Op-amp Integrator Network-Operational Amplifiers Types Tutorials Series

بِسْــــــــــــــــمِ اﷲِالرَّحْمَنِ اارَّحِيم

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السَّلاَمُ عَلَيْكُمْ وَرَحْمَةُ اللهِ وَبَرَكَاتُهُ

Assalamu'alaikum warahmatullahi wabarakatuh

1. Shown below is an op-amp integrator network
�The output will be equal to the integral of the input, as long as the op-amp remains in its linear region
�Due to the virtual short property of the op-amp input, we can write i1 = vIN/R1
�This current i1 starts charging the capacitor C according to the relation i1 = C(dvC/dt).

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2. Since v- remains at GND, the output drops below GND as C charges and the time derivative of vOUT becomes the negative of the time derivative of vC
�since vC = 0 - vOUT�

3. Combining the above equations, we obtain
�dvOUT/dt = -i1/C = -vIN/R1C

4. Solving for vOUT(t) and assuming C is initially uncharged, we obtain
�vOUT(t) = (-1/R1C) � vIN dt where the integral is from 0 to t

Example

CONTINUE READING �








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وَ السَّلاَمُ عَلَيْكُمْ وَرَحْمَةُ اللهِ وَبَرَكَاتُهُ

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