21-Apr-2015: Inverting differentiator

PURPOSE

The purpose of this lab was to construct an inverting differentiator from an op amp and observe the behavior of its output voltages.

PRE-LAB

Figure 1

Before setting up our circuit, we calculated the theoretical output voltages of our inverting differentiator at three different frequencies. We assumed the input voltage to be a cosine function and found its derivative to predict the output voltage at each frequency. This process is shown in Figure 1.

PROCEDURES

Figure 2

After the pre-lab exercises, we set up the circuit as shown above in Figure 2. The circuit was very similar to an inverting op amp, except that a capacitor was connected between the input voltage and the inverting terminal instead of a resistor. As mentioned before, we applied three different input voltages with three different frequencies to the circuit. We then observed the output voltages on an oscilloscope (Figures 3, 4, and 5).

Figure 3: Frequency at 1 kHz

Figure 4: Frequency at 2 kHz

Figure 5: Frequency at 500 Hz

As it can be seen from these graphs, the amplitude of the output voltage increased as the frequency of the input voltage increased. This is what we expected to see based on our pre-lab exercises. As a matter of fact, we compared the theoretical and experimental amplitudes of the output voltages and found their percent differences. These values are shown below in Figure 6.

One last thing to note is that there were not supposed to be any phase differences between the input and output voltages according to the calculations done in the pre-lab. These phase differences can be most likely attributed to the delay between the input of the signal and the response of the circuit.