Homework Assignment 12

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1 Homework Assignment 12 Question 1 Shown the is Bode plot of the magnitude of the gain transfer function of a constant GBP amplifier. By how much will the amplifier delay a sine wave with the following frequencies? (10 points) (a) 500 Hz (b) 5 khz (c) 10 khz (d) 50 khz (e) 500 khz 1

2 Question 2 In the circuit, R = 10K. What should C be so that the circuit delays a 5-kHz signal by 5 μs? (6 points) 2

3 Question 3 Consider an inverting amplifier with voltage gain A V = 100. The amplifier is driven by a sensor with an internal resistance R S = 10K. The amplifier s input resistance is very large and may be ignored. The stray capacitance between the amplifier output and input terminals is C F = 10 pf. A voltage step is applied to the input. What is the rise time of the output voltage? (8 points) Hint: use Miller capacitance concepts to determine an equivalent Miller capacitance and determine the amplifier bandwidth. 3

4 Question 4 R 1 = 200 kω R 2 = 220 kω R C = 2.2 kω R E = 1 kω r s = 100 kω V CC = 5 V R L = 4.7 kω β o = 100 C μ = 2 pf C π = 10 pf V A = V BE(ON) = 0.7 V The coupling capacitors and bypass capacitors are large and may be treated as shorts. (a) Show that I B = 9.3 μa. Note that you cannot assume I B = 0 (4 points) (b) Determine the numerical values for g m and r π (4 points) (c) Draw a detailed small-signal model for the amplifier showing the numerical values of the components. Be sure to include C μ and C π (6 points) (d) Determine the 3-dB frequency for the amplifier (4 points) 4

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6 Question 5 Below is the small-signal model of a BJT amplifier. Determine the so-called Miller capacitance C M,and draw an equivalent small-signal circuit that incorporates C M. Next, determine the circuit time constant and the 3-dB frequency. Finally, does this amplifier have a high-pass or low-pass response? (15 points) 6

7 Question 6 Below is a small-signal model of a BJT amplifier. Determine the so-called Miller capacitance C M, and draw an equivalent small-signal circuit that incorporates C M. Next, determine the circuit time constant, 3-dB frequency, and the midband gain. Finally, does this amplifier have a high-pass or low-pass response? (15 points) R L = 2 K g m = 0.04 A V r π = 5 K R S = 5 K C π = 10 pf C μ = 2 pf 7

8 Question 7 Consider the amplifier below, which amplifies the signal from a sensor with an internal resistance of 1K. Ignore BJT s output resistance, and assume C 1 = C 2 = C 3. β = 100 I C = ma (a) Determine g m, r π (4 points) (b) Using BJT scaling, determine R i see figure (4 points) (c) Using the ratio of the collector and emitter resistors, estimate the overall voltage gain A v = v o v s (4 points) (d) Calculate the voltage gain A v = v o v s, but do not use the approximation that involves the ratio of the collector and emitter resistors, but rather incorporate the β of the transistor (4 points) 8

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10 Question 8 Consider the CE BJT amplifier below. I C = 1 ma β = 185 C π = 100 pf C μ = 14 pf V A C C1 C C2 C C3 (a) Draw a hybrid-π small signal model of the amplifier. Be sure to include C π, C μ, and g m. (8 points) (b) Show that r π = 4.5 kω. (2 points) (c) Estimate the upper 3 db bandwidth. (12 points) 10

11 Question 9 An amplifier is designed to provide a 12 V peak-to-peak swing across a 4 Ω load. Assume sinusoidal signals. (a) Assuming the amplifier has output resistance R o 0 Ω, how much power will the load dissipate? (3 points) (b) Assuming the amplifier has output resistance R o = 0.4 Ω, how much power will the load dissipate? (3 points) 11

12 Question 10 An amplifier has an input resistance R i = 1K, and has a voltage gain of A v = 100 when driven from a signal with internal resistance R s 0. The amplifier is used to amplify a v s = 1 mv signal from a sensor that has an internal resistance of R s 20K. What is the output amplitude? (5 points) Question 11 The parameters for the transistor below are K n = 0.5 ma/v 2, V TN = 1.2 V, and λ = 0. Determine v DS and v GS for I Q = 1 ma. (6 points) 12

13 Question 12 Consider the following circuit, which is a simplifier schematic of an IC audio amplifier. Indicate, by circling and labeling as many of the following sub-circuits you can find: composite pnp transistor, current mirror, class AB output, Darlington pairs. (10 points) 13

14 Question 13 For (a) show that the transfer function is T(s) = v o(s) v i (s) = R 2 R 2 + R 1 (1 + sr 1 C 1 ) 1 + s(r 1 R 2 )C 1 (6 points) Determine the circuit s two time constants (2 points). Sketch the Bode magnitude plot (5 points) and Bode phase plot of T(s) (5 points) For (b), determine the circuit time constant and then ketch the Bode magnitude plot (5 points) and Bode phase plot of T(s) = v o (s) v i (s). (5 points) 14

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16 Question 14 β (pnp) = 10, β npn = 50 For the circuit above, make reasonable assumptions and then (a) Show that r π1 ~ 156 kω (4 points) (b) Use BJT impedance scaling and give a reasonable estimate for the output resistance R O (4 points) 16

17 Question 15 (Final Exam, 2006) In the following circuit, the three transistors are matched and in the same thermal environment. Determine the values for R R and R M to produce an output current of 0.4 ma. You may ignore base currents and make reasonable assumptions about V BE. (5 points) 17

18 Question 16 Consider the MOSFET amplifier below. Draw the small-signal model, incorporating r o. (5 points) Determine the voltage gain v o v i (8 points) and the output resistance R O (8 points). K n = 1 ma V V TN = 1.2 V λ = 0.01 V 1 I DQ = 1 ma 18

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20 Question 17 For the amplifier below, R L = 500 Ω. Determine, R ib, R o and the small-signal voltage gain A v = v o v i. (15 points) R S = 10K V + = 3 V V = 3 V I Q = 2 ma β = 100 V A = 100 V C C 20

21 Question 18 (N EX 7.14) β = 125, C μ = 3 pf, C π = 24 pf, V A = 200, V BE(ON) = 0.7 V A dc analysis shows that I CQ = 0.84 ma. (a) Draw a detailed small-signal model of the amplifier showing the numerical values of the components. (6 points) (b) Calculate the Miller capacitance. (3 points) (c) Determine the upper 3-dB frequency. (3 points) (d) Determine the small-signal mid-band voltage gain. (4 points) 21

Homework Assignment 11

Homework Assignment 11 Question 1 (Short Takes) Two points each unless otherwise indicated. 1. What is the 3-dB bandwidth of the amplifier shown below if r π = 2.5K, r o = 100K, g m = 40 ms, and C L =