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Performing Convolution in ASTAP

IP.com Disclosure Number: IPCOM000099890D
Original Publication Date: 1990-Feb-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 5 page(s) / 233K

Publishing Venue

IBM

Related People

Padula, ML: AUTHOR [+2]

Abstract

The convolution integral has been programmed as a Fortran function in ASTAP for a time domain simulation. With this function, ASTAP has been provided with the capability of representing linear multi-port networks in terms of their terminal characteristics, that is, their transfer functions in the frequency domain. This approach to representing complex multi-port networks in terms of their behavior is a significant advance in modeling. Most models of devices and components are constructed from five basic elements: resistors, capacitors, inductors, current sources, and voltage sources. Some of these elements, particularly the voltage sources and the current sources, may depend on other voltages and currents.

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Performing Convolution in ASTAP

       The convolution integral has been programmed as a Fortran
function in ASTAP for a time domain simulation.  With this function,
ASTAP has been provided with the capability of representing linear
multi-port networks in terms of their terminal characteristics, that
is, their transfer functions in the frequency domain.  This approach
to representing complex multi-port networks in terms of their
behavior is a significant advance in modeling.  Most models of
devices and components are constructed from five basic elements:
resistors, capacitors, inductors, current sources, and voltage
sources.  Some of these elements, particularly the voltage sources
and the current sources, may depend on other voltages and currents.
For the special situation where only the current sources and voltage
sources in a model depend in a linear manner on other currents and
voltages, the circuit for this model is still a linear network.  As
such, it can be represented via the convolution integral at its
terminals as an alternative to describing it in terms of its basic
elements. The terminal representation is particularly appropriate for
the following situations:
      1.   The topological structure of the network between the
terminals is unknown, such as a filter purchased from a vendor.
      2.   The details of the topological structure are not as
important as the transfer function at the terminals, such as for
representing the frequency characteristics of an operational
amplifier.
      3.   The topological structure is not physically realizable,
such as the frequency characteristic of an ideal low-pass filter.
      4.   A topological model does exist, but a simple model is all
that is necessary to verify the concepts that are a bit too complex
for manual calculations.
      5.   A topological model cannot be readily synthesized from the
measurement on existing components in the laboratory, such as for
fiber-optic cable, and yet a model must be developed for simulation
in a circuit analysis program.
      6.   The capabilities of transmission lines in ASTAP are not
adequate to represent their frequency characteristics as cycle times
decrease.
      7.   The modeling of fiber-optic cables.
      8.   The modeling of transmission lines.

      These few situations should be sufficient to demonstrate that
convolution should be a significant advance in representing linear
networks to a circuit analysis program.

      Recall, this particular convolution algorithm performs
convolution in the time domain.  With this in mind, the first step in
this routine is to construct the time domain transfer function from
its frequency domain characteristics at the starting time of the
analysis.  This step is accomplished by applying the Fourier Series
Summation.  This routine treats the transfer function as if it were
periodic, and it constructs h(t).  The number of ter...