Download Equation - Introduction to Microelectronic Circuits - Solved Exam and more Exams Microelectronic Circuits in PDF only on Docsity! ECS 40, Fall 2008
Prof. Chang-Hasnain
Test #2
Version A
10:10 am — 11:00 am, Monday October 27, 2008
Total Time Allotted: 50 minutes
Total Points: 100
4. This is a closed book exam. However, you are allowed to bring one page (8.5” x 11”),
double-sided notes.
2. No electronic devices, i.e. calculators, cell phones, computers, etc.
3. SHOW all the steps on the exam. Answers without steps will be given only a small
percentage of credits. Partial credits will be given if you have proper steps but no final
answers.
4, Remember to put down units. Points will be taken off for missed unit.
Last (Family) Name:,
First Name:
Student ID: Discussion Session:
Signature:
Score:
Problem 1 (40 pts)
Problem 2 (24 pts)
Problem 3 (16 pts)
Problem 4 (20 pts)
Total
Page 1 of 9
Problem 1: Transient Response of RLC circuits (40 pts)
Consider the circuit shown below
a) Derive the differential equation for ii(t) (20 pts)
KVL: K= Rit Y= ~ Ri +L A (1)
kcLoA: I~ 21. = C9 Q)
DA ered de, 13 x
A te
dk ss diy (2)
AL ~ Roe th Ae
Pleo BY3C2)
f hy po dite fe
Tsi,= CAS? ae
Rear rang iG
: / a
ds. ¢hdiv +pels,= ae.
dii = dt
Page 2 of 9
(b) What type of filter does this circuit implement? (3 pts)
OLow-pass O High-pass
AX Band-pass O Band-reject (Notch)
(c) Depending on your answer in part b), answer one of the following 3 questions ((i) — (iii))
(9 pts)
(i) If your answer in part b) is either high- or low-pass filter:
Write down the break frequency wa, the slope of |H(w)*| in dB/decade for very
small and very high frequencies respectively as well as the order of the filter.
Page 5 of 9
(ii) If your answer in part b) is band-pass filter:
Write down the resonance frequency wo, the quality factor Q of the filter as well as
the slope of |H(w)?| in dB/decade for very small and very high frequencies.
fb
slope (w<<) = 2° Ke
slope (w>>) = 20 4
(iii) If your answer in part b) is band-reject (notch) filter:
Write down the resonance frequency Wo, the quality factor Q of the filter as well as
the values of |H(w)?| in dB for very small and very high frequencies.
Oo=
Q=
|H(o<<)| =
|H(@>>)| =
Page 6 of 9
Problem 3: 1° Order Bode Plots (16 pts)
Consider the circuit shown below
Using complex impedances, derive the transfer function H(W)=Vout/Vin as a function
of R and L(6 pts
(6 pts) / /
sre. w= — So Sa
a See eee [ver
a)
b) What is «x or @p (depending on the transfer function you came up with in a)) of the
system? (Give your answer again as a function of R and L) (2 pts)
w, BK
ra
R
an ee
w= 7
@p OF Wo = Oe
Page 7 of 9
