Q. Explain the conditions under which an RC circuit behaves as Integrator?

Integrator is a circuit in which the output voltage is proportional to the integral of the input. Output=k integralof input. Integration means the summation of output from an integrator i.e. the sum of all input wave at any instant. When the input is a square wave, the output is triangular. Here the time constant of circuit is very large in comparison with time period of input signal. Hence the voltage drop across the capacitor will be very small in comparison to the drop across resistor. The current is Vin/R since the whole of Vin is appearing across R, the output voltage across V is Vo=1/C (integral of I with respect to time)=1/(RC) (integral of Vin with respect to time). Voltage drop across 'c' increases as time passes. It is necessary that RC>=1.5T where T is period of input wave. When a pulse waveform is given at the input, the capacitor charges through Rc& the output voltage builds up. As long as the input voltage is present, the capacitor continues to charge. When the input is terminated, output falls to zero as the capacitor discharges. As the value of Rc increases, amplitude of output decrease and output decreases and output waveform becomes linear. It is because charging current does not vary much through a high value resistor. Constant current through a capacitor gives linear output. If input is a square wave, the capacitor charges and discharges from -ve voltage to the positive voltage input.