ECE 3050 – Spring 2004 Page 1
Homework Assignment No. 3 - Solution
1.) The differential amplifier below uses an ideal op amp. Find the values of R1, R2, R3
and R4 if the single-ended input resistances, Rin1 and Rin2 are to be 100kΩ and the output
voltage is to be vout = 10(v1 – v2).
+
-
R
1
R
3
R
4
R
2
v
out
=
10(v
1
-v
2
)
-
+
v
2
v
1
R
in2
R
in1
Fig. S03Q03P1
Solution
The first step is to find vout as a function of v1 and v2 and to find Rin1 and Rin2.
The output voltage can be found by using superposition applied to the inputs v1 and v2.
The result is,
vout =
vout
v1
|
v2=0 +
vout
v2
|
v1=0 =
R1+R2
R1
R4
R3+ R4
v1 -
R2
R1
v2
Rin1 = R3 + R4 (remember to set v2 to zero in this calculation – only one
excitation at a time)
Rin2 = R1 (remember to set v1 to zero in this calculation – only one excitation at a
time)
From the input resistance results, we can write that,
R3 + R4 = 100kΩ and R1 = 100kΩ
Substituting these values in the voltage gain expression gives,
vout =
R1+R2
100kΩ
R4
100kΩ v1 -
R2
100kΩ v2 = 10(v1 – v2)
This gives us R2 = 1MΩ. Substituting this back into the voltage gain expression gives,
vout =
1100kΩ
100kΩ
R4
100kΩ v1 - 10 v2 = 10(v1 – v2)→ R4 = 1000kΩ
11 = 90.9kΩ
Since the sum of R3 and R4 must equal 100kΩ, we get
R3 = 100kΩ - 90.9kΩ = 9.1kΩ
Substituting these values back into the top three equations satisfies the requirements.
