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ECE 3040 Quiz 10 - Circuit Analysis, Quizzes of Electrical and Electronics Engineering

A quiz for ece 3040 students, focusing on circuit analysis. It includes instructions, two problems, and solutions for gain calculation and bode plot sketching. Students are required to find the gain of the circuit at low and high frequencies, draw the expected bode magnitude plot, and use the inverting op-amp gain formula to solve for the transfer function.

Typology: Quizzes

Pre 2010

Uploaded on 08/05/2009

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koofers-user-b63 🇺🇸

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ECE3040Quiz10—July27,2005
Professor Leach Name
Instructions. Print your name in the space above. The quiz is closed-book and closed-notes. The quiz
consists of two problems. Draw a box around all answers. Honor Code Statement: I have neither given
nor received help on this quiz. Initials
1. Use superposition of vi1and vi2to solve for voas a function of vi1and vi2.
vo=R2
R1+R2µ1+R4
R3vi1R4
R3
vi2
2. (a)Whatisthegainofthecircuitatverylowfrequencies?
Vo
Vi
=R2
R1
(b)Whatisthegainofthecircuitatveryhighfrequencies?
Vo
Vi
=R2kR3
R1
(c) Sketch the expected Bode magnitude plot using log-log scales: (i) First sketch the straight-line
asymptotes and label the slopes in decades per decade. (ii) Label the gains on any straight-line
asymptotes that have a zero slope. (iii) Label any pole and zero frequencies, respectively, with the
labels ωpn and ωzm,wherenand mare index integers. It is a low-pass shelving transfer function with
ωp
z.
(d) Finally, use the inverting op-amp gain formula to solve for the transfer function for Vo/Vi:(i)
Express the transfer function as a gain constant Kmultiplied by terms of the form 1+s/ωzand/or
divided by terms of the form 1+s/ωp. (ii) Give the expressions for K,theωz,andtheωp.
Vo
Vi
=R2k(R3+1/Cs)
R1
=K1+s/ωz
1+s/ωp
K=R2
R1
ωp=1
(R2+R3)Cωz=1
R3C
1

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ECE 3040 Quiz 10 — July 27, 2005

Professor Leach Name

Instructions. Print your name in the space above. The quiz is closed-book and closed-notes. The quiz consists of two problems. Draw a box around all answers. Honor Code Statement: I have neither given nor received help on this quiz. Initials

  1. Use superposition of vi 1 and vi 2 to solve for vo as a function of vi 1 and vi 2.

vo =

R 2

R 1 + R 2

μ 1 +

R 4

R 3

vi 1 −

R 4

R 3

vi 2

  1. (a) What is the gain of the circuit at very low frequencies? Vo Vi

R 2

R 1

(b) What is the gain of the circuit at very high frequencies? Vo Vi

R 2 kR 3 R 1

(c) Sketch the expected Bode magnitude plot using log-log scales: (i) First sketch the straight-line asymptotes and label the slopes in decades per decade. (ii) Label the gains on any straight-line asymptotes that have a zero slope. (iii) Label any pole and zero frequencies, respectively, with the labels ωpn and ωzm, where n and m are index integers. It is a low-pass shelving transfer function with ωp < ωz. (d) Finally, use the inverting op-amp gain formula to solve for the transfer function for Vo/Vi: (i) Express the transfer function as a gain constant K multiplied by terms of the form 1 + s/ωz and/or divided by terms of the form 1 + s/ωp. (ii) Give the expressions for K, the ωz , and the ωp. Vo Vi

R 2 k (R 3 + 1/Cs) R 1

= K

1 + s/ωz 1 + s/ωp

K = −

R 2

R 1

ωp =

(R 2 + R 3 ) C

ωz =

R 3 C