An Efficient Variable Gain Homotopy Method Using the SPICE-Oriented Approach

Kuroki, Wataru; Yamamura, Kenichiro; Furuki, Shingo

doi:10.1109/tcsii.2007.896935

Cited by 14 publications

(7 citation statements)

References 18 publications

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“…Five types of practical circuits widely used in analog LSIs are considered in this comparison. These circuits consist of an Ebers-Moll BJT and have convergence issues in the SPICE software but are frequently used as a test circuits [7,8]:…”

Section: Comparison Of the Proposed Algorithm And Other Methodsmentioning

confidence: 99%

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Accelerating the solving of nonlinear equations using the homotopy method: application on finding the operating point of complex circuits

Dhiabi¹,

Boumehraz²

2017

Turk J Elec Eng & Comp Sci

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Analog circuits with nonlinear elements (e.g., diode, BJT, and CMOS) and integrated circuits are very complex systems. As a result, they are very difficult to analyze because of the need to generate a nonlinear equation system solution in order to do so. Solving nonlinear equations is still a challenging problem. Iterative methods, however, are frequently used to solve them. This paper describes a method that can be used to both accelerate the solving of nonlinear equations and find the operating point in various integrated circuits by construction of the global homotopy equation of the analog circuit. This is done by converting the elements in the circuit to their equivalent dependent sources. The proposed method is based on three steps. The first step is the use of the homotopy method to get a continuous function. The second step consists of finding the best direction of the solution by applying prediction and the correction procedures. The third step consists of the control of step size to accelerate the solution search. In order to demonstrate the effectiveness of the proposed method, a new type of software called PyAMS (Python Language for Analog and Mixed Signal) was created by the authors based on the proposed method. A comparison was done between the proposed method and two other methods and, in doing so, many types of integrated circuits were used. Based on the proposed method, an analysis of many universal circuits was carried out to verify the correct function of the circuit.

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Section: Comparison Of the Proposed Algorithm And Other Methodsmentioning

confidence: 99%

“…The continuation method, proposed in [3][4][5][6][7][8][9][10][11], is an effective method to solve nonlinear circuits. The continuation method is based on 3 steps:…”

Section: Introductionmentioning

confidence: 99%

Accelerating the solving of nonlinear equations using the homotopy method: application on finding the operating point of complex circuits

Dhiabi¹,

Boumehraz²

2017

Turk J Elec Eng & Comp Sci

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“…Probability-one homotopy algorithms are a class of embedding algorithms that promise global convergence [5,61]. Various homotopy algorithms have been introduced for finding multiple solutions of nonlinear circuit equations [4,40] and for finding dc operating points of transistor circuits [16,24,28,43,56,58,68]. Homotopy algorithms were implemented in a number of developed stand-alone circuit simulators [69,70], simulators developed based on SPICE [55,58], and proprietary industrial tools designed for simulation of analog circuits such as ADVICE at AT&T [12,34,51,52] and TITAN at Siemens [33].…”

Section: Parameter Embedding and Continuation Methodsmentioning

confidence: 99%

“…The solution is unique if the extended Jacobian matrix (27) is of full rank. Conditions (28) define the starting value of λ, the starting point for x, and ensure that the sign and the magnitude ofẏ are fixed in the implementation. The solutionẏ is found by solving linear differential equation (29) using standard linear solvers via the QR factorization algorithm [30].…”

Section: Numerical Solvermentioning

confidence: 99%

DC operating points of transistor circuits

Trajković

2012

NOLTA

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Abstract:Finding a circuit's dc operating points is an essential step in its design and involves solving systems of nonlinear algebraic equations. Of particular research and practical interests are dc analysis and simulation of electronic circuits consisting of bipolar junction and fieldeffect transistors (BJTs and FETs), which are building blocks of modern electronic circuits. In this paper, we survey main theoretical results related to dc operating points of transistor circuits and discuss numerical methods for their calculation.

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“…Hence, it is much simpler than the method using DC analysis. If we already have the netlist of the original circuit N, then we can obtain the netlist of N p through a small modification to that of N. It is noted that the proposed method is a kind of SPICE-oriented approach [16].…”

Section: Methods Using Transient Analysismentioning

confidence: 99%

Formulating hybrid equations and state equations for nonlinear circuits using SPICE

Yamamura

Mitsuru

2011

Circuit Theory & Apps

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SUMMARYHybrid equations are often used in the theoretical study of nonlinear resistive circuits because they have an easy-to-analyze structure. They are also advantageous in the numerical analysis of nonlinear resistive circuits because they are separable and consist of a relatively small number of variables. However, the hybrid equations are seldom used in practical applications because their formulation is complicated. In this letter, we propose a simple method for formulating the hybrid equations using SPICE. In the proposed method, we only perform the transient analysis of SPICE on a linear circuit that is obtained through a small modification to the original circuit. It is also shown that state equations for nonlinear dynamic circuits can also be formulated by using the proposed method.

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An Efficient Variable Gain Homotopy Method Using the SPICE-Oriented Approach

Cited by 14 publications

References 18 publications

Accelerating the solving of nonlinear equations using the homotopy method: application on finding the operating point of complex circuits

Accelerating the solving of nonlinear equations using the homotopy method: application on finding the operating point of complex circuits

DC operating points of transistor circuits

Formulating hybrid equations and state equations for nonlinear circuits using SPICE

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