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
R3¶vi1−R4
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<ω
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