10.1 This problem deals with the series–shunt feedback amplifier of Fig. 1. The current-mirror loaded differential amplifier has a feedback network consisting of the voltage divider R1, R2, with R1 + R2 = 1 MΩ. The devices are sized to operate at |VOV|= 0.2 V. For all devices, |VA|= 10 V. The input signal source has a zero-dc component.
Figure 1
(a) Show that the feedback is negative.
(b) What do you expect the dc voltage at the gate of Q2 to be? At the output? (Neglect the Early effect.)
(c) Find the A circuit. Derive an expression for A and find its value.
(d) Select values for R1 and R2 to obtain a closed-loop voltage gain Vo/Vs = 5 V/V.
(e) Find the value of Rout.
(f) Utilizing the open-circuit, closed-loop gain (5 V/V) and the value of R out found in (e), find the value of gain obtained when a resistance RL = 10 k is connected to the output.
(g) As an alternative approach to (f) above, redo the analysis of the A circuit including RL. Then utilize the values of R1 and R2 found in (d) to determine β and Af . the value of Af to that found in (f).
10.2
Figure 2 shows a three-stage feedback amplifier:
Figure 2
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A1 has an 82-kΩ differential input resistance, a 20-V/V open-circuit differential voltage gain, and a 3.2-kΩ output resistance.
A2 has a 5-kΩ input resistance, a 20-mA/V short-circuit transconductance, and a 20-kΩ output resistance.
A3 has a 20-kΩ input resistance, unity open-circuit voltage gain, and a 1-kΩ output resistance. The feedback amplifier feeds a 1-kΩ load resistance and is fed by a signal source with a 9-kΩ resistance.
(a) Show that the feedback is negative.
(b) If R1 = 20 kΩ, find the value of R2 that results in a closed-loop gain Vo/Vs that is ideally 5 V/V.
(c) Supply the small-signal equivalent circuit. (d) Sketch the A circuit and determine A.
(e) Find β and the amount of feedback.
(f) Find the closed-loop gain Af ≡ Vo/Vs.
(g) Find the feedback amplifier’s input resistance Rin. (h) Find the feedback amplifier’s output resistance Rout.
(i) If the high-frequency response of the open-loop gain A is dominated by a pole at 100 Hz, what is the upper 3-dB frequency of the closed-loop gain?
(j) If for some reason A1 drops to half its nominal value, what is the percentage change in Af ?
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