The open-loop gain of an amplifier is A = 5 × 104. If the open-loop gain decreases by 10 percent, the closed-loop gain must not change by more than 0.1 percent. Determine the required value of the feedback transfer function β and the closed-loop gain Af.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter12: Power System Controls
Section: Chapter Questions
Problem 12.3P
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The open-loop gain of an amplifier is A = 5 × 104. If the open-loop gain decreases by 10 percent, the closed-loop gain must not change by more than 0.1 percent. Determine the required value of the feedback transfer function β and the closed-loop gain Af.

 

Expert Solution
Step 1

If Af represents the closed-loop gain, then the change in the closed-loop gain can be represented by the following equation:
Electrical Engineering homework question answer, step 1, image 1

According to the given information, if the open-loop gain changes by 10 percent, then the closed-loop gain must nor change by more than 0.1 percent. 

Therefore, 

Electrical Engineering homework question answer, step 1, image 2

 

 

 

Step 2

Plugging the value of the open-loop gain into equation (2), the value of the feedback factor will be

Electrical Engineering homework question answer, step 2, image 1

Therefore, the value of the feedback factor will be

Electrical Engineering homework question answer, step 2, image 2

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