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POLY Expressions
In SPICE2, nonlinear polynomial dependencies are specified using a
rather cumbersome syntax keyed by the word poly. For
compatibility, this syntax is recognized by the dependent sources in
WRspice, making possible the use of the large number of behavioral
models developed for SPICE2.
There are three polynomial equations which can be specified through the
poly(N) parameter.
- poly(1) One-dimensional equation
- poly(2) Two-dimensional equation
- poly(3) Three-dimensional equation
The dimensionality refers to the number of controlling variables; one,
two, or three. These parameters must immediately follow the poly(N) token. The inputs must correspond to the type of the
source, either pairs of nodes for voltage-controlled sources, or
voltage source or inductor names for current-controlled sources.
Following the inputs is the list of polynomial coefficients which
define the equation. These are constants, and may be in any format
recognized by WRspice.
The simplest case is one dimension, where the coefficients c0, c1, ...
evaluate to
c0 + c1x + c2x2 + c3x3 + ...
The number of terms is arbitrary. If the number of terms is exactly one,
it is assumed to be the linear term (c1) and not the constant
term. The following is an example of a voltage-controlled voltage source
which utilizes poly(1).
epolysrc 1 0 poly(1) 3 2 0 2 0.25
The source output appears at node 1 to ground (note that WRspice can use
arbitrary strings as node specifiers). The input is the voltage difference
between nodes 3 and 2. The output voltage is twice the input voltage
plus .25 times the square of the input voltage.
In the two dimensional case, the coefficients are interpreted in the
following order.
c0 + c1x + c2y + c3x2 + c4xy + c5y2 + c6x3 + c7x2y + c8xy2 + c9y3 + ...
For example, to specify a source which produces
3.5*v(3,4) + 1.29*v(8)*v(3,4), one has
exx 1 0 poly(2) 3 4 8 0 0 3.5 0 0 1.29
Note that any coefficients that are unspecified are taken as zero.
The three dimensional case has a coefficient ordering interpretation
given by
c0 + c1x + c2y + c3z + c4x2 + c5xy + c6xz + c7y2 + c8yz + c9z2 + c10x3 + c11x2y + c12x2z +
c13xy2 + c14xyz + c15xz2 + c16y3 + c17y2z + c18yz2 + c19z3 + ...
which is rather complex but careful examination reveals the pattern.
Next: Tran Functions
Up: Voltage and Current Sources
Previous: Source Expressions
Contents
Index
Stephen R. Whiteley
2006-10-23