User`s guide

B
-
2 Conver
g
ence and “Time Step Too Small Errors”
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.
The AC and noise analyses are linear and do not use an iterative
algorithm. The following discussion does not apply to them.
Digital devices are evaluated using boolean algebra and this
discussion does not apply to them either.
Newton-Raphson Requirements
The Newton-Raphson algorithm has the very nice property that
it is guaranteed to converge to a solution. However, this nice
property has some serious strings attached:
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.