Page 90 - Schaum's Outline of Theory and Problems of Electric Circuits

AMPLIFIERS AND OPERATIONAL AMPLIFIER CIRCUITS
CHAP. 5]

Fig. 5-25 79

v 1 v 2 v 3 dv o
þ þ þ C ¼ 0
R 1 R 2 R 3 dt
ð t
v 1 v 2 v 3
v o ¼ þ þ dt ð24Þ
1 R 1 C R 2 C R 3 C
Initial Condition of Integration
The desired initial condition, v o , of the integration can be provided by a reset switch as shown in Fig.
5-26. By momentarily connecting the switch and then disconnecting it at t ¼ t o , an initial value of v o is
established across the capacitor and appears at the output v 2 . For t > t o , the weighted integral of input
is added to the output.
ð t
1
v 2 ¼ v 1 dt þ v o ð25Þ
RC
t o

Fig. 5-26

Differentiator
By putting an inductor in place of the resistor in the feedback path of an inverting amplifier, the
derivative of the input signal is produced at the output. Figure 5-27 shows the resulting differentiator
circuit.
To obtain the input-output relationship, apply KCL to currents arriving at the inverting node:

ð t
1
v 1 L dv 1
þ v 2 dt ¼ 0 or v 2 ¼ ð26Þ
R L 1 R dt