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 = 1 nf? (a) 65.25 khz (b) 10 khz (c) 1.59 khz (d) 10.4 khz 2. What is the time constant of the circuit? 3. Many BJT datasheets do not list ββ explicitly, but list an equivalent h-parameter instead. What is this parameter? 4. A single-pole op-amp has an open-loop gain of 100 db and a unity-gain bandwidth frequency of 2 MHz. What is the open-loop bandwidth of the op-amp? 5. An amplifier has a differential gain of -50,000 and a common-mode gain of 2. What is the common-mode rejection ratio? (a) 87.96 db (b) 44 db (c) -44 db (d) 87.96 db 1

6. For the following circuit, what is the numerical value for the two-port y-parameter y 12? 7. For the following circuit, what is the numerical value for the two-port h-parameter h 21? The definition of the h-parameters are shown.(2 points) v 1 = h 11 i 1 + h 12 v 2 i 2 = h 21 i 1 + h 22 v 2 8. Consider the following circuit, which is the power output stage of an amplifier. (a) What is the name of the shaded sub-circuit around Q 1? (b) Write down one sentence/phrase that describes the purpose of the sub-circuit and constant current source. 9. Explain what the difference is between the units ms and ms. 2

10. A single-pole op-amp has an open-loop gain of 100 db and a unity-gain bandwidth frequency 5 MHz. What is the open-loop bandwidth of the amplifier? The amplifier is used as a voltage follower. What is the bandwidth of the follower? 11. A constant gain-bandwidth amplifier has a 3-dB bandwidth of 1 MHz. By how much (μs) does it delay a 250-kHz sinusoidal signal? 12. A single-pole op-amp has an open-loop gain of 100 db and a unity-gain bandwidth frequency of 2 MHz. What is the open-loop bandwidth of the op-amp? 13. What is the impedance of a 0.1 μf capacitor at f = 1 khz? (a) j1.6 10 3 Ω (b) j10 10 3 Ω (c) +j1.6 10 3 Ω (d) 1.6 10 3 Ω (e) 10K 14. A MOSFET has rated power of 50 W at an ambient temperature T A = 25 o C and a maximum specified junction temperature of 105 o C. What is the thermal resistance between the device case and the junction? 15. A power MOSFET has rated power of 1,250 W at an ambient temperature T A = 25 o C and a maximum specified junction temperature of 175 o C. What is the thermal resistance between the junction and device case? 3

16. What is the maximum theoretical efficiency for a class-b amplifier? 17. What is the purpose of R 3 in the circuit below, and what should the value be to be effective? 18. Assume that your SPICE simulation software (such as Micro-Cap SPICE) do not have a photodiode part. Explain in 1 2 sentences how you can nevertheless simulate a photodiode. Question 2 A constant GBP op-amp has an open loop gain of 100 db, and a unity gain bandwidth of 5 MHz. The op-amp is used in a non-inverting configuration with a gain of 40 db. By how much (μs) does the amplifier delay a 10 khz sine wave? (6 points) 4

Question 3 Determine the h-parameters for the circuit below. (16 points) 5

Question 4 Determine the y-parameters for the circuit shown in (a). The model that defines the y-parameters is in (b). (16 points) (a) (b) 6

Question 5 Determine the y-parameters for the circuit shown in (a). The model that defines the y-parameters is in (b). (12 points) (a) (b) Solution 7

Question 6 You can assume that for all the transistors in the circuit below, ββ is large. Show that I 1 = 0.4 ma. Let v 1 = v 2 = 0 V and then determine V A, V B, V C, V D, V E, and v O. Assume V BE(ON) = 0.7 V for all the transistors. Further, note that R 3 is small: for the purposes on this hand-analysis, ignore its effect. That is, assume R 3 = 0. (14 Points) 8

Question 7 (diodes, load line) Consider the circuit below. Assume V PS = 3.5 V, and R = 180 Ω. Also shown, are the LED s voltage-current characteristics. Draw the circuit s dc load line on the characteristics and find I D and V D (6 points) 9

Question 8 R i = 30K R P = 10K C S = 10 μf C P = 50 pf (a) Determine the open-circuit constant associated with C S, and short-circuit time constant associated with C P (4 points) (b) Determine the corner frequencies and magnitude of the transfer function T(s) = V o (s) I i (s) at midband. (2 points) (c) Sketch the Bode magnitude plot and Bode phase plot of the voltage transfer function. Be sure to add the proper units. (4 points) 10

Question 9 Sketch the Bode magnitude plots of the following functions below. (12 points) T(s) = 10s (s + 20)(s + 2000) T(s) = 10(s + 10) (s + 100) 11

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Question 10 (a) Sketch the Bode magnitude plot of the following function. (6 points) T(s) = 10s (s + 10)(s + 500) (b) What is the midband gain? (2 points) (c) Is there a dominant pole? If so, what is the approximate pole frequency? (2 points) (d) What is the low 3 db frequency? (2 points) 13

Question 11 For the common-emitter amplifier below, the transistor parameters are ββ = 100, V BE(ON) = 0.7 V, and V A =. V CC = 12 V R C = 1 kω R 1 = 10 kω R 2 = 1.5 kω R E = 0.1 kω R S = 0.5 kω C C = 0.1 μf (a) Determine I CQ, g m and r π (8 points) (b) Calculate the lower corner frequency (6 points) (c) Determine the midband voltage gain (6 points) (d) Sketch the Bode plot of the voltage gain magnitude (6 points) 14

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Question 12 For the three-stage amplifier above, make an estimate of the bandwidth and the rise time. (6 points) Hint: note that the amplifiers do not load each other. 16

Question 13 For the circuit below ββ = 120, V BE(ON) = 0.7 V, and V A = (a) Design a bias-stable circuit such that I CQ = 1 ma. (b) Determine the output resistance R o. (c) What is the lower 3 db corner frequency? 17

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Question 14 For the amplifier below, ββ = 100, and a dc analysis reveals that I CQ = 0.838 ma. Estimate the 3-dB bandwidth. Assume that C c2 = 0.1 μf. (15 points) 19

Question 15 Consider the amplifier below. In the circuit, I Ph represents a photodetector. Ignore the MOFET s capacitances. (a) Classify the type of frequency response (high-pass or low-pass) the circuit has. (2 points) (b) Determine the 3-dB frequency. (5 points) 20

Question 16 The maximum transistor power is P D,max = 25 W. Design the circuit (i.e., determine R L and R B ) such that maximum power is delivered to the load. (8-points) 21

Question 17 Q 3, Q 4, R P2, R P4 below form a short circuit protection network for the amplifier. If R P3 = R P4 = 0.15 Ω, what is the maximum i o in case there is a short. That is, when R L = 0? (3 points) 22

Question 18 In the amplifier below, assume V BE(ON) = 0.6 V for all the transistors. (a) Show that the collector current of Q 3 is approximately 1.6 μa. (2 points) (b) Estimate the output resistance. (8 points) (c) Estimate the voltage gain V o V s. (2 points) (d) Find the quiescent, dc voltage at the output. (3 points) Hint: view the transistors as a composite transistor and use BJT impeadance scaling. ββ = 16 ββ = 63 ββ = 100 23

Question 19 The transistor in the amplifier shown has ββ = 350 and V BE(ON) = 0.65 V. Ignore the BJT capacitances. (a) Make reasonable assumptions and show that I CQ 1 ma (3 points) (b) Show that R i 13.7K (5 points) (c) Estimate the lower 3-dB frequency if C C = 1 μf (3 points) 24