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PSpice User Guide Analog behavioral modeling October 2019 342 Product Version 17.4-2019 © 1999-2019 All Rights Reserved. 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/(2π) = 159 hertz and NUM numerator of the Laplace expression DENOM denominator of the Laplace expression