What is the Frequency for Unity Loop Gain in Low-Pass Amplifier with Feedback?

[roam]

Homework Statement

I need some help with the following problem (it is from an old test paper).

Below is the Bode plot of the open loop gain of an amplifier:

A constant fraction β=0.1 of the output is fed back to the input. This feedback does not load the amplifier.

Using the Bode plot determine the frequency for which the magnitude of the loop gain of this circuit is equal to unity.

The Attempt at a Solution

Clearly looking at the first graph $|A|_{dB} = 1$ at around $1500 \ Hz$. I've marked this with a pen on the graph. But my answer was marked as incorrect. Why is that?

Clearly the graph touches 1 dB roughly at $f = 1500 \ Hz$. So why is my answer wrong?

Any help is greatly appreciated.

P.S. The value of the amplifier's closed loop gain at DC was calculated to be -9.1.

 

[NascentOxygen]

If loop gain is defined as A.β
and you are told β=0.1, then you are looking for f where A=10

(I like to write this as 10 volts/volt, whatever, as a reminder it is not 10 dB)

So, how many dB gain are you looking for?

NOTE: 'loop gain' is quite different to 'closed loop gain'. Can you distinguish the difference?

 

[roam]

Thank you so much for your response.

So, in decibel it is $|A|_{dB}=20 \ log_{10} 10 = 20 \ dB$, therefore the frequency would be @ f=500 Hz. Is that right??

Yes, I distinguish the difference, loop gain is Aβ whereas closed loop gain is $A(s)/1-A(s) \beta (s)$.

 

[NascentOxygen]

Thank you so much for your response.

So, in decibel it is $|A|_{dB}=20 \ log_{10} 10 = 20 \ dB$, therefore the frequency would be @ f=500 Hz. Is that right??

That should be right.

Yes, I distinguish the difference, loop gain is Aβ whereas closed loop gain is $A(s)/1-A(s) \beta (s)$.

I would mark that last expression wrong, because it is missing an essential set of parentheses.

 

[roam]

I meant $A(s)/[1-A(s) \beta (s)]$. Thank you very much.