OP AMP 2
CHULWOO BYEON
Integrator
Vout
1
=−
Vin
R1C1s
Vout
2
∫
1
=−
Vin dt
R1C1
Integrator with Pulse Input
∫
1
V1
t 0 < t < Tb
Vout = −
Vin dt = −
R1C1
R1C1
3
Lossy Integrator
Vout
−1
=
Vin 1  1 
+ 1 +  R1C1s
A0  A0 
 When finite op amp gain is considered, the integrator becom
es lossy as the pole moves from the origin to -1/[(1+A0)R1C1].
 It can be approximated as an RC circuit with C boosted by a f
actor of A0+1.
4
Differentiator
Vout
Vout
R1
=−
= − R1C1s
1
Vin
C1s
dVin
= − R1C1
dt
5
Differentiator with Pulse Input
Vout =  R1C1V1δ (t )
6
Lossy Differentiator
Vout
− R1C1s
=
Vin 1 + 1 + R1C1s
A0
A0
 When finite op amp gain is considered, the differentiator bec
omes lossy as the zero moves from the origin to –(A0+1)/R1C1
 It can be approximated as an RC circuit with R reduced by a f
actor of (A0+1).
7
Voltage Adder
Vout
Ao
Vout
 V1 V2 
= − RF  + 
 R1 R2 
− RF
(V1 + V2 )
=
R
If R1 = R2=R
 If Ao is infinite, X is pinned at ground, currents proportional to
V1 and V2 will flow to X and then across RF to produce an out
put proportional to the sum of two voltages.
8