UNIVERSITY OF CALIFORNIA
Electrical Engineering and Computer Sciences
145L MIDTERM #1 (take-home)
September 19, 1994
Due Monday, September 26, 1994
(100 points total, 3 points deducted for each school day late)
(no credit after graded midterms have been returned to students)
PROBLEM 1 (16 points)
For the differential amplifier circuit shown in Course Reader Figure 2.4, and assum-
ing that the open loop gain A is infinite, do the following:
a. Derive the expression for the output V0 as a function of the four variables R1, R2,
R3, and R4. Your result should be of the form V0 = aV2 – bV1.
b. Derive expressions for the differential gain G± and the common mode gain Gc in
terms of R1, R2, R3, R4, using the expression from part a. and the following:
V0 = aV2 – bV1 = (a + b)(V2 – V1)/2 + (a – b)(V2 + V1)/2
= G± (V2 – V1) + Gc Vc, where Vc = (V1 + V2)/2
c. Using your expressions from step b., derive an expression for the CMRR in terms
of R1, R2, R3,R4.
d. Under what conditions does Gc = 0?
e. When Gc = 0 is satisfied, what does your expression for G± reduce to?
f. For G± = 1 and G± = 1000, first set R2/R1 = R4/R3 = G± and then find the percent-
age variation in R3 that causes CMR ≈ 120 dB. Note that G± changes very little.
Comment on the resistor accuracy required for a good CMRR at the two differ-
ential gains.
Note: G± is primarily determined by R2/R1 and R3 (or R4) can be used to “fine tune”
Gc.
PROBLEM 2 (16 points)
You are given an instrumentation amplifier with a gain that is adjustable from 1 to
1000. At a gain of 1, the bandwidth is 106 Hz. At a gain of 1000, the bandwidth is 104
Hz.
a. Both input terminals are connected to ground with 5-MΩ resistors. If the input
leakage currents on the two inputs are 0.5 nA and 1.5 nA, what is resulting output
offset at a gain of 1000? At a gain of 1?
b. What is the output noise in the 104-Hz bandwidth at a gain of 1000 due only to the
room-temperature Johnson noise in the 5-MΩ resistors? (Hint: If two uncorre-
lated noise sources are added, the rms noises combine as the square root of the
sum of their squares.)
c. When the inputs are connected directly to ground, the output-voltage noise with
a gain of 1000 is 1 mV rms in the 104 Hz bandwidth. When the gain is reduced to
EECS 145L Midterm #1 page 1 Due Sept. 26, 1994
