Elementary AC circuit analysis

[Theo Markettos]

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.

 

[BobW]

"Theo Markettos" <theom+news@chiark.greenend.org.uk> wrote in message
news:A-n*wQgHs@news.chiark.greenend.org.uk...

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

A perfect dc supply will not change its voltage regardless of the current or
change in current through it. So, by definition, its delta(v)/delta(i) (its
impedance) would be zero.

A supply or battery's internal impedance depends on the supply itself. A
brand new fully energized car battery has an internal impedance in the low
milliohms (under 20mohms?). A 9V battery might have an impedance of over 1
ohm when it's fully energized, or several ohms when it's pooping out. A
bench supply would certainly be below an ohm before it current limits.

For your analysis, it's probably safe to set the DC source's impedance to
zero.

Bob
--
== All google group posts are automatically deleted due to spam ==

 

[Theo Markettos]

BobW <nimby_GIMME_SOME_SPAM@roadrunner.com> wrote:

A perfect dc supply will not change its voltage regardless of the current
or change in current through it. So, by definition, its delta(v)/delta(i)
(its impedance) would be zero.

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

Theo

 

On May 18, 2:35 pm, Theo Markettos <theom+n...@chiark.greenend.org.uk>
wrote:

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.

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

resistance. "

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

George Herold

 

[Jasen Betts]

On 2009-05-19, ggherold@gmail.com <ggherold@gmail.com> wrote:

On May 18, 2:35 pm, Theo Markettos <theom+n...@chiark.greenend.org.uk
wrote:
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     |
|       |      |
+-------+------+


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.)

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

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

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

 

[Theo Markettos]

ggherold@gmail.com wrote:

Cool circuit, If I make RL an LED it looks like a simple modulation
technique.

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

(in which case I'd like to add a bit of inductance to R2. No sense
wiggling the battery around at AC.)

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.

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

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

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

Theo

 

On May 19, 1:26 pm, Theo Markettos <theom+n...@chiark.greenend.org.uk>
wrote:

ggher...@gmail.com wrote:
Cool circuit, If I make RL an LED it looks like a simple modulation
technique.

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

(in which case I'd like to add a bit of inductance to R2.  No sense
wiggling the battery around at AC.)

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.

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

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

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

Theo

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

Hmm, I didn't mention a frequency. I've only done this with a diode
laser as load up to 200MHz (which is the highest 'easy' frequency I
have available at the moment.) But I've got dreams of 3.X or 6.7 GHz.
(the hyperfine resonance's of Rubidium.)

BTW a current source as DC driver is the way to go. (As mentioned by
someone else.) The inductor in the DC path is still a good idea.
(Though not mine, I stole it from Libbrecht and Hall, RSI, circa
1992)

George Herold