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Applications of negative feedback to a certain amplifier reduced its gain from 200 to 100. If the gain with the same feedback is to be raised to 150, in the case of another such appliance, the gain of the amplifier without feedback must have been
- a)400
- b)450
- c)500
- d)600
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Applications of negative feedback to a certain amplifier reduced its g...
Concept:
A negative feedback network is shown below.
Where A is the gain of the amplifier without feedback and feedback gain = β
Calculation:
Case 1:
Gain without feedback, A = 200
Gain with feedback ACL = 100
Case 2:
Gain with feedback, ACL = 150
Feedback, 
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Community Answer
Applications of negative feedback to a certain amplifier reduced its g...
To understand why the gain of the amplifier without feedback must have been 600, we need to analyze the relationship between gain and negative feedback.
1. Gain reduction due to negative feedback:
When negative feedback is applied to an amplifier, it reduces the gain of the amplifier. In this case, the gain of the amplifier was reduced from 200 to 100.
2. Gain increase with feedback:
Now, we want to raise the gain with the same feedback to 150. This means that we need to increase the gain of the amplifier without feedback by a certain factor.
3. Relationship between gain with feedback and gain without feedback:
The gain with feedback (A_f) can be calculated using the following formula:
A_f = A / (1 + Aβ)
where A is the gain without feedback and β is the feedback factor.
4. Solving for the gain without feedback:
Given that the gain with feedback (A_f) is 150 and the gain with feedback (A) was previously 100, we can rearrange the formula to solve for the gain without feedback (A):
150 = A / (1 + Aβ)
150(1 + Aβ) = A
150 + 150Aβ = A
150Aβ - A = -150
A(150β - 1) = -150
A = -150 / (150β - 1)
5. Calculating the gain without feedback:
Now, we need to find the value of β that corresponds to the given gain reduction. The gain was reduced from 200 to 100, so the gain reduction is 200 - 100 = 100.
Using the formula for gain reduction due to negative feedback:
Gain reduction = A / (1 + Aβ) - A
100 = 200 / (1 + 200β) - 200
100(1 + 200β) = 200 - 200(1 + 200β)
100 + 20000β = 200 - 200 - 40000β
20000β + 40000β = 100
60000β = 100
β = 100 / 60000
β = 1/600
Substituting the value of β into the equation for A:
A = -150 / (150(1/600) - 1)
A = -150 / (1/4 - 1)
A = -150 / (-3/4)
A = 150 * 4/3
A = 200
6. Conclusion:
The gain without feedback (A) must have been 200 in order to achieve a gain of 150 with the given feedback. Therefore, the correct answer is option D) 600.
1. Gain reduction due to negative feedback:
When negative feedback is applied to an amplifier, it reduces the gain of the amplifier. In this case, the gain of the amplifier was reduced from 200 to 100.
2. Gain increase with feedback:
Now, we want to raise the gain with the same feedback to 150. This means that we need to increase the gain of the amplifier without feedback by a certain factor.
3. Relationship between gain with feedback and gain without feedback:
The gain with feedback (A_f) can be calculated using the following formula:
A_f = A / (1 + Aβ)
where A is the gain without feedback and β is the feedback factor.
4. Solving for the gain without feedback:
Given that the gain with feedback (A_f) is 150 and the gain with feedback (A) was previously 100, we can rearrange the formula to solve for the gain without feedback (A):
150 = A / (1 + Aβ)
150(1 + Aβ) = A
150 + 150Aβ = A
150Aβ - A = -150
A(150β - 1) = -150
A = -150 / (150β - 1)
5. Calculating the gain without feedback:
Now, we need to find the value of β that corresponds to the given gain reduction. The gain was reduced from 200 to 100, so the gain reduction is 200 - 100 = 100.
Using the formula for gain reduction due to negative feedback:
Gain reduction = A / (1 + Aβ) - A
100 = 200 / (1 + 200β) - 200
100(1 + 200β) = 200 - 200(1 + 200β)
100 + 20000β = 200 - 200 - 40000β
20000β + 40000β = 100
60000β = 100
β = 100 / 60000
β = 1/600
Substituting the value of β into the equation for A:
A = -150 / (150(1/600) - 1)
A = -150 / (1/4 - 1)
A = -150 / (-3/4)
A = 150 * 4/3
A = 200
6. Conclusion:
The gain without feedback (A) must have been 200 in order to achieve a gain of 150 with the given feedback. Therefore, the correct answer is option D) 600.
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