ECE 101 Final Exam
Summer 2021
Please staple all your work with this
exam.
Please present your work clearly and
legibly, and box your final answers.
Please show all steps and units to receive
full credit.
No essay writing!
Name: (First, Last)
Student ID:
Email Address:
Final Score: /100
HONOR CODE: Please certify the integrity of the exam by signing below:
In recognition of the integrity of the engineering profession and the UCSC Honor Code, I certify
that I have kept the contents of this exam personal and confidential, and have neither given nor
received unauthorized aid.
Signature:______________________________________________
Short-Answer Questions (20 points total):
1) Given the 2nd-order characteristic equation below. Determine the type of response
and calculate the associated damping frequency in Hz if there is any. (10 pts)
S2 + 5000S+ 109 = 0
2) Determine the root location for each type of response for a 2nd-order system.
Please indicate the level of stability for each response, i.e. label “1” for the most
stable case and “4” for the least stable (or unstable) case. (10 pts).
underdamped
undamped
overdamped
critically damped
Analytical Questions (80 points total):
1)
a) Please find VC(t) for t > 0. Assume the circuit is in steady state prior to t = 0.
(Please clearly state every step and assumption to receive full credit) (15 pts)
b) Plot Vc(t) and mark the values of Vc(t) when t = τ and t = 5τ. (5 pts)
2)
Given RS = 0.1 kΩ, RL = 10 KΩ, primary coil inductance (LP) = 0.398 µH, and
fo = 1 MHz, determine the turn ratio (n), and secondary coil inductance (LS), and
capacitor (C) for maximum power transfer. Assume the transformer is lossless and has
a perfect coupling (K = 1). (15 pts)
3)
Please determine R1 and R2 so that the circuit is a first-order low-pass filter with
H(0) = -2 and ωc =10 rad/sec. (15 pts)
4)
a) Express the transfer function of the network. (3 pts)
b) Determine the type of filter response and the cutoff frequency in Hz. (4 pts)
c) Sketch the Bode plot (log-log scale) of the network, including the important
information, i.e. slope, corner (cutoff) frequency, and magnitude and phase at both DC
and very high frequency. (8 pts)
5)
a) Sketch the voltage waveform after the capacitor (5 pts).
b) Please find the average AC power delivered to the 50 ohm load in both Watt and
dBm. (10 pts)