User Guide

Chapter B Convergence and “time step too small errors”
380
Introduction
In order to calculate the bias point, DC sweep and
transient analysis for analog devices PSpice must solve a
set of nonlinear equations which describe the circuit's
behavior. This is accomplished by using an iterative
technique—the Newton-Raphson algorithm—which
starts by having an initial approximation to the solution
and iteratively improves it until successive voltages and
currents converge to the same result.
In a few cases PSpice cannot find a solution to the
nonlinear circuit equations. This is generally called a
“convergence problem” because the symptom is that the
Newton-Raphson repeating series cannot converge onto a
consistent set of voltages and currents. The following
discussion gives some background on the algorithms in
PSpice and some guidelines for avoiding convergence
problems.
The transient analysis has the additional possibility of
being unable to continue because the time step required
becomes too small from something in the circuit moving
too fast. This is also discussed below.
Newton-Raphson requirements
The Newton-Raphson algorithm is guaranteed to converge
to a solution. However, this guarantee has some
conditions:
1 The nonlinear equations must have a solution.
2 The equations must be continuous.
3 The algorithm needs the equations' derivatives.
4 The initial approximation must be close enough to the
solution.
Each of these can be taken in order. Remember that the
PSpice algorithms are used in computer hardware that
T
h
e AC an
d
noise ana
l
yses are
l
inear an
d
d
o
not use an iterative algorithm, so the
following discussion does not apply to
them.
Pspug.book Page 380 Wednesday, November 11, 1998 1:14 PM