Elementary AC circuit analysis

I'm trying to calculate a voltage in a circuit, and having the problem that
I can't quite remember simple circuit theory.

I have a circuit that boils down to something like this:

+-C-R1--+--R2--+
| | |
AC R3 DC
| | |
| RL |
| | |
+-------+------+

where AC = an AC frequency source of frequency F, DC = a DC power supply and
RL is a complex semiconductor load (where I know the current at a given
value of DC, but in general it'll be nonlinear).

Reactance of capacitor C at F is approximately zero - it's simply a DC
blocking capacitor. So everything is in phase, more or less.

Now I'm trying to work out the theoretical AC voltage across R3 due to the
AC signal. That's no problem for the lefthand loop (I can assume the AC
reactance of RL is zero). What I can't quite remember is what to do for the
DC source. In DC analysis, voltage sources are treated as having infinite
resistance. But what happens in AC analysis? I thought that they were
treated as having zero AC resistance (low impedance, hence short circuit).
But I'm not quite sure if I remember this right.

So if the impedance of the righthand loop as seen across the midpoints is
given by (R3+RL) // (R2+R(DC)), what's a reasonable value to assume for
R(DC) - zero or infinity?

What sort of reactance do DC voltage sources have in reality? I'd have
thought fairly low, given all those smoothing caps floating around.

Thanks
Theo

PS This isn't a homework question, this is the kind of thing you do in
school and then never use again. So I've forgotten the vital detail.

 

Thanks. That's what I thought I'd worked out from first principles, but my
brain was having a day off

Theo

 

Cool circuit, If I make RL an LED it looks like a simple modulation
technique.
(in which case I'd like to add a bit of inductance to R2. No sense
wiggling the battery around at AC.)

">In DC analysis, voltage sources are treated as having infinite

Opps, DC or AC ideal voltage sources have zero impedance.

George Herold

 

Or you could replace R2 with a current source if the inductance needed
proves too bulky.

 

Well spotted, that's exactly what I'm doing! (but at higher frequencies)

That's an interesting idea... 'wiggling the battery around' was indeed what
I was trying to avoid, especially with power supplies that are chock full of
smoothing capacitors.

That was my brain fart. And the more I stared at it the more my head
started going round in circles

Theo