First-Order OP AMP Circuit(Integrator)

In this experiment, we will use op-amp as an application with an additional capacitor to maki it into a integrator.
With the integrator, we shell see the change of waveforms for 1000Hz of sine,triangle, square waves


Here is the diagram of circuit

If we do analysis of this circuit and treat the op-amp as an idea op-amp. Also by making R_f>>R_i, will make the current through the capacitor equal to the current trough R_i.

using KCL
we obtain
V_in/R1=ic+(-V_out/Rf)
V_in/R1=-C*(dV_out/dt)
V_out=-1/C*int((V_in/R1) dt)+V_C


Next, we assemble the circuit and have a AC power supply run into the circuit and oscilloscope hook up into the computer to see the change in the wave form

Next, we shell see the picture that appear on the computer


1. Sine Wave

The blue wave is the input wave
the result is in red, which is a inverted sine wave


2. Triangle wave

We can easily see the input is a triangle wave
the output wave is trying to make it into a square wave, but with the lack of the equipment, we  can also see the top of the wave is trying to make it into flat line

3. Square Wave

The input clearly is in a square shape
The output is look somewhat like triangle shape or spike shape



Question

When we have a DC component present in the circuit, the capacitor will act like an open switch, thus give us infinite resistance. In this case, the out put voltage will always be the saturated voltage due to the op-amp. Even with high frequency, DC offset will add up as time pass by, and eventually end up with saturated voltage. Thus, we need to add a resistor that is parallel to the capacitor to get rit of any charges that will store in the capacitor.