User`s guide

6
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18 Analo
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Behavioral Modelin
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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
attributes for the symbol.
Note
Volta
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es, 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 1
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/(2π) =
159 hertz and a roll-off of 6 dB per octave after 159 Hz. There
is also a phase shift centered around 159 Hz. In other words, the
NUM numerator of the Laplace expression
DENOM denominator of the Laplace expression