84-5 Simple capacitor-OP-AMP-circuits Integrator op-amp circuit (Integrator): R1 >00 at node a: 4=-L2 i+=0 rU2() Ut=D2(0) v, dt R,C when 02(0)=0 02(0= JO 2 The output is proportional to the integral of the input
1 §4-5 Simple capacitor-OP-AMP-circuits Integrator op-amp circuit (Integrator): = = − − t dt R C when t 0 1 1 2 2 2 1 (0 ) 0 ( ) The output is proportional to the integral of the input. 1 2 at node a : i = −i − = − t dt R C or t 1 1 2 2 1 ( ) dt d C R 2 2 1 1 = − = − − t dt R C 0 1 1 2 2 1 (0 ) C2 2 i 1 i = 0 + i = 0 − i R1 a − + 2 − + 1 + + −
Differential op-amp circuit(differentiator): R2 1 ●● du 十 dt R 2 dD at The output is proportional to the derivative of the input
2 Differential op-amp circuit (differentiator): dt d R C 1 2 2 1 = − 2 1 2 1 1 2 dt R d C i i = − = − The output is proportional to the derivative of the input. C1 R2 − i + i 2 i 1 i a − + 2 − + 1 + + −
Differentiator:.v =RC,ei Pulse waveform 0 Derivation of this waveform The output waveform R2C1So
3 Differentiator: dt d R C 1 2 2 1 = − Pulse waveform Derivation of this waveform The output waveform 0 s 0 s 2 1 0 − R C s
Integrator: 02(t)= 0, dt r,C2 E pulses(uu) 3Ao 2A4 KAo R,C The output voltage at any instant tells us how many pulses have arrived up to that instant at the input (pulse counter)
4 Integrator: 0 A0 0 2A 0 3A ( ) pulses 1 0 1 2 2 1 kA R C = − The output voltage at any instant tells us how many pulses have arrived up to that instant at the input (pulse counter). = − t dt R C t 0 1 1 2 2 1 ( )