0195136047.pdf

5.4 APPLICATIONS OF OPERATIONAL AMPLIFIERS 251

which corresponds to the response of adifferential amplifier.Usually resistor values are so chosen
thatR 3 =R 1 andR 4 =R 2 for some practical reasons. Improved versions of differential amplifiers
are available commercially.

Integrators

Figure 5.4.10 shows anoninverting integrator,which can be seen to be a negative impedance
converter added with a resistor and a capacitor. Noting thatvo= 2 v 1 andi 3 =v 1 /R, the total
capacitor current is

i=iin+i 3 =

vin−v 1

R

+

v 1

R

=

vin

R

(5.4.36)

The capacitor voltage is given by

v 1 (t)=

1

C

∫t

−∞

i(ξ)dξ=

1

RC

∫t

−∞

vin(ξ)dξ (5.4.37)

Thus,

vo(t)=

2

RC

∫t

−∞

vin(ξ)dξ (5.4.38)

which shows that the circuit functions as an integrator.
ReplacingR 2 in the inverting amplifier of Figure 5.4.1 by a capacitanceCresults in the
somewhat simpler integrator circuit shown in Figure 5.4.11, known as an inverting integrator, or
Miller integrator. With ideal op-amp techniques,iC=iin=vin/R. The voltage acrossCis just
vo, so that

−

+

vo

R (^1) v
1
v 1
iin i 3
i
C
R 1
R
Negative impedance converter
R
vin
Figure 5.4.10Noninverting integrator.
−

• vo
  1
  2 3
  C
  iC
  iin
  R
  vin
  Figure 5.4.11Inverting integrator (Miller integrator).