Question 12.21: Objective: Determine the shift in the 3 dB frequency when an...
Objective: Determine the shift in the 3 dB frequency when an amplifier is operated in a closed-loop system.
Consider an amplifier with a low-frequency open-loop gain of A_{o} = 10^{6} and an open-loop 3 dB frequency of f_{P D} = 10 Hz. The feedback transfer ratio is β = 0.01.
The low-frequency closed-loop gain is
A_{f} (0) = \frac{A_{o}}{(1 + β A_{o})} = \frac{10^{6}}{1 + (0.01)(10^{6})} \cong 100
From Equation (12.124), the closed-loop 3dB frequency is
A_{f} ( f ) = \frac{A_{o}}{(1 + β A_{o})} × \frac{1}{1 + j \frac{f}{f_{P D}(1 + β A_{o})}} (12.124)
f_{C} = f_{P D}(1 + β A_{o}) = (10)[1 + (0.01)(10^{6})]
or
f_{C} \cong 10^{5} Hz = 100 kHz
Comment: Even though the open-loop 3 dB frequency is only 10 Hz, the closedloop bandwidth is extended to 100 kHz. This effect is due to the fact that the gain–bandwidth product is a constant