Page 87 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
76
R 4 ðR 1 þ R 2 Þ R 2 [CHAP. 5
v o ¼ v 2 v 1 ð17Þ
R 1 ðR 3 þ R 4 Þ R 1
When R 3 ¼ R 1 and R 2 ¼ R 4 ,(17) is reduced to (16).

5.10 CIRCUITS CONTAINING SEVERAL OP AMPS
The analysis and results developed for single op amp circuits can be applied to circuits containing
several ideal op amps in cascade or nested loops because there is no loading effect.

EXAMPLE 5.15 Find v 1 and v 2 in Fig. 5-21.

Fig. 5-21

The first op amp is an inverting circuit.
v 1 ¼ ð3=1Þð 0:6Þ¼ 1:8V
The second op amp is a summing circuit.
v 2 ¼ ð2=1Þð0:5Þ ð2=2Þð1:8Þ¼ 2:8V

EXAMPLE 5.16 Let R s ¼ 1k
in the circuit of Fig. 5-22, find v 1 ; v 2 ; v o ; i s ; i 1 ; and i f as functions of v s for
(a) R f ¼1 and (b) R f ¼ 40 k

Fig. 5-22

þ
(a) R f ¼1. The two inverting op amps are cascaded, with v ¼ 0. By voltage division in the input loop we have
5 5
v 1 ¼ v s ¼ v s ð18Þ
5 þ 1 6
From the inverting amplifiers we get