Page 106 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
CHAP. 5]
The circuit is a difference amplifier. 95

5.23 Find v o in the circuit of Fig. 5-46.

Fig. 5-46

Apply KCL at node B. Note that v B ¼ v A ¼ v 2 . Thus,
v 2 v 1 v 2 v o
þ ¼ 0
R 1 R 2
Solving for v o , we get v o ¼ v 2 þðR 2 =R 1 Þðv 2 v 1 Þ.

5.24 Find v o in the circuit of Fig. 5-47.

Fig. 5-47

The left part of the circuit has a gain of ð1 þ R 1 =R 2 Þ. Therefore, v 3 ¼ð1 þ R 1 =R 2 Þv 1 . Using results of
Problem 5.23 and substituting for v 3 results in

R 2 R 2 R 2 R 1 R 2
v o ¼ v 2 þ ðv 2 v 3 Þ¼ 1 þ v 2 1 þ v 1 ¼ 1 þ ðv 2 v 1 Þ
R 1 R 1 R 1 R 2 R 1

6
6
5.25 In Fig. 5-48 choose resistors for a differential gain of 10 so that v ¼ 10 ðv v Þ.
o
1
2
The two frontal op amps are voltage followers.
and
v A ¼ v 1 v B ¼ v 2
From (16), Sec. 5.9, we have
R 2 R 2
v o ¼ ðv B v A Þ¼ ðv 2 v 1 Þ
R 1 R 1
6
To obtain the required differential gain of R 2 =R 1 ¼ 10 , choose R 1 ¼ 100
and R 2 ¼ 100 M
.