Inverting Differentiator

In this lab, we are going to make Inverting differentiator and input sin wave in input voltage. We are going to calculate the estimated output voltage and finally, we are going to measure the output voltage at different frequency sin waves(at same amplitude).

We first calculated output voltage as a function of input voltage and time.

We calculated at what frequency we have gain of 1(V_o=V_in). We found that happens when the frequency is 234 Hz.

Setup(1)

Setup(2)

Setup(3)

We measured actual Capacitance and Resistance, it is 0.945 μF and 668-ohm respectively.

We measured output voltage at 500Hz, 250Hz, and 100Hz.

100Hz 1V

250Hz 1V

500Hz 1v

At the end, we calculated theoretical V_out and compared with the measured value. It has very small percentage of difference.

Summary: This lab went great, we got our estimated value. we calculated the circuit will have gain of 1 at 234Hz and we got gain of 1.1 at 250 Hz, so we would get value very close to 1 when we input 234Hz sin wave. We have higher gain in higher frequency because when we differentiate input voltage the angular velocity-omega will go out and multiply with amplitude due to chain rule. Omega can be also expressed as 2fπ, f stands for frequency.