Day 15 (Day17 on notes)

Today we went over op amps in RC circuits, Did an Inverting Differentiator Lab, and learned about singularity functions.

The differentiator op amp is an op amp circuit where the output voltage is proportional to the rate of change of the input voltage. Also, any noise can result in high or low saturation.

The integrator op amp output voltage is proportional to the integral of the input voltage. This op amp can lead to saturation fairly quick so it requires a feedback resistor to be added.

Inverting Differentiator Lab:

The purpose of this lab is to test the behavior of the differentiator op amp. We will then compare measured output voltage with theoretical values.

The first picture is the input voltage of 1V at 1kHz and the bottom picture is the output voltage.

The first picture is the input voltage of 1V at 2kHz and the bottom picture is the output voltage.

The first picture is the input voltage of 1V at 500Hz and the bottom picture is the output voltage.

Above we see the theoretical output voltage amplitudes and in pink are the measured output voltage amplitudes. The large percent error may be due to the op amp having saturation. It can be noted that as we decreased the frequency of the input voltage, the percent error decreases so it may imply that our op amp is more efficient at lower frequencies. When taking this into account, we can conclude that the output voltage is proportional to the rate of change of the input voltage.

Above is an example of circuit analysis using singularity functions to approximate the current in the
RC circuit shown. Singularity functions are functions that are either discontinuous or have discontinuous derivatives.

Above is another example of circuit analysis that uses singularity functions.