30
WARNING -- It should be delayed by at least 4.86374e-013 sec.
Non-causality more than a few percent can lead to highly inaccurate results, depending on what feature
of the impulse response has been lost through truncating values for t<0. The following are guidelines for
improving the simulations.
Try adding phase delay to the Laplace expression by multiplying by exp(-s*), where
is the recommended delay in the output file.
Use a Laplace expression of the form a+b*sqrt(s). sqrt(s) is fundamentally non-causal, but is has a
known phase of 45 degrees. Larger b/L ratios lead to higher amounts of non-causality
(L=inductance). Check if calculations will allow this ratio to be reduced.
Larger ratios of / increase the degree of non-causality due to the
limited resolution of the FFT used to compute the impulse response. Try to run shorter simulations to
simulate with frequency dependent loss expressions, then run longer simulations with single
frequency loss expressions.
Lastly, consider using a constant value for R and G, by using values corresponding to the driving
frequencies of interest in the simulation. For sinusoidal signals, this is a simple matter. For digital
(pulse) inputs, use 2/Tr for the frequency. If loss must be considered at multiple frequencies, run a
simulation with each value to find the worst case results.
REFERENCES
[1] Roychowdhury, J.S. and D.O. Pederson, "Efficient Transient Simulation of Lossy Interconnect", 28
th
ACM/IEEE Design Automation Conference, 1991, pp. 740-745.
[2] Tripathi, V.K., and J.B. Rettig, "A SPICE Mode for Multiple Coupled Microstrips and other
Transmission Lines", IEEE MTT-S Digest, 1985, pp. 703-706.
[3] Banzhaf, W., "Simulating Lossy Transmission Lines With PSpice", RF Design, January 1993, pp. 25-
27.
[4] Cooper Industries, Belden Wire and Cable Master Catalog, 1996.
[5] Paul , C.R., Analysis of Multiconductor Transmission Lines, Wiley Series in Microwave and Optical
Engineering, K. Chang (Ed.), John Wiley & Sons, Inc., 1994.
[6] Wadell, B.C., Transmission Line Design Handbook, Artech House, 1991.
[7] National Semiconductor, F100K ECL 300 Series Databook and Design Guide, 1992.
[8] Johnson , H.W. and M. Graham, High-Speed Digital Design: A Handbook of Black Magic", Prentice
Hall PTR, 1993.
[9] Deutsch et. al., A., "High-speed signal propagation on lossy transmission lines", IBM J. Res. Dev., Vol.
34, No. 4, pp. 601-615, July 1990.
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