Page 107 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
96

Fig. 5-48 [CHAP. 5

The circuit of Fig. 5-48 can have the same gain as that of Fig. 5-45, but its input resistance is infinite.
However, it employs two small and large resistors which are rather out of ordinary range.

5.26 Resistors having high magnitude and accuracy are expensive. Show that in the circuit of Fig. 5-
6
49 we can choose resistors of ordinary range so that v o ¼ 10 ðv 2 v 1 Þ.

Fig. 5-49

The two frontal op amps convey the input voltages v 1 and v 2 to the terminals of R G , creating an upward
current i ¼ðv 2 v 1 Þ=R G in the resistor. The current also goes through the two R 3 resistors, creating
voltage drops iR 3 across them. Therefore,

R 3 R 3
v A ¼ v 1 R 3 i ¼ v 1 ðv 2 v 1 Þ v B ¼ v 2 þ R 3 i ¼ v 2 þ ðv 2 v 1 Þ
R G R G

2R 3
v B v A ¼ 1 þ ðv 2 v 1 Þ
R G

R 2 R 2 2R 3
and v o ¼ ðv B v A Þ¼ 1 þ ðv 2 v 1 Þ
R 1 R 1 R G
6
For a differential gain of 10 we must have

v o R 2 2R 3 6
¼ 1 þ ¼ 10
v 2 v 1 R 1 R G
Choose R 1 ¼ R G ¼ 1k
, R 2 ¼ 100 k, and R 3 ¼ 5M
.