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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) (b) (c) (d) (e) 500 Hz 5 kHz 10 kHz 50 kHz 500 kHz 1 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 2 In the circuit, π = 10K. What should πΆ be so that the circuit delays a 5-kHz signal by 5 πs ? (6 points) 2 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 3 Consider an inverting amplifier with voltage gain π΄π = β100. The amplifier is driven by a sensor with an internal resistance π π = 10K. The amplifierβs input resistance is very large and may be ignored. The stray capacitance between the amplifier output and input terminals is πΆπΉ = 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 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 4 π 1 = 200 kΞ© π 2 = 220 kΞ© π πΆ = 2.2 kΞ© π πΈ = 1 kΞ© ππ = 100 kΞ© ππΆπΆ = 5 V π πΏ = 4.7 kΞ© π½π = 100 πΆπ = 2 pF πΆπ = 10 pF ππ΄ = β ππ΅πΈ(ππ) = 0.7 V The coupling capacitors and bypass capacitors are large and may be treated as shorts. (a) Show that πΌπ΅ = 9.3 πA. Note that you cannot assume IB = 0 (4 points) (b) Determine the numerical values for ππ and ππ (4 points) (c) Draw a detailed small-signal model for the amplifier showing the numerical values of the components. Be sure to include πΆπ and πΆπ (6 points) (d) Determine the 3-dB frequency for the amplifier (4 points) 4 55:041 Electronic Circuits. The University of Iowa. Fall 2013. 5 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 πΆπ ,and draw an equivalent small-signal circuit that incorporates πΆπ . 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 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 πΆπ , and draw an equivalent small-signal circuit that incorporates πΆπ . 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) π πΏ = 2 K ππ = 0.04 AβV ππ = 5 K π π = 5 K πΆπ = 10 pF πΆπ = 2 pF 7 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 BJTβs output resistance, and assume πΆ1 = πΆ2 = πΆ3 β β. π½ = 100 πΌπΆ = 0.245 mA (a) Determine ππ , ππ (4 points) (b) Using BJT scaling, determine π π βsee figure (4 points) (c) Using the ratio of the collector and emitter resistors, estimate the overall voltage gain π΄π£ = π£π βπ£π (4 points) (d) Calculate the voltage gain π΄π£ = π£π βπ£π , but do not use the approximation that involves the ratio of the collector and emitter resistors, but rather incorporate the π½ of the transistor (4 points) 8 55:041 Electronic Circuits. The University of Iowa. Fall 2013. 9 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 8 Consider the CE BJT amplifier below. πΌπΆ π½ πΆπ πΆπ ππ΄ πΆπΆ1 πΆπΆ2 πΆπΆ3 = 1 mA = 185 = 100 pF = 14 pF β β β β β β β β (a) Draw a hybrid-π small signal model of the amplifier. Be sure to include πΆπ , πΆπ , and ππ . (8 points) (b) Show that ππ = 4.5 kΞ©. (2 points) (c) Estimate the upper 3 dB bandwidth. (12 points) 10 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 Ξ© load. Assume sinusoidal signals. (a) Assuming the amplifier has output resistance π π β 0 Ξ©, how much power will the load dissipate? (3 points) (b) Assuming the amplifier has output resistance π π = 0.4 Ξ©, how much power will the load dissipate? (3 points) 11 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 10 An amplifier has an input resistance π π = 1K, and has a voltage gain of π΄π£ = 100 when driven from a signal with internal resistance π π β 0. The amplifier is used to amplify a π£π = 1 mV signal from a sensor that has an internal resistance of π π β 20K. What is the output amplitude? (5 points) Question 11 The parameters for the transistor below are πΎπ = 0.5 mA/V2, πππ = 1.2 V, and π = 0. Determine π£π·π and π£πΊπ for πΌπ = 1 mA. (6 points) 12 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) 13 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 13 For (a) show that the transfer function is π(π ) = π 2 (1 + π π 1 πΆ1 ) π£π (π ) = π£π (π ) π 2 + π 1 1 + π (π 1 βπ 2 )πΆ1 (π π©π¨π’π§ππ¬) Determine the circuitβs two time constants (2 points). Sketch the Bode magnitude plot (5 points) and Bode phase plot of π(π ) (5 points) For (b), determine the circuit time constant and then ketch the Bode magnitude plot (5 points) and Bode phase plot of π(π ) = π£π (π )βπ£π (π ). (5 points) 14 55:041 Electronic Circuits. The University of Iowa. Fall 2013. 15 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 14 π½(πππ) = 10, π½πππ = 50 For the circuit above, make reasonable assumptions and then (a) Show that ππ1 ~ 156 kΞ© (4 points) (b) Use BJT impedance scaling and give a reasonable estimate for the output resistance π π (4 points) 16 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 π π and π π to produce an output current of 0.4 mA. You may ignore base currents and make reasonable assumptions about VBE. (5 points) 17 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 16 Consider the MOSFET amplifier below. Draw the small-signal model, incorporating ππ . (5 points) Determine the voltage gain π£π βπ£π (8 points) and the output resistance π π (8 points). πΎπ = 1 mAβV πππ = 1.2 V π = 0.01 V β1 πΌπ·π = 1 mA 18 55:041 Electronic Circuits. The University of Iowa. Fall 2013. 19 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 17 For the amplifier below, π πΏ = 500 Ξ©. Determine, π ππ , π π and the small-signal voltage gain π΄π£ = π£π βπ£π . (15 points) π π π+ πβ πΌπ π½ ππ΄ CC 20 = 10K = 3V = β3 V = 2 mA = 100 = 100 V ββ 55:041 Electronic Circuits. The University of Iowa. Fall 2013. Question 18 (N EX 7.14) π½ = 125, πΆπ = 3 pF, πΆπ = 24 pF, A dc analysis shows that ICQ = 0.84 mA. ππ΄ = 200, ππ΅πΈ(ππ) = 0.7 V (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

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