Conversion of MNA equations to state variable form for nonlinear dynamical circuits

Kang, Yixin; Lacy, Jack

doi:10.1049/el:19920783

Cited by 8 publications

(8 citation statements)

References 2 publications

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“…This has been achieved avoiding the use of conditional sentences in the kernel code and decomposing the computations into single multiply and accumulate operations as shown in Algorithm 1. where the jacobian J is negative definite and diagonally dominant. The equation has been obtained through nodal analysis and manual transformation, although for more complex circuits, the method detailed in [17] may be useful. For the coupled interconnect model shown in Fig 2 .b, the space state equation is given by:…”

Section: Simulation On a Many-core Computermentioning

confidence: 99%

An Efficient Numerical Solution Technique for VLSI Interconnect Equations on Many-Core Processors

Doménech‐Asensi

Kázmierski

2019

2019 IEEE International Symposium on Circuits and Systems (ISCAS)

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This paper presents a technique to accelerate transient simulations of analog circuits using an explicit integration method parallelised on a many-core computer. Usual methods used by SPICE-type simulators are based on Newton-Raphson iterations, which are reliable and numerically stable, but require long CPU processing times. However, although the integration time step in explicit methods is smaller than that used in implicit methods, this technique avoids the calculation of time-consuming computations due to the Jacobian matrix inversion. The proposed method uses an explicit integration scheme based on the fourth order Adams-Bashforth formula. The algorithm has been parallelised on a NVIDIA general purpose GPU using the CUDA programming model. As a case study, the RC ladder model of a VLSI interconnect is simulated on a general purpose graphic processing unit and the achieved performance is then evaluated against that of a multiprocessor CPU. The results show that the proposed technique achieves a speedup of one order of magnitude in comparison with implicit integration techniques executed on a CPU.

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Section: Simulation On a Many-core Computermentioning

confidence: 99%

An Efficient Numerical Solution Technique for VLSI Interconnect Equations on Many-Core Processors

Doménech‐Asensi

Kázmierski

2019

2019 IEEE International Symposium on Circuits and Systems (ISCAS)

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“…Equation (5) has been obtained through nodal analysis and manual transformation. However, for circuits with increased complexity, the method described in [17] can be useful.…”

Section: Example Of Cmos-c Network For Time-mentioning

confidence: 99%

Simulation Acceleration of Image Filtering on CMOS Vision Chips Using Many-Core Processors

Doménech‐Asensi

Kázmierski

2019

2019 Forum for Specification and Design Languages (FDL)

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This paper describes an efficient numerical solution to speed up transient simulations of analog circuits on a many-core computer. The technique is based on an explicit integration method, parallelised on a multiprocessor architecture. Although the integration step is smaller than the required one by traditional simulation methods based on Newton-Raphson iterations, explicit methods do not require to compute complex calculations such us matrix factorizations, which lead to long CPU simulation times. The proposed technique has been implemented on a NVIDIA GPU and has been demonstrated simulating Gaussian filtering operations performed by a CMOS vision chip. These type of devices, which are used to perform computation on the edge, include built-in image processing functions, turning them into very complex and time consuming circuits during their design. The proposed method is faster that Ngspice for different image sizes, and for 128 x 128 pixels image size it achieves a speed up of two orders of magnitude.

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“…Hence, using the idea of the multilevel Newton-Raphson algorithm [17,Section 8.3.3], we can apply various numerical integration methods (such as the implicit Runge-Kutta method) to the nonlinear state equations. Example 3 Consider the nonlinear dynamic circuit shown in Figure 7(a) [18]. Replace the independent voltage source, capacitor, inductor, and diodes with pulse sources as shown in Figure 7(b), where the branch voltages and current of the pulse sources are given in Figure 8.…”

Section: Formulating State Equations Using Spicementioning

confidence: 99%

“…Consider the nonlinear dynamic circuit shown in Figure 7(a) [18]. Replace the independent voltage source, capacitor, inductor, and diodes with pulse sources as shown in Figure 7(b), where the branch voltages and current of the pulse sources are given in Figure 8.…”

Section: Examplementioning

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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Conversion of MNA equations to state variable form for nonlinear dynamical circuits

Cited by 8 publications

References 2 publications

An Efficient Numerical Solution Technique for VLSI Interconnect Equations on Many-Core Processors

An Efficient Numerical Solution Technique for VLSI Interconnect Equations on Many-Core Processors

Simulation Acceleration of Image Filtering on CMOS Vision Chips Using Many-Core Processors

Formulating hybrid equations and state equations for nonlinear circuits using SPICE

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