User Guide

Chapter 6 Analog behavioral modeling
164
Laplace transform part
The LAPLACE part specifies a Laplace transform which is
used to determine an output for each input value.
LAPLACE
The LAPLACE part uses a Laplace transform description.
The input to the transform is a voltage. The numerator
and denominator of the Laplace transform function are
specified as properties for the part.
Note
Voltages, currents, and TIME may not appear in a Laplace
transform specification.
The output of the part depends on the type of analysis
being done. For DC and bias point, the output is the zero
frequency gain times the value of the input. The zero
frequency gain is the value of the Laplace transform with
s=0. For AC analysis, the output is then the input times the
gain times the value of the Laplace transform. The value
of the Laplace transform at a frequency is calculated by
substituting j·
ω for s, where ω is 2π·frequency. For
transient analysis, the output is the convolution of the
input waveform with the impulse response of the
transform. These rules follow the standard method of
using Laplace transforms.
Example one
The input to the Laplace transform is the voltage at net 10.
The output is a voltage and is applied between nets 5 and
0. For DC, the output is simply equal to the input, since the
gain at s = 0 is 1. The transform, 1/(1+.001·s), describes a
simple, lossy integrator with a time constant of 1
millisecond. This can be implemented with an RC pair
that has a time constant of 1 millisecond.
For AC analysis, the gain is found by substituting j·
ω
for s.
This gives a flat response out to a corner frequency of
1000/(2
π
) = 159 hertz and a roll-off of 6 dB per octave after
NUM
numerator of the Laplace expression
DENOM denominator of the Laplace expression
Pspug.book Page 164 Wednesday, November 11, 1998 1:14 PM