Hi again Electrician,
Yes when i say 'numerical analysis' what i really mean is 'analytical analysis' followed
up by a numerical evaluation. A 'simulation' is any form of analysis where there's
only a set of models involved instead of actual physical parts connected together, but
in today's lingo 'simulation' usually refers to when someone uses a ready made program
and obviously you understood this. The better wording might have been 'circuit analysis
by hand' or something like that. That's a little misleading too i guess though, because
what i really do is throw the netlist at my NetList_To_Laplace program which spits out
the equations and then i solve the equations for all the nodes and usually pick out the
one or two of interest. Then i actually evaluate them numerically using a program that
spits out the answers much faster than i can read them.
And then a lot of times when we refer to a 'numerical analysis' we are really talking
about the way the differential equations are solved: analytically or numerically.
And yes there is some question as to why one would do this instead of using a simulator.
If we didnt need lots of results in numerical form (part of the terminology used in calling
it numerical analysis) then it would make much more sense to use a ready made simulator.
With that we could easily step values and see what the graphs look like. No prob.
But information to be analyzed by a computer is best in pure mathematical form or just
in plain old numerical form, not in graph form. The human likes to see the graphs and
make judgments, but the computer works with numbers so it needs a set (sometimes large)
of numbers to work with. That having, we can do an optimization, not by human eye, but
but computer analysis and without doubt the most exacting way to handle it.
And there are other ways of representing the result data in a more organized way than just
a list. True, a human can look at a list and make judgments, but a computer can work
wonders with a more organized list: the matrix.
Having the right matrix(s) [this starts to sound like a well known movie] we have a set of
data that represents the way the results change for every part in the circuit. Following
those changes we have systematic ways of finding optimizations for various target criteria
as well as various fit criteria so we are not limited in any way. This allows us to
explore the results in a systematic way rather than trial and error. Without the numerical
data we would have to read the graphs into the program and work from there...which of
course is possible but i felt that having the equations in the program would be a nicer
way of doing it and interesting to some degree
As far as "a lot of number crunching" you are right, but the computer does this quickly.
And this is no different than curve fitting, and if you've ever tried to fit even a
simple curve by hand and then compared the result to a curve fitting strategy then
you know what i mean. The optimization is nothing more than a curve fit.
The data usually takes the form of the deviations from the target criteria and their
derivatives, all in neat matrix form. Various fit criteria are then evaluated and the
results tested. Different fit criteria fit different applications better than others,
some would benefit from sum of squares and others from max deviation from perfection,
etc.
All that being said (little chuckle here) you noticed too that the most interesting area
of exploration is in the gains for each sub section itself. Thus maybe i'll start off
with an exploration of those three values and see what comes of it. I think you already
chose some decent values though so in a real life scenario we probably wouldnt have to
worry too much with this circuit, but it's still interesting to look at.
Also, was thinking of including in the optimization (why not right) the ability to get
the pots all centered at their mid travel points when the gain is 0db (or about 16db
overall including the first gain stage).
Yes the simulators use Gear or Trap usually. Gear usually being preferred due to
it's accuracy.
I'll have to see how the next few days go, i have other things that i have to do first.