A voltage amplifier with an open loop gain problem

[spark8217]

can anybody explain how to solve the following please
A voltage amplifier with an open loop gain of 10^4 has applied to it in turn 1% negative feedback and 5% negative feedback .
For each case calculate the effect on:
Gain magnitude
Gain stability if Av varies by ± 6%
Bandwidth assuming B(Av) =40KHz
Signal to noise ratio with feedback if S/N=20dB.

many thanks
spark8217

 

[ericgibbs]

hi spark,

Have you sketched out the circuit for a voltage amplifier, [use the conventional OPA symbol] showing the Rin and Rfeedback resistors that fix the closed loop gain.??

E

 

[MrAl]

Hi,

An equation which describes your output is:
Vout=Vin/(p+1/Av)

and you can simplify this to:
Vout=1/(p+1/Av)

where p is the percent of feedback expressed as a fraction, and Av is the voltage gain of the amplifier.

The gain is simply Vout/Vin.

So for example for an Av gain of 10000 and percent feedback equal to 1 percent we have:

Av=10000
p=0.01

Using the simplified equation above we get:
Vout=99.009900990099

and so the gain is:
99/1=99 approximately.

You can then go back and vary the Av internal gain by 6 percent and calculate again to see what happens.

The bandwidth is considered to be the open loop bandwidth divided by the gain.

 

[spark8217]

Hi
Thank you for taking the time to explain and your help ericgibbs & MrAl , i shall proceed and try to solve the question.

 

[MrAl]

Hi again,


Eric you beat my to the first reply by 2 minutes

spark:
You are welcome, and good luck with finding the result. As Eric suggested, you can also post your circuit so we can take a look, if that is possible.

 

[spark8217]

Thanks
In erics post he refers to [use the conventional OPA symbol] i am not familiar with the term can you please expand on this ? as the question set to me was just a simple amplifier are you referring to a op amp ?

Thanks
spark8217

 

[ericgibbs]

Thanks
In erics post he refers to [use the conventional OPA symbol] i am not familiar with the term can you please expand on this ? as the question set to me was just a simple amplifier are you referring to a op amp ?

Thanks
spark8217

Hi,
Look at this image.

Consider the ratio of Rin and Rfb for your percentage feedback relative to the -terminal of the OPA

E

 

[spark8217]

Thank you thats a big help eric !
cheers
spark8217

 

[Winterstone]

Thank you thats a big help eric !
cheers
spark8217

Hi spark8217,

just a short remark:
* Eric forgot to show the input (otherwise no gain can be given)
* Eric forgot to connect the neg. power node to a (negative) voltage source (rather than to ground the node). For single supply operation the circuit needs some specific provisions for correct biasing.

 

[ericgibbs]

Hi spark8217,

just a short remark:
* Eric forgot to show the input (otherwise no gain can be given)
* Eric forgot to connect the neg. power node to a (negative) voltage source (rather than to ground the node). For single supply operation the circuit needs some specific provisions for correct biasing.

I did NOT forget to show any input signal.. I just posted the OPA symbol.............

I did NOT forget the +Vin voltage,,, I just posted the OPA symbol.

The OP did not ask for an OPA design just the symbol, for goodness sake, read the posts!

 

[Winterstone]

I did NOT forget to show any input signal.. I just posted the OPA symbol.............
I did NOT forget the +Vin voltage,,, I just posted the OPA symbol.
The OP did not ask for an OPA design just the symbol, for goodness sake, read the posts!

Eric - excuse me for giving a comment to your post.

I`ve got the impression that the subject of this thread is "voltage amplifier..."
More than that, on my screen I can see not only a symbol but an amplifier - consisting of a feedback network and showing one single power supply.
More than that, a gain formula is given.

I am still of the opinion - in spite of your "sensitive" reaction - that we all should try to help the questioner as much as possible (and to avoid misinterpretations or misunderstandings caused by incomplete information).

To spark8217:
The circuit and the gain formula as given by eric is an inverting amplifier (input signal at Rin).
However, the simple gain formula belongs to an idealized operational amplifier (gain infinite) - in contrast to your case with an open-loop gain of 1E4.
In this case, you must use the formula as given by MrAl in post#3.

But I have an additional question to you regarding the given frequency properties of the amplifier: B= 40 kHz.
I assume this is the 3dB bandwidth (correct?).
However, in this case it is important to know the frequency of the signal to be amplified. Otherwise, the information on bandwidth is useless.

Winterstone

 

[ericgibbs]

hi W,
How can you say my symbol post was a possible cause of (misinterpretations or misunderstandings caused by incomplete information).??

Are you saying the simplified formula for Gain = Rfb/Rin is invalid in the OPA symbol I have drawn.??

Surely even though there is no input signal, the OPA symbol as posted, will still have an inherent gain which is determined by Rfb/Rin.??

Regarding 0V on the OPA's Vee terminal, how do you know that the OP is not going amplify DC levels above the 0V ground or perhaps a AC signal superimposed upon a DC offset level.??

