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From: Bitrex on 1 Apr 2010 19:05
Jim Thompson wrote:
> 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.

The type of circuit I'm trying to analyze via this method is here:

http://s227.photobucket.com/albums/dd240/bitrex2007/?action=view&current=Feedback.jpg

(note there should be a DC blocking capacitor after R5).


Basically I'm trying to calculate the voltage gain and voltage feedback
ratio, and current gain and current feedback ratio independently using
superposition and a cascaded hybrid-pi model of the two transistor
circuit. I'm starting to conclude that it's pretty much an equivalent
amount of math to using nodal or mesh analysis, with the downside that
it can't be automated via computer! The only advantage I can see is that
one could analyze the effects of the current feedback and voltage
feedback paths independently, while an expression for the gain and input
impedance using nodal analysis will be a huge expression with everything
jumbled together, making it hard to know directly what changes in either
feedback network will have on the parameters.

>
>> 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
From: Howard Swain on 2 Apr 2010 17:33

"Bitrex" <bitrex(a)de.lete.earthlink.net> wrote in message news:0rCdnRc8-vsMuijWnZ2dnUVZ_gydnZ2d(a)earthlink.com...
> Jim Thompson wrote:
>> 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.
>
> The type of circuit I'm trying to analyze via this method is here:
>
> http://s227.photobucket.com/albums/dd240/bitrex2007/?action=view&current=Feedback.jpg
>
> (note there should be a DC blocking capacitor after R5).
>
>
> Basically I'm trying to calculate the voltage gain and voltage feedback
> ratio, and current gain and current feedback ratio independently using
> superposition and a cascaded hybrid-pi model of the two transistor
> circuit. I'm starting to conclude that it's pretty much an equivalent
> amount of math to using nodal or mesh analysis, with the downside that
> it can't be automated via computer! The only advantage I can see is that
> one could analyze the effects of the current feedback and voltage
> feedback paths independently, while an expression for the gain and input
> impedance using nodal analysis will be a huge expression with everything
> jumbled together, making it hard to know directly what changes in either
> feedback network will have on the parameters.

The gain and impedances of that circuit are discussed in
"A Wide-Band Ultralinear Amplifier from 3 to 300 MHz" by
Meyer, Eschenbach, and Chin in IEEE Journal of Solid Stated
Circuits, vol. SC-9, no. 4 (Aug. 1974), pp. 167-175.
There are some brief derivations and the resultant equations
are shown.

>>
>>> 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
From: miso on 3 Apr 2010 00:43
On Apr 1, 11:23 am, Tim Wescott <t...(a)seemywebsite.now> wrote:
> "Bitrex" <bit...(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 consultingwww.wescottdesign.com

I think "signal flow graph" would get you a relevant google search.
Next up is Mason's rules. My understanding is they haven't taught that
stuff in EE courses since the late 80s, at least in any detail. I
doubt anyone could make a leapfrog filter design these days since
signal flow graph theory is just glossed over in colleges.

Is the original poster over complicating the question? I mean, app a
voltage source to the input and compute the current, then get the
impedance. Who cares if the box has feedback. Think of it as a black
box.
From: Bitrex on 3 Apr 2010 03:51
miso(a)sushi.com wrote:
> On Apr 1, 11:23 am, Tim Wescott <t...(a)seemywebsite.now> wrote:
>> "Bitrex" <bit...(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 consultingwww.wescottdesign.com
>
> I think "signal flow graph" would get you a relevant google search.
> Next up is Mason's rules. My understanding is they haven't taught that
> stuff in EE courses since the late 80s, at least in any detail. I
> doubt anyone could make a leapfrog filter design these days since
> signal flow graph theory is just glossed over in colleges.
>
> Is the original poster over complicating the question? I mean, app a
> voltage source to the input and compute the current, then get the
> impedance. Who cares if the box has feedback. Think of it as a black
> box.

Thanks for your replies, everyone. Miso - I think your approach would be
fine if I were given the task of just analyzing a circuit that existed
out in the world someplace to discover its particular behavior. However,
if I actually want to design a circuit using such a topology, that
method doesn't give me much intuition as to what changing various
component values independently will do to the behavior of the circuit.

I've started reading up on Mason's rules and I think they might work
along with superposition in analyzing the behavior of this circuit. If
it has, for example, both current sampling current mixing and voltage
sampling voltage mixing feedback I could do the following: analyze the
amplifier as a current amplifier with current feedback with Mason's rule
to find the current gain, use that to find the voltage gain of the
amplifier with only the current feedback network, then use Mason's rule
again with that value of voltage gain and the voltage feedback network.
From: JosephKK on 3 Apr 2010 11:26
On Thu, 01 Apr 2010 19:05:35 -0400, Bitrex <bitrex(a)de.lete.earthlink.net> wrote:

>Jim Thompson wrote:
>> 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.
>
>The type of circuit I'm trying to analyze via this method is here:
>
>http://s227.photobucket.com/albums/dd240/bitrex2007/?action=view&current=Feedback.jpg
>
>(note there should be a DC blocking capacitor after R5).
>
>
>Basically I'm trying to calculate the voltage gain and voltage feedback
>ratio, and current gain and current feedback ratio independently using
>superposition and a cascaded hybrid-pi model of the two transistor
>circuit. I'm starting to conclude that it's pretty much an equivalent
>amount of math to using nodal or mesh analysis, with the downside that
>it can't be automated via computer! The only advantage I can see is that
>one could analyze the effects of the current feedback and voltage
>feedback paths independently, while an expression for the gain and input
>impedance using nodal analysis will be a huge expression with everything
>jumbled together, making it hard to know directly what changes in either
>feedback network will have on the parameters.
>
>>
>>> 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

I would approach it with a more primitive T model and a spreadsheet.
First calculate the operating point, it will give you nice clues to
the rest of the response. And finally hit it with LTspice, just to
compare.
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Next: Heat dissip. series vs. parallel