1
§ 4-5 Simple capacitor-OP-AMP-circuits
Integrator op-amp circuit (Integrator):
????? t dtCRtwh en 0 1
21
22
1)(0)0( ???
The output is proportional to the integral of the input.
21,iian o d eat ??
? ???? t dtCRtor 1
21
2
1)( ??
dt
dC
R
2
2
1
1 ?? ??
??? ? t dtCR 0 1
21
2
1)0( ??
2C2i
1i
0??i
0??i
1R a
?
?
2??
?
1?
??
?
?
?
2
Differential op-amp circuit (differentiator):
dt
dCR 1
122
?? ???
2
21
1
21
Rdt
d
C
ii
??
??
??
The output is proportional to the derivative of the input.
1C
2R
?i
?i
2i
1i a
?
?
2??
?
1?
??
?
?
?
3
Differentiator:
dt
dCR 1
122
?? ???
Pulse waveform
Derivation of
this waveform
The output
waveform
0s
0s
012 sCR?
4
Integrator:
0
0A
02A
03A
)( 1?p ulses?
0
21
2
1 kA
CR???
The output voltage at any instant tells us how
many pulses have arrived up to that instant at the
input (pulse counter).
??? t dtCRt 0 1
21
2
1)( ??