An amplifier of gain 1000 is made into a feedback amplifier by feeding 9.9% of its output voltage in series with the input opposing. If fl = 20Hz and fh= 200kHz for the amplifier without feedback then due to the feedback what is the new frequency (in kHz)?Correct answer is '20000'. Can you explain this answer?

Question

Answer

Introduction:
In a feedback amplifier, a portion of the output voltage is fed back to the input in a manner that opposes the input signal. This is done to stabilize the amplifier's gain and other characteristics. In this particular case, an amplifier with a gain of 1000 is converted into a feedback amplifier by feeding 9.9% of its output voltage in series with the input signal.

Given Information:
- Amplifier gain without feedback (A) = 1000
- Feedback fraction (β) = 9.9% = 0.099
- Lower cutoff frequency (fl) = 20Hz
- Upper cutoff frequency (fh) = 200kHz

Determination of New Frequency:
The introduction of feedback affects the overall frequency response of the amplifier. To determine the new frequency, we need to consider the effect of feedback on the amplifier's bandwidth.

Effect of Feedback on Bandwidth:
Feedback reduces the bandwidth of the amplifier by a factor of (1 + Aβ). The bandwidth with feedback (Bf) can be calculated using the formula:

Bf = B / (1 + Aβ)

Where B is the bandwidth without feedback.

Calculation of New Frequency:
In this case, the upper cutoff frequency without feedback (fh) is given as 200kHz. Let's assume the new frequency with feedback is f'.

Using the formula for bandwidth with feedback, we can write:

Bf = fh - fl

Substituting the given values:

fh - fl = (fh' - fl) / (1 + Aβ)

Since the lower cutoff frequency (fl) remains the same, we can simplify the equation:

fh - fl = fh' / (1 + Aβ)

Rearranging the equation:

fh' = (fh - fl) * (1 + Aβ)

Substituting the given values:

fh' = (200kHz - 20Hz) * (1 + 1000 * 0.099)

Calculating the expression:

fh' = 198kHz * 100.99

fh' ≈ 19800kHz

Converting kHz to Hz:

fh' ≈ 19800 * 1000Hz

fh' ≈ 19800000Hz

Therefore, the new frequency with feedback is approximately 19800000Hz, which is equivalent to 19800kHz or 20000kHz when rounded to the nearest kilohertz.

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