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

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

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

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)

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

Question 3 Consider an inverting amplifier with voltage gain 𝐴𝑉 = −100. The amplifier is driven by a sensor with an internal resistance 𝑅𝑆 = 10K. The amplifier’s input resistance is very large and may be ignored. The stray capacitance between the amplifier output and input terminals is 𝐶𝐹 = 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.

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

Question 4

𝑅1 = 200 kΩ 𝑅2 = 220 kΩ 𝑅𝐶 = 2.2 kΩ 𝑅𝐸 = 1 kΩ 𝑟𝑠 = 100 kΩ 𝑉𝐶𝐶 = 5 V 𝑅𝐿 = 4.7 kΩ 𝛽𝑜 = 100 𝐶𝜇 = 2 pF 𝐶𝜋 = 10 pF 𝑉𝐴 = ∞ 𝑉𝐵𝐸(𝑂𝑁) = 0.7 V

The coupling capacitors and bypass capacitors are large and may be treated as shorts.

(a) Show that 𝐼𝐵 = 9.3 𝜇A. Note that you cannot assume IB = 0 (4 points) (b) Determine the numerical values for 𝑔𝑚 and 𝑟𝜋 (4 points) (c) Draw a detailed small-signal model for the amplifier showing the numerical values of the

components. Be sure to include 𝐶𝜇 and 𝐶𝜋 (6 points) (d) Determine the 3-dB frequency for the amplifier (4 points)

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

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

Question 5 Below is the small-signal model of a BJT amplifier. Determine the so-called Miller capacitance 𝐶𝑀,and draw an equivalent small-signal circuit that incorporates 𝐶𝑀. 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)

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

Question 6 Below is a small-signal model of a BJT amplifier. Determine the so-called Miller capacitance 𝐶𝑀, and draw an equivalent small-signal circuit that incorporates 𝐶𝑀. 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)

𝑅𝐿 = 2 K 𝑔𝑚 = 0.04 A V⁄ 𝑟𝜋 = 5 K 𝑅𝑆 = 5 K 𝐶𝜋 = 10 pF 𝐶𝜇 = 2 pF

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

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 𝐶1 = 𝐶2 = 𝐶3 → ∞.

𝛽 = 100 𝐼𝐶 = 0.245 mA

(a) Determine 𝑔𝑚, 𝑟𝜋 (4 points) (b) Using BJT scaling, determine 𝑅𝑖—see figure (4 points) (c) Using the ratio of the collector and emitter resistors, estimate the overall voltage gain

𝐴𝑣 = 𝑣𝑜 𝑣𝑠⁄ (4 points) (d) Calculate the voltage gain 𝐴𝑣 = 𝑣𝑜 𝑣𝑠⁄ , 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)

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

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

Question 8 Consider the CE BJT amplifier below.

𝐼𝐶 = 1 mA 𝛽 = 185 𝐶𝜋 = 100 pF 𝐶𝜇 = 14 pF 𝑉𝐴 → ∞ 𝐶𝐶1 → ∞ 𝐶𝐶2 → ∞ 𝐶𝐶3 → ∞

(a) Draw a hybrid-𝜋 small signal model of the amplifier. Be sure to include 𝐶𝜋, 𝐶𝜇, and 𝑔𝑚. (8 points)

(b) Show that 𝑟𝜋 = 4.5 kΩ. (2 points) (c) Estimate the upper 3 dB bandwidth. (12 points)

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

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 𝑅𝑜 ≈ 0 Ω, how much power will the load dissipate? (3 points)

(b) Assuming the amplifier has output resistance 𝑅𝑜 = 0.4 Ω, how much power will the load dissipate? (3 points)

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

Question 10 An amplifier has an input resistance 𝑅𝑖 =1K, and has a voltage gain of 𝐴𝑣 = 100 when driven from a signal with internal resistance 𝑅𝑠 ≈ 0. The amplifier is used to amplify a 𝑣𝑠 = 1 mV signal from a sensor that has an internal resistance of 𝑅𝑠 ≈ 20K. What is the output amplitude? (5 points)

Question 11 The parameters for the transistor below are 𝐾𝑛 = 0.5 mA/V2, 𝑉𝑇𝑁 = 1.2 V, and 𝜆 = 0. Determine 𝑣𝐷𝑆 and 𝑣𝐺𝑆 for 𝐼𝑄 = 1 mA. (6 points)

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

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)

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

Question 13

For (a) show that the transfer function is

𝑇(𝑠) =𝑣𝑜(𝑠)𝑣𝑖(𝑠)

=𝑅2

𝑅2 + 𝑅1(1 + 𝑠𝑅1𝐶1)

1 + 𝑠(𝑅1‖𝑅2)𝐶1 (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) = 𝑣𝑜(𝑠) 𝑣𝑖⁄ (𝑠). (5 points)

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

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

Question 14

𝛽(𝑝𝑛𝑝) = 10, 𝛽𝑛𝑝𝑛 = 50

For the circuit above, make reasonable assumptions and then (a) Show that 𝑟𝜋1~ 156 kΩ (4 points) (b) Use BJT impedance scaling and give a reasonable estimate for the output resistance 𝑅𝑂

(4 points)

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

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

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

Question 16 Consider the MOSFET amplifier below. Draw the small-signal model, incorporating 𝑟𝑜. (5 points) Determine the voltage gain 𝑣𝑜 𝑣𝑖⁄ (8 points) and the output resistance 𝑅𝑂 (8 points).

𝐾𝑛 = 1 mA V⁄ 𝑉𝑇𝑁 = 1.2 V 𝜆 = 0.01 V−1 𝐼𝐷𝑄 = 1 mA

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

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

Question 17 For the amplifier below, 𝑅𝐿 = 500 Ω. Determine, 𝑅𝑖𝑏 ,𝑅𝑜 and the small-signal voltage gain 𝐴𝑣 = 𝑣𝑜 𝑣𝑖⁄ . (15 points)

𝑅𝑆 = 10K 𝑉+ = 3 V 𝑉− = −3 V 𝐼𝑄 = 2 mA 𝛽 = 100 𝑉𝐴 = 100 V CC → ∞

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

Question 18 (N EX 7.14)

𝛽 = 125, 𝐶𝜇 = 3 pF, 𝐶𝜋 = 24 pF, 𝑉𝐴 = 200, 𝑉𝐵𝐸(𝑂𝑁) = 0.7 V

A dc analysis shows that ICQ = 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)

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