# MATHEMATICS

QUESTION #1

Answer the following questions with a single sentence.

A) What is body effect in CMOS circuits?

B) What does “dead zone” of a phase detector refer to?

C) What is the primary difference between linear and nonlinear oscillators?

D) What is the primary difference between a latch and a flip-flop?

E) What is hysteresis effect? Provide an example to illustrate how it can be used.3/15/12 ESE 324 Midterm Exam STUDENT’S NAME________________________

QUESTION #2

Two circuits are shown in the figure above. Assume Vdd=7. The threshold voltage for NMOS

transistors is 3 V and the threshold voltage for PMOS transistors is -4 V. Initially both inputs are

at zero voltage. Nodes A and B are also initially at zero voltage. C is at Vdd. Similarly, nodes A’

and B’ are initially at zero voltage and C’ is at Vdd. Both inputs have a step transition to Vdd.

Determine the final voltage at nodes A, B, C, A’, B’, and C’. 3/15/12 ESE 324 Midterm Exam STUDENT’S NAME________________________

QUESTION #3

A relaxation based nonlinear oscillator is shown in the figure above. Note that Vdd=12 Volts and

Vss= -12 Volts.

A) Based on the resistances and capacitance, calculate the oscillation frequency at the

output.

B) What can be done to decrease the oscillation frequency?

Hint: The voltage of a capacitor that is charging or discharging through a resistor R toward a

final voltage Vf is determined by

( ) ( ) where V is the voltage at t 0 and RCis the time constant 0

f f

v t V V V e