An efficient interval method for global analysis of non-linear resistive circuits

A new method for finding the set of all operating points of non-linear resistive circuits is suggested. It takes into account the fact that the circuit equations are in the so-called separable form where any equation f_i(x) is the sum of terms f_ij(x_j), each term depending on a single variable. The method is based on the introduction of an approximation of every real non-linear function f_ij(x_j) by an appropriate linear interval function, i.e. by a real linear function having an additive interval term. The parameters of the linear interval approximations are dynamically updated at each iteration of the computational process. Numerical experiments show that the computational efficiency of the new method is vastly superior to that of other known methods for global analysis, especially for circuits of large size. © 1998 John Wiley & Sons, Ltd.     

A switching-parameter algorithm for finding multiple solutions of nonlinear resistive circuits

An efficient algorithm for finding multiple solutions of a system of nonlinear algebraic equations is presented. This algorithm consists of solving an associated system of first order nonlinear differential equations whose independent variable may be switched from one variable to another during each integration step. The choice of the forward Euler predictor and Newton-Raphson corrector for integrating the differential equations leads to an extremely efficient method for implementing this switching-parameter algorithm. This approach involves only the recursive solution of an associated system of linear algebraic equations and can be easily programmed. The switching-parameter algorithm can also be used to derive the driving-point or transfer characteristic curve of multivalued resistive nonlinear networks.     

An algorithm for solving the equations of monotone non-linear resistive networks

An algorithm related to the PQ theorem is given for solving the equations of a large class of monotone non-linear resistive networks. the algorithm converges to a solution whenever a solution exists, while it produces an unbounded sequence of iterates if there is no solution.     

An interval method for finding all operating points of non-linear resistive circuits

A new method for finding the set of all d.c. operating points of non-linear electronic circuits is suggested. it is applicable in the case where the circuit equations are written in the hybrid-representation form. In the general case, the non-linear elements involved may be described by non-monotone continuous characteristics. The method suggested is based on interval analysis techniques. Unlike other non-interval methods, this approach guarantees that all operating points will be found within prescribed accuracy in a finite number of steps. The computational efficiency of the present method is illustrated by a numerical example.     

Non-linear non-reciprocal resistive circuits with a structurally unique solution

A purely topological criterion is given, which allows one to determine when a non-linear non-reciprocal resistive circuit has exactly one solution, irrespective of its element characteristics. If the criterion is satisfied then it is shown that the solution has the same regularity as the element characteristics.     

A substitution algorithm for solving nonlinear circuits with multi-frequency components

In this paper, we present an efficient algorithm for calculating the steady-state response of nonlinear circuits such as forced circuits driven by multi-frequency-component signals, forced oscillators, and coupled oscillators. We call the technique a substitution method because the variation at each step is calculated by solving an associated time-invariant sensitivity circuit at each frequency component of the residual error, whose circuit is derived from a relaxation method. the algorithm is very simple and efficient, and it can be applied to a wide variety of nonlinear circuits.     

An interval algorithm for finding all solutions of non‐linear resistive circuits

In this letter, an efficient algorithm is proposed for finding all solutions of non‐linear (not piecewise‐linear) resistive circuits. This algorithm is based on interval analysis, the dual simplex method, and the contraction methods. By numerical examples, it is shown that the proposed algorithm could find all solutions of systems of 500–700 non‐linear circuit equations in acceptable computation time. Copyright © 2004 John Wiley & Sons, Ltd.     

求取电路最小测试集的优化算法的比较研究

离散事件系统（DES）理论的发展为数模混合电路中的数字信号和模拟信号的测试提供了一种统一、系统、有效的方法。在基于DES理论的电路可测试性研究中,其中重要的一项工作就是求取电路的最小测试集。首先介绍了目前求取电路最小测试集的几种优化算法的思想和实现方案,然后对它们进行了比较,并对下一步研究方向进行了展望。     

An efficient algorithm for analysis of piecewise-linear resistive circuits: Driving-point and transfer characteristic plots

A new efficient algorithm is presented for finding all driving-point characteristic (DP) and transfer characteristic (TC) plots for a broad class of piecewise-linear (PWL) resistive circuits without the need for initial points for each solution branch. the piecewise-linear circuits to be considered need not be continuous nor need their linear regions be divided by grid-like hyperplanes. the computation of the new algorithm is based on zone-by-zone instead of the conventional region-by-region. Since each zone includes several regions and only one matrix inversion is needed for each zone, a significant reduction of computation can be achieved. Furthermore, the computational complexity for finding all solution branches, i.e. finding the DC operating points over the entire range of input values u, is no more than for finding all DC operating points over a single value u as far as the number of matrices needed to be inverted is concerned.     

