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From: Bitrex on 1 Apr 2010 01:58
I'm wondering how one calculates the gain and impedances of a multistage
amplifier where, for example, one is both sampling the output voltage
and mixing it in series with the input stage, and also the output
current and mixing it in shunt. Does one calculate the voltage gain and
voltage feedback ratio for the first feedback loop, and the current gain
and current feedback ratio for the second feedback loop, and then just
apply the feedback equation twice for both sets of values? Does it
matter in which "order" the two equations are applied? Thanks.
From: Tim Wescott on 1 Apr 2010 11:27
Bitrex wrote:
> I'm wondering how one calculates the gain and impedances of a multistage
> amplifier where, for example, one is both sampling the output voltage
> and mixing it in series with the input stage, and also the output
> current and mixing it in shunt. Does one calculate the voltage gain and
> voltage feedback ratio for the first feedback loop, and the current gain
> and current feedback ratio for the second feedback loop, and then just
> apply the feedback equation twice for both sets of values? Does it
> matter in which "order" the two equations are applied? Thanks.

If the equations are exact then you should be able to apply them in
either order and get the same answer.

I dimly remember being presented with the whole feedback equation thing
in 3rd-year circuits and wondering if they were exact or if there were
approximations being made that were only usually true. I never went
back and verified, because if you're just analyzing one circuit it's
easier to grind the whole thing out using mesh or nodal analysis.

Easier yet, use LTSpice and believe it 'cause the Computer Says So.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
From: Jim Thompson on 1 Apr 2010 11:53
On Thu, 01 Apr 2010 08:27:50 -0700, Tim Wescott <tim(a)seemywebsite.now>
wrote:

>Bitrex wrote:
>> I'm wondering how one calculates the gain and impedances of a multistage
>> amplifier where, for example, one is both sampling the output voltage
>> and mixing it in series with the input stage, and also the output
>> current and mixing it in shunt. Does one calculate the voltage gain and
>> voltage feedback ratio for the first feedback loop, and the current gain
>> and current feedback ratio for the second feedback loop, and then just
>> apply the feedback equation twice for both sets of values? Does it
>> matter in which "order" the two equations are applied? Thanks.
>
>If the equations are exact then you should be able to apply them in
>either order and get the same answer.

Where it gets tricky is with multiple loops within a circuit... when
one loop is not totally contained within the other.

Like some DC common mode loops, with differential _signal_ feedback.

>
>I dimly remember being presented with the whole feedback equation thing
>in 3rd-year circuits and wondering if they were exact or if there were
>approximations being made that were only usually true. I never went
>back and verified, because if you're just analyzing one circuit it's
>easier to grind the whole thing out using mesh or nodal analysis.
>
>Easier yet, use LTSpice and believe it 'cause the Computer Says So.

It gets quite nasty. I end up having to totally trust transient
analysis and over-shoot estimations :-(

...Jim Thompson
--
| James E.Thompson, CTO | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
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The only thing bipartisan in this country is hypocrisy
From: Tim Williams on 1 Apr 2010 13:35
Theorems of "block diagram algebra" say you can take a diagram with loops
(which may be intersecting) and move branch points around (obviously, this
is done by introducing a factor of H or 1/H in the branch, in order to move
it in front of or after the block H), thus simplifying it to a diagram with
no intersecting loops, which can be reduced, ultimately, to the single loop
T = G/(1+GH) form (a formula which can be proven by the same rule, if you
don't mind chugging one step further).

In electronic terms, you might as well write the system of equations and
play with that. You can reduce it to block form if you like, it's an
equivalent approach.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"Bitrex" <bitrex(a)de.lete.earthlink.net> wrote in message
news:48SdnRp6KZ54qynWnZ2dnUVZ_rednZ2d(a)earthlink.com...
> I'm wondering how one calculates the gain and impedances of a multistage
> amplifier where, for example, one is both sampling the output voltage and
> mixing it in series with the input stage, and also the output current and
> mixing it in shunt. Does one calculate the voltage gain and voltage
> feedback ratio for the first feedback loop, and the current gain and
> current feedback ratio for the second feedback loop, and then just apply
> the feedback equation twice for both sets of values? Does it matter in
> which "order" the two equations are applied? Thanks.


From: Tim Wescott on 1 Apr 2010 14:23
"Bitrex" <bitrex(a)de.lete.earthlink.net> wrote in message
news:48SdnRp6KZ54qynWnZ2dnUVZ_rednZ2d(a)earthlink.com...
> > I'm wondering how one calculates the gain and impedances of a
multistage
> > amplifier where, for example, one is both sampling the output
voltage and
> > mixing it in series with the input stage, and also the output
current and
> > mixing it in shunt. Does one calculate the voltage gain and voltage
> > feedback ratio for the first feedback loop, and the current gain and
> > current feedback ratio for the second feedback loop, and then just
apply
> > the feedback equation twice for both sets of values? Does it matter in
> > which "order" the two equations are applied? Thanks.

Tim Williams wrote:
> Theorems of "block diagram algebra" say you can take a diagram with loops
> (which may be intersecting) and move branch points around (obviously, this
> is done by introducing a factor of H or 1/H in the branch, in order to move
> it in front of or after the block H), thus simplifying it to a diagram with
> no intersecting loops, which can be reduced, ultimately, to the single loop
> T = G/(1+GH) form (a formula which can be proven by the same rule, if you
> don't mind chugging one step further).
>
> In electronic terms, you might as well write the system of equations and
> play with that. You can reduce it to block form if you like, it's an
> equivalent approach.

I'll often do this sort of thing with block diagrams, if I can figure
out which dynamic elements to ignore. Grinding through the system of
equations won't take you any more time than the block diagram way, but
the block diagrams _may_ give you more insight into why the system
operates the way it does.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com
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