An amplifier has open-loop voltage gain of 40. 10 % of negative feedback is effected. What will be the gain with feedback ?
8
Substitute directly into the negative-feedback formula.
\(A_{f}=\dfrac{A}{1+A\beta}\)
with \(A=40\) and \(\beta=0.1\):
\(A\beta=40\times0.1=4\)
\(A_{f}=\dfrac{40}{1+4}=\dfrac{40}{5}=8\)
— option 4.
Reading the numbers. "10 % of negative feedback" means one tenth of the output is returned to the input in opposition, so \(\beta=0.1\). The quantity \(A\beta=4\) is the loop gain, and \(1+A\beta=5\) is the amount of feedback or desensitivity factor — the factor by which everything about the amplifier is improved, and by which the gain is reduced.
| Property | Effect of the feedback | Here |
|---|---|---|
| Gain | Divided by 1 + Aβ | 40 → 8 |
| Gain stability | Improved by 1 + Aβ | 5× steadier |
| Bandwidth | Multiplied by 1 + Aβ | 5× wider |
| Distortion | Divided by 1 + Aβ | 5× lower |
| Input impedance (series) | Multiplied by 1 + Aβ | 5× higher |
| Output impedance (voltage) | Divided by 1 + Aβ | 5× lower |
What the trade buys. Gain is the one thing given up, and it is the cheapest thing to give up because more stages can always supply it. Everything else improves by the same factor of 5. The stability improvement is the most valuable:
\(\dfrac{dA_{f}}{A_{f}}=\dfrac{1}{1+A\beta}\dfrac{dA}{A}\)
so a 20 % change in the open-loop gain — from temperature, ageing, or device spread — becomes a 4 % change in the closed-loop gain here.
The limiting case is worth noting: when \(A\beta\gg1\), the formula collapses to \(A_{f}\approx1/\beta\) — the gain depends only on the feedback network, and not on the amplifier at all. That is why an op-amp circuit's gain is set purely by two resistors. With \(A\beta=4\) the approximation would give 10 against the true 8, so this amplifier is not yet deep enough into feedback for it to hold.
Hence, the gain with feedback is 8.
Similar Questions
Match the following lists :
List – I List – II a. Voltage series feedback i. Trans resistance amplifier b. Current series feedback ii. Current shunt feedback c. Current amplifier iii. Trans-conductance d. Voltage shunt feedback iv. Voltage amplifier Codes :
Match the following :
List – I List – II a. voltage shunt negative feedback i. increase of CMRR b. constant current source differential amplifier ii. O/P voltage attenuated by a factor 1/29 c. Phase shift oscillator iii. FSK decoder d. PLL iv. decrease of O/P impedance Codes :
Negative feedback in amplifier results in
1. reduced voltage gain
2. reduced bandwidth
3. increased S/N ratio
4. reduced distortionMatch List - I with List - II.
List - I (Feedback connection type) List - II (Input/output impedance) (A) Voltage series feedback (I) \(Z_{of}=\dfrac{Z_{o}}{1+\beta A}\) (B) Voltage shunt feedback (II) \(Z_{of}=Z_{o}\left(1+\beta A\right)\) (C) Current series feedback (III) \(Z_{if}=\dfrac{Z_{i}}{1+\beta A}\) (D) Current shunt feedback (IV) \(Z_{if}=Z_{i}\left(1+\beta A\right)\) Choose the correct answer from the options given below :
Negative Feedback in amplifiers :
(a) improves signal to noise ratio at the output
(b) increases distortion
(c) reduces input offset voltage
(d) increases bandwidth
Options :
Read the following statements :
(a) Whatever the mode of feedback be, the gain after negative feedback is \(\dfrac{A}{1+A\beta}\)
(b) A negative feedback reduces the bandwidth of the amplifier.
(c) A negative feedback increases the output impedance
(d) A negative feedback enhances the stability of operationWhich of the above statements are correct ?
Given below are two statements :
Statement I : For negative feedback systems, the open loop gain decreases by a certain factor.
Statement II : Negative feedback systems are better in terms of system stability
In the light of the above statements, choose the correct answer from the options given below :
Important Questions from Feedback Amplifier
Arrange the following amplifiers in the order of maximum achievable -3dB frequency. Assume the transconductance ($g_m$) of the driver transistor (M1) same in all the circuits.
Choose the correct answer from the options given below:
Arrange the following amplifiers in the order of maximum achievable voltage gain. Assume the geometry and overdrive voltage is same for the transistor M1 in all the circuits and $R_D < <r_{o1}$.
choose the correct answer from the options given below:
The voltage gain of a certain amplifier without feedback is 10. With feedback its voltage gain reduces to 5. Determine its feedback factor.
Match the following lists :
List – I List – II a. Voltage series feedback i. Trans resistance amplifier b. Current series feedback ii. Current shunt feedback c. Current amplifier iii. Trans-conductance d. Voltage shunt feedback iv. Voltage amplifier Codes :
Match the following :
List – I List – II a. voltage shunt negative feedback i. increase of CMRR b. constant current source differential amplifier ii. O/P voltage attenuated by a factor 1/29 c. Phase shift oscillator iii. FSK decoder d. PLL iv. decrease of O/P impedance Codes :