Characterization of integration algorithms for the timing analysis of mos vlsi circuits

Displacement techniques used for the timing analysis of VLSI circuits are presented under a new perspective. Their numerical properties such as stability, accuracy, consistency and convergence are investigated.     

Variable scaling hybrid differential evolution for solving network reconfiguration of distribution systems

This paper presents an effective method-variable scaling hybrid differential evolution (VSHDE)-for solving the network reconfiguration for power loss reduction and voltage profit enhancement of distribution systems. The network reconfiguration of distribution systems is to beneficially recognize load transfers so that the objective function composed of power losses is minimized and the prescribed voltage limits are satisfied. The variable scaling factor based on the 1/5 success rule is used in the VSHDE method to overcome the drawback of the fixed and random scaling factor and alleviate the problem of the selection of a mutation operator in the hybrid differential evolution (HDE). One three-feeder distribution system from the literature and one practical distribution network of Taiwan Power Company (TPC) are used to compare the performance of the proposed method with the HDE, genetic algorithms (GAs), and simulated annealing (SA). Numerical results show that the performance of the proposed method is better than the other methods.     

Performance evaluation of the LP test algorithm for finding all solutions of piecewise‐linear resistive circuits

In this letter, the performance of the LP test algorithm, which is an algorithm for finding all solutions of piecewise‐linear resistive circuits, is evaluated by numerical experiments. It is shown that the algorithm could find all solutions of large‐scale problems (including those where the number of variables is 200–300 and the number of linear regions is 10²⁰⁰–10³⁰⁰) in practical computation time. Copyright © 2000 John Wiley & Sons, Ltd.     

A new approach to overcome the overflow problem in computer-aided analysis of nonlinear resistive circuits

This paper is addressed to the so-called overflow problem commonly encountered in the computer simulation of nonlinear resistive circuits containing rapidly varying nonlinearities—such as exponentials found in the models of diodes and transistors. A novel approach which makes use of the arc-lengths of the nonlinear characteristic curves as the variables of iteration is proposed. It is proved, under rather mild conditions, that the arc-length approach not only overcomes the overflow problem, but also leads to a more rapid rate of convergence. Moreover, it is proved that for most practical diode-transistor circuits, the region of convergence associated with the arc-length approach is larger and the convergence of the Newton-Raphson algorithm is not sensitive to the initial guess. Since it is more difficult to make good initial guesses when the size of the network is large, in so far as choosing the initial guess is concerned, the advantage for using the arc-length approach over the conventional approach increases with the size of the network. Extensive numerical experiments confirm the superior convergence property of this approach even for circuits which violate the sufficient conditions invoked by the rigorous mathematical proofs. Although the approach is applicable to a much wider class of nonlinear networks, particular emphasis is focused on diode-transistor networks in this paper.     

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

An efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10³⁰⁰, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.     

Design of transmission line filters and matching circuits using genetic algorithms

A method for designing microwave filters and impedance matching circuits using transmission lines is presented. Transmission line filters with shunt‐connected open circuit stubs and continuously varying transmission line matching circuits are described in detail. The proposed method is based on genetic algorithms and can effectively be applied to various filter and matching circuit design problems without increasing theoretical and computational complexity. Design examples are provided, and the proposed method is demonstrated to be effective in designing transmission line filters and matching circuits. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

求解门级时序电路稳定状态的仿真方法

详细分析求解电路稳定状态方法的优缺点,提出用仿真软件实现稳定状态的方法,深入研究电路输入端值之间的关系.使用EDA工具软件,仿真正常电路的波形,发现如果按照规则定义有效设置输入端值的比例关系,可很快得到完全或者不完全稳定状态.仿真结果表明此方法可实现正常电路的稳定状态,是一种加速实现时序电路故障测试生成的有效方法.     

A reliable approach for solving the transmission network expansion planning problem using genetic algorithms

This paper presents a reliable approach for solving the transmission network expansion planning (TNEP) problem through a genetic algorithm (GA). GAs have demonstrated the ability to deal with non-convex, non-linear, integer-mixed optimization problems, such as the TNEP problem, better than a number of mathematical methodologies. The procedure presented consists on finding unfeasible solutions for the problem through the GA. These solutions are used for predicting the cost of the optimum solution using a ‘loss of load limit curve’, of the transmission system. Once this cost is estimated, the optimum solution can be found by performing a local search starting from the unfeasible solutions that have costs close to the estimated cost. This approach makes the GA more robust and reliable for solving the problem for different transmission systems.