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Circuit Transient Analysis
Using State Space Equations
Kai Chi Alex Lam and Mark Zwolinski
School of Electronics and Computer Science
University of Southampton
Southampton, UK SO17 1BJ
{kcal1g10,mz}@ecs.soton.ac.uk
Abstract.
The method to rearrange the classic transient analysis cir-
cuit simulation algorithm is presented in this paper. The steps of trans-
forming circuit equations into state variable equations are illustrated.
Explicit fourth order Runge Kutta method written in C is selected to
solve the transformed equations in order to break the time dependen-
cies, and hence to permit parallel transient analysis. Results of imple-
menting the new algorithm on non-linear example circuits are reported.
This approach can obtain significant speedup as compared to the simu-
lation on the same circuit using tradition method. The proposed ideas of
extracting parallelism are also discussed.
Keywords:
Circuit simulation, SPICE, Parallel Computing.
1 Introduction
Circuit simulation is an essential tool for predicting the behaviour of integrated
circuits. As transistors decrease in size with each generation of CMOS technology,
their variability is increasing, so there is a need to characterize digital systems
at the circuit level. Conventional algorithms for transient analysis such as those
used in SPICE, have many features that are inherently sequential and have
proven very dicult to parallelize. With the speed of conventional processors
limited to less than 4GHz, it is essential that parallel algorithms are found. A
number of attempts to accelerate circuit simulation algorithms in some of the new
computing architectures such as GPGPUs [1-3] , Multi-core CPUs or clusters [4-
6] were published recently. However, they are based on the traditional methods
as described in [7, 8]. Although the device evaluation phase can be naturally
executed in parallel, matrix solution can not. Also there is barrier between these
two phases. According to Amdahl's law [9], the barrier is the bottleneck for
further speedup of the algorithm. A state space approach is therefore proposed
to solve the circuit simulation parellization problem.
This paper first demonstrates the process of converting an MNA equation to
an SV equation in section 2. Section 3 describes solving non-linear circuit blocks
using the new method. Section 4 gives results of simulation of selected circuits
and section 5 discusses the possibility of parallelizing transient analysis using
the SV method. Section 6 has the conclusions.
