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Generalizing ASTAP'S Transmission Line Capability to Handle Complex Transfer Functions

IP.com Disclosure Number: IPCOM000102026D
Original Publication Date: 1990-Oct-01
Included in the Prior Art Database: 2005-Mar-17
Document File: 4 page(s) / 160K

Publishing Venue

IBM

Related People

Padula, ML: AUTHOR [+2]

Abstract

Disclosed is a process to handle complex transfer functions in the Advanced Statistical Analysis Program (ASTAP) for both a time domain and a frequency domain simulation. These techniques can be applied to any circuit simulation program with a similar formulation, thus adding a powerful capability. Recall that the transfer function of a system is used in a time domain simulation to convolve it with an input function of time, and, in a frequency domain simulation, to multiply it with an input function of frequency. Performing convolution in a time domain simulation has already been proven feasible by utilizing an external user written FORTRAN function.

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Generalizing ASTAP'S Transmission Line Capability to Handle Complex Transfer Functions

       Disclosed is a process to handle complex transfer
functions in the Advanced Statistical Analysis Program (ASTAP) for
both a time domain and a frequency domain simulation.  These
techniques can be applied to any circuit simulation program with a
similar formulation, thus adding a powerful capability.  Recall that
the transfer function of a system is used in a time domain simulation
to convolve it with an input function of time, and, in a frequency
domain simulation, to multiply it with an input function of
frequency. Performing convolution in a time domain simulation has
already been proven feasible by utilizing an external user written
FORTRAN function.  When the same FORTRAN function is utilized to
perform complex multiplication in a frequency domain simulation,
ASTAP fails to correctly process the partial derivatives of the
complex parameters as specified by a user.

      A very detailed study of ASTAP's tableaux formulation revealed
that ASTAP is capable of performing this necessary complex
multiplication because that is the exact procedure already being done
during a Transmission Line analysis.  The study demonstrated that
ASTAP considers a single Transmission Line to be a two-port, model
just as one would do when using a set of transfer functions for an
analysis. To use transfer functions via convolution or
multiplication, a two-port, model is created using two mutually
dependent current sources and utilizing admittance matrix parameters.
For this description, admittance parameters are chosen, realizing
that these are the same matrix parameters used by ASTAP when it
creates a two-port model for a single Transmission Line.
      The two-port model is shown below:

      Each current source, JIN and JOUT, depends upon the voltage
across the other current source and the voltage across itself. For a
frequency domain analysis, ASTAP must calculate partial derivatives
for both the real and imaginary components of the complex transfer
function with respect to the complex voltages, for each of the
dependent current sources in the two-port model.  The complex current
sources are functions of complex voltages in the two-port model as
follows:

                            (Image Omitted)

JIN = f(VJIN,VJOUT)
JOUT = g(VJIN,VJOUT)

      The current sources can then be defined in terms of admittance
parameters and put into matrix form.

      Expanding the admittance parameters, voltages and currents into
their real and imaginary components, and, performing the matrix
multiplication, produces the following equations: JINR + JINI(j) =
(Y11R + (j)Y11I)(VJINR + (j)VJINI) + (Y12R (J)Y12I)(VJOUTR +
(j)VJOUTI) JOUTR + JOUTI(j) = (Y21R + (j)Y21I)(VJINR + (j)VJINI) +
(Y22R (j)Y22I)(VJOUTR = (j)VJOUTI)

      The input current source is expressed into its real and
imaginary components. JINR = Y11R(VJINR) -...