Day 15 Inverting DIfferentiator

The objective of this lab was to examine the forced response of a circuit which performs a differentiation, where the output voltage is the derivative with respect to time of the input voltage.

Given the circuit below:

By using KCL and setting current through the resistor equal to the negative current through the capacitor, we derive the input/output relationship to be:

Current through a capacitor is the derivative of voltage multiplied by the capacitance value. Because the input voltage is supplied to the negative terminal of the op amp, we have an inverting function.

For our lab, the input voltage is a sinusoid in the form of 

Vin(t) = Acos(wt)

Below is the final derivation of our output voltage as well as the calculations of the output voltage from different frequencies of our input voltage.

Below is the final construction of the inverting differentiator circuit:

Using the oscilloscope function of the analog discovery, we measured the following output voltages from frequencies of:

f = 1kHz, 2kHz, and 500Hz respectively.

After a closer look at the capacitor used, it turns out that instead of being C = 470nF, it was in fact C = 4.7uF. All pre-lab measurements were done using the 470nF capacitance value. In order to get more accurate theoretical and measured values, the calculations were redone. As instructed, here is a table comparing the measured outputs to the true theoretical outputs:

Once again, the objective of this lab was to observe and understand the characteristics of an inverting differentiator OP Amp. Throwing a capacitor into the mix with our use of OP amps seemed very convoluted and intimidating at first. Once we consider the nature of current and voltage through and across an OP amp, the task of utilizing an inverting differentiator op amp seems a lot less daunting. Again, we see one of the many ways that OP amps can be connected in a circuit, and the usefulness of it.