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Asymptotic principle on feedback amplifiers

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CAMALEAO

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Hi all,

I heard about the asymptotic principle on feedback amplifiers in a YouTube video for the first time and I would like to know if someone else has also heard about to help me understand one thing.

The person who is talking about this, a professor I think, said the following for a simple opamp with the negative terminal connected to the output through a resistor and the positive terminal connected to a 1V battery:

To have a finite output voltage with an infinite gain the input voltage difference has to be zero.

And then he mention that this is the asymptotic principle of feedback amplifiers.

Does this make any sense? How come this?

BR.
 

The full term used in the lecture is "asymptotic equality principle". Asymptotic equality is a mathematic term, I don't recognize it as commonly understood term in circuit analysis because it's not used in popular text books.

I believe the meaning is similar to the more popular terms "virtual ground" or "virtual short".
 

Yes, but it is funny that he uses it to derive all the equations in several types of amplifiers not only the opamp one, without using the traditional method of analysing feedback amplifiers.

I have found a couple of papers on this but they don't mention this thing that I have described above.

I will probably email the teacher to ask him.

Thanks.
 

without using the traditional method of analysing feedback amplifiers
I don't agree. What I've seen in a cursory review of the lecture seems quit similar to usual analysis with ideal OP. Not surprising, the analysis ends up with the same transfer function.
 

Take a look a the others. When he is analysing cascade amplifiers with feedback using BJTs or MOSFETs. It is very interesting. I have never heard about it and it looks much simpler. The only problem that I have is understand how the heck he can make the statement I replicated above. BTW I have forgotten to add that he adds a K that tends to infinite to do the analisis.
So basically it is something like:

As the constant K goes to infinite, (k*Av*Vin), to maintaining a finite output voltage Vin has to be/go to zero. I simply don't get this.
 

As the constant K goes to infinite, (k*Av*Vin), to maintaining a finite output voltage Vin has to be/go to zero. I simply don't get this.

Do you agree that - formally (mathematically) spoken - a finite and fixed and stable output voltage at the output node of an IDEAL opamp (infinite open-loop gain) with negative feedback requires an input voltage between the opamps input terminals that tends to be zero? Note, I spoke about the voltage between the opamps input nodes - and NOT about the signal input!
(The product of zero and infinite may be a constant)
 

Why it tends to zero?

I could have placed v+ to 1V.
 

If the amplifier output voltage range and feedback network allows, v- will follow the input voltage so that the differential input voltage becomes zero, or more exactly Vout/Av.
 

I see the point. Basically if you imagine that Av is increasing, Vin = Vp - Vn is decreasing and it will reach zero at some point. Basically we can't look at the expression k*Av*Vin in a literal way I mean, as it looks, we have to look at it conceptually. By increasing K you are seeing what will happen to the circuit in the limit.

So you increase K, Vin decreases, you increase K again and Vin will decrease further till Vin is zero and this will oblige the opamp to have a finite voltage at the output.

I think it is this? Is this thinking correct?

Now when it comes to simple cascade amplifiers the thing are no so obvious. I will try to post a sketch and the comments from that professor.

But basically the Vgs of the dependent source you have chosen is going to be zero.
 

Hi All,

Here it goes:

circuit.png

Basically, he applies the same concept of asymptotic equality and says something like this:

Asymptotic equality says that to get a finite output voltage with K equals infinite, V_pi ha tobe zero, meaning that the current I_pi is zero, which means that the current I_R2 has to the same as I_in - asymptotically.

Then you get V_out = -R2 * I_in -> H_infinity = V_out / V_in when K = infinity is -R2.

Now the BIG doubt here is how come V_pi equals zero?

Do you get the point? The OPAMP we can understand OK taking into account that we are already familiar with the virtual ground concept. What about this example? And he has got some other examples where he put the voltage on the controlled current source equal to zero. WTF?
 

The calculation scheme is correct, but of course you know that the gain of a single transistor stage is far from reaching infinity. In so far it's more appropriate to calculate circuit voltages and currents for actual transistor gain instead of assuming infinity.

The virtual ground concept can be still good for a first estimation of circuit parameters.
 

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