A comparison of interval methods in symbolic circuit analysis applications

Symbolic circuit analysis involves deriving symbolic expressions for performance measures, such as voltage gain, input impedance, and evaluating them to obtain more insight into the behaviour of a circuit. In modern semiconductor technologies, it is more useful to evaluate the symbolic expressions using interval methods in order handle variations in parameter values. We compare the performance of different interval methods in evaluating symbolic expressions. Our experiments show that Generalised Interval Arithmetic is the most efficient method in affine form for our application. However, this method should be modified to suit long chains of computation. Our modification yields tighter interval bounds compared with other interval methods. References Francisco Fernandez et al., Symbolic Analysis Techniques Applications to Analog Design Automation IEEE Press, 1998. L. Kolev, Optimal Multiplication of G-intervals Reliable Computing, 13, pp.399--408, 2007. L. Kolev, New Formulae for Multiplication of Intervals, Reliable Computing, 12, pp.281--292, 2006. F. Messine and A. Touhami, A General Reliable Quadratic Form: An Extension of Affine Arithmetic, Reliable Computing, 12, pp.171--192, 2006. Xuan-Ha Vu, Rigourous solution techniques for numerical constraints satisfaction problems, PhD thesis no. 3155 (2005), Swiss Federal Institute of Technology, Lausanne, Switzerland 2005. G. Manson, Calculating frequency response functions for uncertain systems using complex affine analysis, J. Sound and Vibration, 288, pp.487--521, 2005. L. H. d. Figueiredo and J. Stolfi, Self-Validated Numerical Methods and Applications, IMPA, Rio de Janeiro, Brazil, July 1997. B. Thanigaivelan et al., A modified mosfet small-signal model based on Affine Arithmetic concepts, Proceedings of Asia Pacific Conference on Postgraduate Research In Microelectronics and Electronics, Shangai, China, 2009. Bozena Kaminska et al. Analog and Mixed-Signal Benchmark Circuits-First Release Proceedings of ITC, pp.183--190, 1997 S. M. Rump. (July 2010). Interval Laboratory. http://www.ti3.tu-harburg.de/rump/intlab/