University of Massachusetts Amherst Department of Electrical and Computer Engineering ECE 210 Circuits and Electronics I, Final Exam Thursday December 20, 2018, 8:00 am
———————————————————————————- Name:______________________ Student ID:__________________ ———————————————————————————-
Do not open until instructed to do so. You have 2 hours
Closed book and notes.
Show your work to receive full credit..
Put your work only on the front or back of the page with the problem statement.
Problem 1 (15pts)
Write the node voltage equations for the circuit to the right using the node voltages v1 and v2 as labeled. Note that there is a dependent voltage source that depends on the current ix via the constant z. Your equations should have only v1, v2, R1, R2, R3, z, is.
Problem 2 (20pts)
a) Find the Thevenin equivalent circuit for the circuit below. The terminal pair is identified by the circles. Your answer is numerical. Put the answers in the boxes to the right.
Vth =
Rth =
b) Find the Thevenin equivalent circuit for the circuit below. The terminal pair is identified by the circles. Your answer is numerical. Note that there is a dependent current source that depends on the current ix. Put the answers in the boxes to the right.
Vth =
Rth =
Problem 3
In the circuit to the right the voltage vi has been 0 for a long time and then changes from 0 to 5 V at t = 0. The NMOS device shown has parameters: Kn = 0.125 A/V2 and VTn = 1 V.
For parts a, b, c, d, Vdd = 9V.
For parts a, b, c, put answers in boxes to the right.
a) (4pts) Find the power, in watts, being supplied by the Vdd source at t = 0-.
PVdd = vo(0+) = We =
b) (4pts)What is vo(0+)?
c) (4pts)Find the energy stored in C at t = 0+. Answer in Joules
d) (4pts) At t = 0+, is M in triode, saturation, or cutoff? Show why. No evidence = no credit.
e) (14pts) In this part Vdd is 3V (and has been for all time.) And, again, vi has been 0 for a long time and then changes from 0 to 5 V at t = 0. Find vo(t) for t > 0.
Problem 4 (15pts)
For the opamp circuit to the right. Assume the diode is ¡°on¡± and use
the constant voltage drop model.
a) Find vo. Put your answer in the box to the right.
vo =
b) Was it correct to assume the diode is on? Why? No evidence = no points.
Problem 5(20pts)
In the circuit to the right, device M parameters are: Kp = 1 mA/V2 and VTp = -1. When vI is set so that M is ¡°on¡± , its on resistance is 600 ohms. Put your answers in the boxes to the right.
a) What is vi when M is ¡°on¡±?
b) M has been ¡°off¡± for a long time and then turns ¡°on¡± at t = 0. What is vx(0+)?
vi(on) = c) The differential equation for vo in this circuit when M is ¡°on¡± is, +
d2vo +Req dvo +vo = F dt2 L dt LC LC
What is Req and what is F? Numerical answers please.
d) What is the final value of vo(t)?
e) What is the Q of this circuit for t > 0?
f) What is the period , in seconds, of the ringing in the transient response?
g) How long in seconds does it take for the ringing to settle to within (roughly) 4% of final value?
vx(0)=
Req = F=
Final value =
Q=
Period =
Settle time =
Detach this sheet from the exam and use it as scratch paper. Do not turn it in. You will be graded only by what you put on a problem sheet or on the back of a problem sheet.