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Subject: Re: SPICE and amp stability
References: <3DDBC8B8.16BF2A6D@ieee.org> <3DDD150A.9BBBF272@ieee.org>
NNTP-Posting-Date: Fri, 22 Nov 2002 17:53:59 GMT
Organization: AT&T Broadband
Date: Fri, 22 Nov 2002 17:53:59 GMT
Jim Thompson, analog, Jim Thompson, analog wrote:
>>>> You obviously are a Pspice aficionado, Jim. There is a rather clever
>>>> way to force any circuit containing behavioral models, no matter how
>>>> non-linear, to always successfully reach an initial operating point
>>>> solution. It takes full advantage of Pspice's scheme of cutting back
>>>> all power source as a convergence seeking ploy together with a unity
>>>> voltage source as a reference node for taming the behavioral models.
>>>> Can you guess what it is?
>>> You lost me there "analog", what are you driving at? Parameterizing
>>> behavioral gains proportionate to power supplies??
>> Almost. Have you ever modeled the low frequency behavior of switching
>> power supplies using average duty cycle controlled sources to replace
>> the semiconductor switches? One essentially use E and G sources to
>> make a "dc transformer" with a dynamic turns ratio that depends on the
>> node voltage representing duty cycle. These behavioral expressions
>> contain product terms, but what really gives the simulator fits are
>> higher order expressions with both numerator and denominator terms and
>> with terms that include sums, differences, especially involving
>> constants. There are lots of non-linear real world devices that don't
>> have a suitable built-in model in Pspice the behavior of which can,
>> nevertheless, be captured quite well via behavioral modeling. Tunnel
>> diodes, vacuum tube, arc discharges, high level control system blocks
>> all come to mind.
>> However, there are many ways to express essential the same model
>> within Pspice. The trick is to come up with one that doesn't give the
>> simulator fits when either it is searching for an initial solution to
>> the system matrix or when it is running a transient simulation. That
>> is what my question was about.
> One of the tricks I've used is to give OpAmps a sine-squared transfer
> function, smoothing the derivatives.
That probably helps both during the initial solution and transient runs.
Anything that makes the network approach linearity as either the sources
or time steps are scaled back should help the matrix solver converge on
a solution. And to that end, I've found that during the initial solution
any behavioral expression, no matter how wildly nonlinear, can be made to
converge simply by multiplying it by a special node set up with a source
such that the node's voltage is normally one volt dc.
Obviously, multiplying an ill behaved expression by this "unity node" one
or more times will not change its value during an analysis, but it *does*
have the happy effect of forcing even the rudest expression to approach
zero if Pspice panics during the initial solution and starts cutting back
all independent sources.
Does your bad boy expression contain constants in the numerator that
allow it to "stay up" past its time for going to zero like all the other
well behaved expressions? A judicious application of the unity node to
its numerator will make it behave.
Is one of your temperamental expressions so ill conditioned with an
overly "fast" denominator that it "blows up" every time its sources are
"grounded" by Spice's initial solver? Don't let a spoiled expression
ruin your simulations. Even the fastest denominator can be beaten to
zero by an ordinary numerator multiplied by the unity node raised to a
high enough power.
The lesson here is that, if Pspice has to cut back the sources when
seeking an initial solution, it will succeed *every time* if all the
behavioral expressions have numerators that approach zero faster than
their denominators do. This simple technique is so effective and so
powerful I often wonder why no simulator vendor has incorporated it
within their product offering. (By the way, I first developed the
"unity node" method when I was frustrated with trying to simulate
switching power supplies in the late 80's.)
Well, gotta run, so my hopefully helpful hints for taming transient
troubles will have to wait for another time. -- analog
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