You will note I have not included in my symbol any reference to an input signal, thats because I do not what it is.!

So how would I know what the OPA biassing arrangement would have to be.??

The level of detail in my answers to an OP posts are based simply on the question being asked, if the OP wants a more in depth explanation I will answer in greater detail.

I see little purpose in filling a reply post with information the OP has not requested.

If you choose to answer a post in greater detail , thats your choice, but I do not think it appropriate to suggest that answers that other members have given are open to,
(misinterpretations or misunderstandings caused by incomplete information).??

E.

 

[Winterstone]

hi W,
How can you say my symbol post was a possible cause of (misinterpretations or misunderstandings caused by incomplete information).??

Well, spark8217 is an absolute beginner.
When you present a circuit diagram and a gain formula without indicating the signal input node (one out of two alternatives) and without a correct power supply I am afraid this can cause some misunderstandings, don`t you think so? It does not matter if your main intention was to show the symbol only. A symbol as part of an incomplete and not working circuit diagram is not the best way to help a newcomer.
Was I wrong with my comments?
Am I not allowed to complete some information that you give?

Are you saying the simplified formula for Gain = Rfb/Rin is invalid in the OPA symbol I have drawn.??
Surely even though there is no input signal, the OPA symbol as posted, will still have an inherent gain which is determined by Rfb/Rin.??
E.

Yes - that`s what I am saying. The symbol does not contain any information about the open-loop gain.
Remember: The questioner speaks about Aol=1E4 - and that is the reason he should use the complete formula as given by MrAl in post#3 (and not the approximation, valid for very large Aol) - in particular because he has a specification that is expressed in % of feedback!.

What do you mean with "the OPA symbol...inherent gain which is determined by Rfb/Rin"?
This sounds very confusing. The symbol is associated with an "inherent" gain which is called "open-loop" gain Aol. In the present case: Aol=1E4.
Only for very large values for Aol (1E5...1E6) the total gain of the amplifier with feedback can be given as -Rfb/Rin. These are basics!

Regarding 0V on the OPA's Vee terminal, how do you know that the OP is not going amplify DC levels above the 0V ground or perhaps a AC signal superimposed upon a DC offset level.??
You will note I have not included in my symbol any reference to an input signal, thats because I do not what it is.!
So how would I know what the OPA biassing arrangement would have to be.??

Eric - is this really your position? When a newcomer is asking a simple question about opamps I would at first refer to the basic inverting or non-inverting configuration, which does not require any additional considerations regarding dc offset and/or biasing circuitry. Why do you argue in such a way?

hi W,
The level of detail in my answers to an OP posts are based simply on the question being asked, if the OP wants a more in depth explanation I will answer in greater detail.
I see little purpose in filling a reply post with information the OP has not requested.
E.

I didn`t criticize not at all the "level of detail" in your answer. I just have given some additional information to the questioner - important for application of such a circuit.
Was there any error in my comments?
It is really surprising that you react in such a sensitive way.
Perhaps you have overlooked that the start of this thread was not only a question about the symbol of an opamp.
The questioner has formulated some specific questions about amplifiers, feedback, sensitivity,...

hi W,
If you choose to answer a post in greater detail , thats your choice, but I do not think it appropriate to suggest that answers that other members have given are open to,
(misinterpretations or misunderstandings caused by incomplete information).??
E.

Perhaps you remember: My first comment was only "Eric forgot to mention..." (not very unpolite).
And it was only later - as reply to your "outcry: "for goodness sake, read the posts.." - that I gave my justification for this first comment (misinterpretation, incomplete information)
However, was anything wrong from the technical viewpoint?
My only intention was and is to provide the questioners with some helpful information. I am sure that this is also your aim - even if my answer is more detailed as you consider as appropriate.

Regards
W.

 

[ericgibbs]

hi W,

Forgive me, but I really don't have time to waste on these pointless' tit for tat' discussions.

You answer OP's questions the way you see fit and I will do the same.

The OP was satisfied with my replies, thats good enough for me, they are not written to meet any criteria set by you.

E.

 

[Winterstone]

hi W,
Forgive me, but I really don't have time to waste on these pointless' tit for tat' discussions.

Yes, I`ll forgive you.
And I kindly ask you to forgive me trying to complete one of your explanations.
And - the readers of this thread may decide if I have tried to set new criteria (as you think) or if it was only an attempt from my side to give the questioner some additional technical hints.

With kind regards
W.

 

[RichTheDude]

Hi spark8217,

* Eric forgot to show the input (otherwise no gain can be given)

Since when did gain become input dependent?

 

[Winterstone]

Since when did gain become input dependent?

Of course it is - in case there are two possible inputs with two different gain values.
Don`t forget - the initial question came from a beginner who even did not know the symbol for an opamp.

By the way: I have detected another error in post#7. However, perhaps the questioner doesn`t care about it, because he didn`t react upon my question regarding the frequency properties.