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

• roam
In summary, the conversation discusses the process of determining the frequency for which the magnitude of the loop gain of an amplifier is equal to unity. The Bode plot of the open loop gain is used, along with the value of the amplifier's closed loop gain at DC, to calculate the frequency. The difference between loop gain and closed loop gain is also mentioned.
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.

#### Attachments

• 2014-04-07 20.27.07.jpg
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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?

1 person
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)##.

roam said:
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.

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

## What is a Low-Pass Amplifier Bode Plot?

A Low-Pass Amplifier Bode Plot is a graph that shows the frequency response of a low-pass filter. It represents the relationship between the input frequency and the output voltage of the amplifier.

## Why is a Low-Pass Amplifier Bode Plot important?

A Low-Pass Amplifier Bode Plot is important because it allows us to analyze the performance of a low-pass filter and determine its cutoff frequency. It also helps in understanding the filter's ability to pass low-frequency signals while blocking high-frequency signals.

## What information can be obtained from a Low-Pass Amplifier Bode Plot?

A Low-Pass Amplifier Bode Plot provides information about the gain and phase response of the amplifier, as well as the cutoff frequency and bandwidth. It also shows the filter's roll-off rate and its ability to attenuate high-frequency signals.

## How is a Low-Pass Amplifier Bode Plot calculated?

A Low-Pass Amplifier Bode Plot can be calculated by plotting the magnitude and phase of the amplifier's transfer function against the input frequency on a logarithmic scale. The transfer function is determined by the amplifier's circuit components and their values.

## What are the applications of a Low-Pass Amplifier Bode Plot?

A Low-Pass Amplifier Bode Plot is commonly used in the design and analysis of electronic filters, audio amplifiers, and communication systems. It is also useful in understanding the behavior of active and passive filters, and in troubleshooting circuit performance issues.

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