Homework Assignment 11 - University of Iowas-iihr64.iihr.uiowa.edu/.../HomeworkAssignment11.pdf · Homework Assignment 11 . Question 1 (Short Takes) Two points each unless otherwise

55:041 Electronic Circuits. The University of Iowa. Fall 2013.

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 𝑟𝜋 = 2.5K, 𝑟𝑜 = 100K, 𝑔𝑚 = 40 mS, and 𝐶𝐿 = 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

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6. For the following circuit, what is the numerical value for the two-port y-parameter 𝑦12?

7. For the following circuit, what is the numerical value for the two-port h-parameter ℎ21? The definition of the h-parameters are shown.(2 points)

𝑣1 = ℎ11𝑖1 + ℎ12𝑣2 𝑖2 = ℎ21𝑖1 + ℎ22𝑣2

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 𝑄1? (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”.

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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 × 103 Ω

(b) 𝑗10 × 103 Ω (c) ≈ +𝑗1.6 × 103 Ω (d) −1.6 × 103 Ω (e) 10K

14. A MOSFET has rated power of 50 W at an ambient temperature 𝑇𝐴 = 25oC and a maximum specified junction temperature of 105oC. 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 𝑇𝐴 = 25oC and a maximum specified junction temperature of 175oC. What is the thermal resistance between the junction and device case?

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16. What is the maximum theoretical efficiency for a class-B amplifier?

17. What is the purpose of 𝑅3 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)

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

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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)

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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

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Question 6 You can assume that for all the transistors in the circuit below, 𝛽𝛽 is large. Show that 𝐼1 = 0.4 mA. Let 𝑣1 = 𝑣2 = 0 V and then determine VA, VB, VC, VD , 𝑉𝐸 , and 𝑣𝑂 . Assume

𝑉𝐵𝐸(𝑂𝑁) = 0.7 V for all the transistors. Further, note that 𝑅3 is small: for the purposes on this hand-analysis, ignore its effect. That is, assume 𝑅3 = 0. (14 Points)

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Question 7 (diodes, load line) Consider the circuit below. Assume 𝑉𝑃𝑆 = 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 𝐼𝐷 and 𝑉𝐷 (6 points)

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Question 8

𝑅𝑖 = 30K 𝑅𝑃 = 10K 𝐶𝑆 = 10 𝜇F 𝐶𝑃 = 50 pF

(a) Determine the open-circuit constant associated with 𝐶𝑆, and short-circuit time constant associated with 𝐶𝑃 (4 points)

(b) Determine the corner frequencies and magnitude of the transfer function 𝑇(𝑠) = 𝑉𝑜(𝑠) 𝐼𝑖(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)

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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)

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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)

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Question 11 For the common-emitter amplifier below, the transistor parameters are 𝛽𝛽 =100,𝑉𝐵𝐸(ON) = 0.7 V, and 𝑉𝐴 = ∞.

𝑉𝐶𝐶 = 12 𝑉 𝑅𝐶 = 1 kΩ 𝑅1 = 10 kΩ 𝑅2 = 1.5 kΩ 𝑅𝐸 = 0.1 kΩ 𝑅𝑆 = 0.5 kΩ 𝐶𝐶 = 0.1 𝜇F

(a) Determine 𝐼𝐶𝑄 , 𝑔𝑚 and 𝑟𝜋 (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)

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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.

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Question 13 For the circuit below 𝛽𝛽 = 120,𝑉𝐵𝐸(𝑂𝑁) = 0.7 V, and 𝑉𝐴 = ∞

(a) Design a bias-stable circuit such that 𝐼𝐶𝑄 = 1 mA. (b) Determine the output resistance 𝑅𝑜 . (c) What is the lower 3 dB corner frequency?

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Question 14 For the amplifier below, 𝛽𝛽 = 100, and a dc analysis reveals that 𝐼𝐶𝑄 = 0.838 mA. Estimate the 3-dB bandwidth. Assume that 𝐶𝑐2 = 0.1 𝜇F. (15 points)

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Question 15 Consider the amplifier below. In the circuit, 𝐼𝑃ℎ 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)

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Question 16

The maximum transistor power is PD,max = 25 W. Design the circuit (i.e., determine RL and RB) such that maximum power is delivered to the load. (8-points)

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Question 17 Q3, Q4, RP2, RP4 below form a short circuit protection network for the amplifier. If RP3 = RP4 = 0.15 Ω, what is the maximum io in case there is a short. That is, when RL = 0? (3 points)

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Question 18 In the amplifier below, assume 𝑉𝐵𝐸(𝑂𝑁) = 0.6 V for all the transistors. (a) Show that the collector current of 𝑄3 is approximately 1.6 𝜇A. (2 points) (b) Estimate the output resistance. (8 points) (c) Estimate the voltage gain 𝑉𝑜 𝑉𝑠⁄ . (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 = 63

𝛽𝛽 = 100

𝛽𝛽 = 16

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Question 19 The transistor in the amplifier shown has 𝛽𝛽 = 350 and 𝑉𝐵𝐸(𝑂𝑁) = 0.65 V. Ignore the BJT capacitances. (a) Make reasonable assumptions and show that 𝐼𝐶𝑄 ≈

1 mA (3 points) (b) Show that 𝑅𝑖 ≈ 13.7K (5 points) (c) Estimate the lower 3-dB frequency if 𝐶𝐶 = 1 𝜇F

(3 points)

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Homework Assignment 11 - University of Iowas-iihr64.iihr.uiowa.edu/.../HomeworkAssignment11.pdf · Homework Assignment 11 . Question 1 (Short Takes) Two points each unless otherwise