Re: [Help-gnucap] ua741 simulation

[Al Davis]

On Thursday 04 November 2004 10:59 am, Enrico Strocchi wrote:
> Why the solution not converge

The composite of your circuit and the limiting algorithm throws 
the iteration algorithm into a limit cycle, so after some 
number of iterations you get the same incorrect results as 
before.  In this case, the length of the limit cycle is 7 
iterations, which is unusual.  It is rare to have a limit cycle 
this long.

The terms "limiting algorithm" and "limit cycle" have nothing to 
do with each other, in spite of the fact that both use the word 
"limit".

A "limiting algorithm" is a method used by the simulator to 
limit differences between values on subsequent iterations.

A "limit cycle" means that the iterations bounce between values.  
A "limit cycle of length 7" means that every 7 iterations are a 
repeat of the previous 7.  Once it enters a limit cycle, 
convergence failure is guaranteed.  By adding "trace 
iterations" to a dc command (or op or tran) you can see every 
iteration, which may give you insight into the problem.

In this case,to make it converge, all you need to do is make any 
change to break the symmetry,  The easiest is ".option 
dampmax=.99".  More generally, the default value is 1.  One way 
to help convergence is to lower the value until it converges.  
Usually, just a little, such as .99, will work.  Sometimes you 
need to go farther.  If you need to lower it to less than 
about .6, the results should not be trusted even if it does 
converge.

What it does is simple..  Suppose we have a guess of "1", and 
the next iteration produces a value of "2".  With dampmax=1, 
the value of 2 will be used exactly.  With dampmax=.9 a value 
of 1.9 will be used instead.  (.9 times the difference)

So. suppose it is in a limit cycle alternating between 1 and 2.  
That is, iterations are 1 2 1 2 1 2 1 2  etc.  With dampmax 
= .9, it starts at 1, then 2 becomes 1.9 instead.  The next 
iteration might be something like 1.1, which becomes something 
like 1.2...   So it breaks the repeat.