensiones en los brazos de la estructura y en su base. Los resultados muestran que las tensiones son significativamente modificadas por la presencia del suelo con parámetros dependientes de la frecuencia, en especial las amplitudes, y que un análisis preciso del transitorio en los sistemas eléctricos debe llevar en cuenta ese fenómeno.