Lindy Mayfield wrote:
> How do you "understand" how a circuit
> works and how do you create with your imagination a new one?

I'm going to answer the second question first.  I've seen several replies
from others and I think they are missing the question, which I think is "How
do you synthesize a circuit given a task you want it to perform?".

I design circuits for a living and I think I'm pretty good at it.  However,
it's not a easy process to explain because I'm not sure myself what all of
it is.  How would you explain to someone how to ride a bike?  However I was
intrigued by your question as a opportunity to think about the design
process itself in a structured way, something that hadn't occurred to me
before.  There are probably much better ways to break it down since I've
only had time for a few knee jerk thoughts, but off the top of my head I can
think of four components to designing a circuit.  I'll call them knowledge
of fundamentals, knowledge of components, synthesis, and details.

Knowledge of fundamentals is only partly what others have mentioned.  Yes of
course you need to know, and more importantly truly understand, Ohm's law
and others.  These are absolutely essential foundations without which any
further effort is pointless.  However they shouldn't be as daunting as
others have made them out to be.  Ohm's law is about as simple as it gets,
usually expressed as V=IR.  I usually think of it in the units form: Volts =
Amps x Ohms.  But just knowing the equation is only worth about 20 points
out of 100.  You must be able to truly feel or visualize what a resistor
does.  As you force more current thru it, the voltage accross it builds up.
As you make the resistor bigger, the voltage accross it builds up.  The
exact math isn't as important as the general feel and intuition that should
pop into your head whenever you think "resistor".  Now flip it around: Amps
= Volts / Ohms.  Can you feel that as you put more voltage accross a
resistor the current thru it will go up?  The third form, Ohms = Volts /
Amps is for the details part later.

Just like resistors, you must understand capacitors and inductors at this
same level.  The traditional equations are all over the books you've got,
but the way I *think* about a capacitor is Volts = Amps x Seconds / Farads.
Actually that should be "delta Volts", but we're getting into details.
Again, just being able to write and manipulate the equation is worth 20
points.  The other 80 points is for truly understanding and being able to
visualize what a capacitor does, screw the exact math.

With the addition of the equivalent description of a inductor, Amps = Volts
x Seconds / Henrys, you've got the fundamentals for most circuit work.

Knowledge of components means you need to know what's out there for use as
building blocks.  Just like when you write a computer program, you always
keep in the back of your mind the basic constructs: IF statement, GOTO
statement, FOR loop, computed GOTO, subroutine call, etc.  Your whole
program is built from these.  Your job as the programmer is to combine these
basic constructs into a bigger program that does what you want.  Obviously
there are resistors, capacitors, and inductors out there.  But knowledge of
components means knowing what real world realizations of these are actually
available and in what way they are limited.  The equations might look great
with a 5 Farad capacitor or 2 Henry inductor, but you have to know that such
parts are unrealistic for your little breadboard.  similarly you have to not
only understand the basics of how a NPN transistor works, for example, but
also know roughly the limitations of real parts and what real world
parameters are achievable.  For example, a real NPN transistor will have a
upper limit on collector current, it will turn on pretty quickly when you
cram current thru it's base, but won't shut off as fast.  You don't need to
remember the detailed numbers, just the general principles.  Data sheets are
there to answer the detailed questions.  This section is about knowing the
questions to ask.  Eventually you will remember details of things you use
often.

Synthesis is the part I think you were really asking about.  I mentioned the
other two first because you can't get here without them.  Synthesis is also
the hardest to describe and I have no idea how to teach it.  I've always
been pretty good at it, and don't really know how I learned it.  Again, how
did you learn to ride a bike?  How would you describe it to someone who has
never ridden a bike?  It does feel a lot like writing a program.  You know
what you want to achieve, so apply cleverness and creative thought into
stringing together the available components to meet that goal.  One
difference is that there is a lot more stuff you have to be aware of when
designing a circuit than when designing a program.  I think that is because
there are more differnet electrical components available, and they each have
their own set of real world quirks, unlike program components which always
do exactly what they're defined to do.  There are a few analogous quirks in
programming too though where you have to know what's really going on.  For
example, something might be nicely solvable by using a array.  If I wanted
all the prime numbers below 100, I could put them all in a array then cross
off ever second, every third, etc.  That works fine.  On paper that works
perfectly fine for prime numbers up to 1M or 10M too, but this is where a
real programmer realizes that this method eats up a lot of memory.  Maybe
that's fine, and maybe not, but this is the kind of quirk a good programmer
has to keep in the back of his mind when synthesizing a program.  A
theoretically correct program that requires 1Mbyte of array space is of no
value on a 18F252.  There are a few orders of magnitude more of these when
synthesizing a circuit, but it's kindof the same thought process.

Up until know you are only working out the basic form, often called
topology, of the circuit.  At some point you have to get out the fine tooth
comb and crank out the actual resistor values, check all the power
dissipations, etc.  In other words, you have to work out the details.  Just
like with programming where you've decided to generate prime numbers by
crossing off non-primes in a array, now it's time to sit down and write the
actual detailed code.  To me this is a very different thought process,
although of course the two are not always sequential and they are
intertwined.  You might think out the overall circuit in rough terms, then
design the details of a particular section, which might cause you to rethink
some of the higher levels as you find there isn't enough voltage here for
the range of something you want to do, too slow, too power hungry, etc, etc.
Sometimes this requires minor tweaks, sometimes more major (crap, I was
hoping to get away without boosting the voltage here, but working around it
turns out to be even worse).  Software works the same way.  Once you start
implementing the lower layers, you sometimes find that your original concept
of the overall structure needs some readjusting.

Your first question about how to understand a existing circuit it easier to
answer, although often I find it easier to design a circuit than to analyze
someone else's without having some idea what it does.  I think this is a lot
like computer code.  It's easier to write your own program to generate prime
numbers than to take someone else's undocumented code and figure out that it
generates prime numbers.  The solution is also the same in both cases.  You
go thru the design piece by piece to figure out what each of the parts do,
then build up to figure out what the overall thing does.  I think this is
where studying others' designs that have a good theory of operation writeup
is useful.  This is just like studying others' well documented code to see
how they solved a particular problem.  After a while you will learn some
tricks too that can be applied to your own designs.

If you want a exercise, take a look at the schematic to my USBProg PIC
programmer, http://www.embedinc.com/products/eusb2/eusb2.pdf.  I haven't
written up a theory of operation yet, so this is a good opportunity to try
to figure it out on your own.  Start at the beginning on the first page and
try to figure out what each component is doing, and what a few groups of
components are doing and why.  I'll be happy to explain a piece at a time
once you've taken a stab at it yourself.

Sorry my answers sounds more like "Zen and the Art of Circuit Design", but
there is no esacping the need for being able to visualize the voltages
(pressures) and currents (flow) and how all the components react to them.
In the end there is a strong component of intuition and "lore" from
experience that I find hard to describe.


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