Day 15

Inverting Differentiator

For this lab we were looking at the forced response of a circuit that performs a differentiation. This means that the circuit will output the derivative with respect to time of an input. To make things interesting we will use a sinusoidal voltage of varying frequencies and compare the output with our theoretical analysis.

Pre-Lab

With the power of MATH we derived a formula that allowed us to find what the output voltage would be in our circuit. The calculated theoretical values of V(out) for frequencies of 1khz, 2kHz, and 500Hz are below.

Because we all love sexy circuit pics, here is the built circuit for our Inverting Differentiator.

Data

The first frequency we used was 1kHz. From the graph we can see that the peak value is 1.1544V. Our theoretical value at 1kHz was 1.388V. This means our percent error was 16.8%. This is probably due to those flying monkeys with ninja stars again. Note to self, we need to train monkey bodyguards asap.

The second frequency we used was 2kHz. From the graph we can see that the peak value is 2.217V. Our theoretical value at 2kHz was 2.217V. This means our percent error was 20.1% which means there is still experimental error in the form of ninja stars.

The third frequency we used was 500 Hz. From the graph we can see that the peak value is 0.603V. Our theoretical value at 500 Hz was 0.649V. Our percent error was 7.1% which means that with a lower frequency our experimental errors aren't as noticeable.

Here is just a collection of all the data that was collected for the experiment.

Our percentage error for all the experiments range from 7.1% to 20.1%. The equipment we used could be the cause of these errors as there are slight inaccuracies in the resistors and the capacitors. Overall, we got familiar with using capacitors along with op amps. This is the exact same technique I used to develop my circuit for my Function Generator where I needed to integrate a square wave to get a triangle wave.