Spring 2021 - Final Solutions

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San Diego State University *

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430

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Electrical Engineering

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Apr 3, 2024

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San Diego State University EE 430 Analysis and Design of Electronic Circuits Spring 2021 Final Name: SDSU ID: Important notes for all questions: 1. If you make any assumptions, clearly state the assumption (and if needed briefly justify your assumption.) 2. For derivation questions, clearly show every step. 3. There will be partial credits for clearly showing the “steps” for all questions, if they are correct. Problem Points Marks 1 25 2 25 3 25 4 25 Total 100

Problem 1. (25 pts) In the circuit above, include the Early Effect for all devices. All bias current sources, 𝐼 , are ideal and thus have infinite output resistances. a. (6 pts) Find the expression for the midband gain ? ? ? 𝑖𝑑 . b. (6 pts) Find the expression for the midband gain ? ? ? ? . c. (6 pts) Find the expression for the midband gain ? 𝑜?? ? ? . d. (7 pts) If all devices have identical overdrive voltages, 𝑉 𝑂𝑉 , and Early Voltages, |𝑉 𝐴 | ; find an expression for the midband gain ? 𝑜?? ? 𝑖𝑑 in terms of 𝑉 𝑂𝑉 and 𝑉 𝐴 . e. (Bonus=5 pts) If |𝑉 𝐴 | = 20𝑉 𝑂𝑉 = 4 𝑉 , calculate ? 𝑜?? ? 𝑖𝑑 .

Problem 2. (25 pts) In the negative feedback circuit above, the feedforward amplifier, A , is implemented by cascading a common-emitter using Q 1 and a source-follower (=common-drain) using Q 2 . Note that Q 1 is an npn and Q 2 is an nMOS device. The input to the circuit is 𝑖 ? and the output is 𝑖 ??? . Include 𝒓 ? . a. (2 pts) Provide the 𝛽 -network and provide the types of connections (shunt OR series) at both terminals of the 𝛽 -network. b. (2 pts) Provide the gain expression for the 𝛽 -network. c. (3 pts) Including the loading of 𝛽 -network (i.e., 𝑅 11 and 𝑅 22 ), draw the modified feedforward amplifier, 𝐴 . d. (9 pts) Derive A , R in and R out of the feedforward amplifier, A , in part d. (Note that input and output are current type. Therefore, when obtaining R in and R out , think about the resistances that the current signals see along their corresponding branches) e. (9 pts) Provide the expressions for the closed-loop gain, A CL , closed-loop input resistance, R if , and closed-loop output resistance, R of .

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Problem 3. (25 pts) Transfer function of a feedforward amplifier, A , is given below and it has four poles: 𝐴 = 𝐴 ?? 1 (1 + ? 𝜔 ?1 )(1 + ? 𝜔 ?2 )(1 + ? 𝜔 ?3 )(1 + ? 𝜔 ?4 ) The pole frequencies are calculated as 𝝎 ?? = 𝝎 ?? = 1𝑥10 5 ?𝑎𝑑/? , 𝝎 ?? = 1𝑥10 7 ?𝑎𝑑/? , and 𝝎 ?? = 1𝑥10 8 ?𝑎𝑑/? . Note that two of the poles, 𝝎 ?? and 𝝎 ?? , overlap. The dc-gain is found as 𝐴 ?? = 10 4 𝑉/𝑉 . a. (8 pts) The amplifier is used in a negative feedback configuration, where 𝛽 = 1 . Draw the Bode plots for the loop gain.

b. (8 pts) Justify why the negative feedback amplifier is UNSTABLE when 𝛽 = 1 . c. (9 pts) What is the maximum 𝛽 value that puts the negative feedback amplifier at the edge of being UNSTABLE?

Problem 4. (25 pts) a. You want to characterize the noise-suppression performance of a differential amplifier. When you input the amplifier with a differential signal of 1 mV pp , you measure an output of 1 V pp . When you input a common-mode signal (noise) of 0.01 mV pp , you measure an output of 0.001 mV pp i. (3 pts) What is the differential gain? ii. (3 pts) What is the common-mode gain? iii. (4 pts) What is the common-mode rejection ratio in dB? b. (3 pts) Which property of a MOSFET would you change to increase its output resistance? i. Length ii. Width iii. Width/Length iv. Color :) c. (3 pts) The method of open-circuit time constant is used to predict upper 3-dB frequency, 𝑓 𝐻 i. True ii. False d. (3 pts) The discrete coupling and bypass capacitors in a discrete amplifier cause the amplifier gain to fall off at …………….. frequencies. i. high ii. low e. (3 pts) Common- gate amplifier is used as a ………….. buffer i. voltage ii. current f. (3 pts) Emitter- follower amplifier is used as a …………… buffer i. voltage ii. current

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