Objective: Determine the dominant pole required to stabilize a feedback system. Consider a three-pole feedback amplifier with a loop gain given by $T (f) = \frac{1000}{\left(1 + j \frac{f}{10^{4}}\right) \left(1 + j \frac{f}{10^{6}}\right) \left(1 + j \frac{f}{10^{8}}\right)}$

Insert a dominant pole, assuming the original poles do not change, such that the phase margin is at least 45 degrees.

Question

Objective: Determine the dominant pole required to stabilize a feedback system. Consider a three-pole feedback amplifier with a loop gain given by $T (f) = \frac{1000}{\left(1 + j \frac{f}{10^{4}}\right) \left(1 + j \frac{f}{10^{6}}\right) \left(1 + j \frac{f}{10^{8}}\right)}$

Insert a dominant pole, assuming the original poles do not change, such that the phase margin is at least 45 degrees.

Accepted Answer

By inserting a dominant pole, we change the loop gain function to
[latex]T_{P D}( f ) = \frac{1000}{\left(1 + j \frac{f}{f_{PD}}\right)\left(1 + j \frac{f}{10^{4}}\right) \left(1 + j \frac{f}{10^{6}}\right) \left(1 + j \frac{f}{10^{8}}\right)}[/latex]

We assume that [latex]f_{P D} \ll 10^{4} Hz[/latex]. A phase of −135 degrees, giving a phase margin of 45 degrees, occurs approximately at [latex]f_{135} = 10^{4} Hz[/latex].
Since we want the loop gain magnitude to be unity at this frequency, we have
[latex]|T_{P D}(f_{135})| = 1 = \frac{1000}{\sqrt{1 + \left(\frac{10^{4}}{f_{P D}} \right)^{2}} \sqrt{1 + \left(\frac{10^{4}}{10^{4}} \right)^{2}} \sqrt{1 + \left(\frac{10^{4}}{10^{6}} \right)^{2}} \sqrt{1 + \left(\frac{10^{4}}{10^{8}} \right)^{2}}}[/latex]
or
[latex]1 = \frac{1000}{\sqrt{1 + \left(\frac{10^{4}}{f_{P D}}\right)^{2}} (1.414)(1)(1)}[/latex]
Solving for the dominant pole frequency [latex]f_{P D}[/latex], we find
[latex]f_{P D} = 14.14 Hz[/latex]
Comment: With high-gain amplifiers, the dominant pole must be at a very low frequency to ensure stability of the feedback circuit.

Question 12.20: Objective: Determine the dominant pole required to stabilize...

Related Answered Questions

Verified Answer:

Verified Answer:

Verified Answer:

Verified Answer:

Objective: Determine the effect of feedback on the source signal and noise signal levels. Consider the four possible amplifier configurations shown in Figure 12.3. The amplifiers are designed to provide the same output signal voltage. Determine the effect of the noise signal vn . ...

Verified Answer:

Objective: Calculate the feedback transfer function β, given A and Af. Case A. Assume that the open-loop gain of a system is A = 10^5 and the closed-loop gain is Af = 50 Case B. Now assume that the open-loop gain is A = −10^5 and the close-loop gain is Af = −50. ...

Verified Answer:

Verified Answer:

Objective: Determine the pole of the gain stage that includes a feedback capacitor. Consider a gain stage with an amplification A = 10³ , a feedback capacitor CF = 30 pF, and a resistance R2 = 5 × 10^5 Ω. ...

Verified Answer:

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 Ao = 10^6 and an open-loop 3 dB frequency of fP D = 10 Hz. The feedback transfer ratio is β = 0.01. ...

Verified Answer:

Verified Answer: