When solving node/loop equations manually, it's generally necessary to
resort to phasor analysis with its underlying assumptions, or Laplace
transforms. The latter does have the capability of producing a time
response. But the solution requires finding the inverse transform, a
process similar to integration in that there's no single direct rule,
and often it's impossible to find a solution except for simple cases.

Computers can be programmed to solve complex problems numerically, using
fundamental time-domain current/voltage relationships (such as the
relationship V(t) = L di/dt for an inductor, or even more generally,
V(t) = L di/dt + I dl/dt for a time-varying inductance). This is
basically what SPICE does, and it's able to easily solve problems which
are simply not possible to do manually, either because of the enormous
time that would be required, or the impossibility of finding a reverse
Laplace transform -- or its equivalent, the solution to a high-order
differential equation if Laplace transforms aren't used. A google search
on 'SPICE "time step" equations' brought a number of hits. I'm sure you
can find an adequate explanation of the inner workings of SPICE among them.

Roy Lewallen, W7EL

Steve Nosko wrote:
. . .
Correct me if I am wrong (like I need to say this here, eh?)
I believe the underlying basis is the collection of loop / node equations
used (by Engineers) to model circuits. We know the behavior of resistors,
inductors and capacitors and have mathematical models for them. To this we
add the active devices, etc. and develop an "engine" which does all the
calculations for us. [[we used to do them by hand/slide rule -- yes, I am
included in this we]]. These loop and node equations provide us with a
mathematical model of the behavior of electronic circuits. If done
carefully, this is a general purpose model which applies to all the
situations for which our component models are valid.
Some time later there were bare engines into which we had to type the part
values and node numbers (the sane things you can see in printouts from
Spice). As computers got more powerful, schematic entry was developed. I
believe these programs to be very useful, but as with any model or
simulation, it is best to understand the limitations.
Thre is an alternate method. It is also possible to derive equations for
each type of situation and use these calculations each time you need to
solve that type of problem. I am sure you are familiar with the equations
for things such as parallel capacitors and resonance and so forth. These
are specific solutions of the properties of components in those specific
circuits.
. . .

"Airy R. Bean" wrote in message
...
Question - what is the internal modelling technique used
by these various programs, and can we produce our own package?

Is it based upon successive delta-time increments, and if so, what
is the increment? What prompted the last question is an attempt
I made to create a sine-wave generator using the identity that
sin dTheta = dTheta, but I had to go for an _extremely_ small
value of dTheta (ISTR 10^ -18) before getting anything like a
decent sine wave, and even that degenerated after a few cycles.

So, these circuit simulators - what is their underlying technique
for circuit simulation?
[clip]

The simulators basically offer 2 types of direct analysis ...
An "AC" analysis and a "Transient" analysis. Their answers come via
different maths methods.
Basically the much less useful 'AC' analysis examines all the wire
connection points 'nodes' in the circuit diagram and enters the found
components in 2 matrices. Each (square) matrix is sized to hold node^2
elements. One is for 'real' components, the other for quadrature components.
All non linear components in the circuit must first be simplified/replaced
by linear equivalants (messy). Matrices are filled in a manner similar to
kirchoffs loops anaysis. Reactive components entering the imaginary matrix.
Ie lots of real/imag simultaneous equations need solving which is of course
why the computer is handy.
After they are filled the matrices are mathematically inverted to give a
complete set of solved phase and ac voltage data for all the node points in
the circuit. Nice for filters useless for oscillators!.

The more useful transient analysis is similar to as you mention (Babbage's
difference engine?) but based simply on the differentials V=L i/t and V=i/C
and uses near complete maths models for the semicons or other non linear
elements. Nodes examined in turn and time steps selected purely on the
basis of how fast the results are changing. time steps can be a problem as
too long and the final results get 'smeared out' hence phase lag artifacts
cause overall loop stability problems.
The TA is conceptually very simple and surprisingly easy and fun to
programme for set piece or well observed circuits but gets *really* spagetti
code messy if it is to work smoothly with any input circuit. Big problems
can turn up getting the results to converge or balance and much progging
effort is needed in this direction.
regards
john

"J M Noeding" wrote in message
...
On Sun, 17 Oct 2004 15:00:49 +0100, "Airy R. Bean"
wrote:
[clip]
But for Radcom, I must admit that I mainly read G3VA's "Technical
topics"

My radio club was Worcester &DARC, suppose it is not so much activity
there now....

---
J. M. Noeding, LA8AK, N-4623 Kristiansand
http://home.online.no/~la8ak/c.htm


To me, Pat Hawker is the defining spirit of UK amateur radio.
I've also picked up much fascinating stuff from his technical-topics and the
mentions of his SOE work in WW2.
regards
john