CHAP. 5]

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS

95

The circuit is a diﬀerence ampliﬁer.

5.23

Find vo in the circuit of Fig. 5-46.

Fig. 5-46 Apply KCL at node B.

Note that vB ¼ vA ¼ v2 .

Thus,

v2  v1 v2  vo þ ¼0 R1 R2 Solving for vo , we get vo ¼ v2 þ ðR2 =R1 Þðv2  v1 Þ.

5.24

Find vo in the circuit of Fig. 5-47.

Fig. 5-47 The left part of the circuit has a gain of ð1 þ R1 =R2 Þ. Therefore, v3 ¼ ð1 þ R1 =R2 Þv1 . Using results of Problem 5.23 and substituting for v3 results in       R R R R R vo ¼ v2 þ 2 ðv2  v3 Þ ¼ 1 þ 2 v2  2 1 þ 1 v1 ¼ 1 þ 2 ðv2  v1 Þ R1 R1 R1 R2 R1

5.25

In Fig. 5-48 choose resistors for a diﬀerential gain of 106 so that vo ¼ 106 ðv2  v1 Þ. The two frontal op amps are voltage followers. vA ¼ v1

and

vB ¼ v2

From (16), Sec. 5.9, we have vo ¼

R2 R ðv  vA Þ ¼ 2 ðv2  v1 Þ R1 B R1

To obtain the required diﬀerential gain of R2 =R1 ¼ 106 , choose R1 ¼ 100  and R2 ¼ 100 M.

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An