Inverting Differentiator Lab

Inverting Differentiator Lab

Overview: In this lab we examined the forced response of a circuit which performs differentiation. By applying sinusoidal voltages of varying frequencies, we were able to analyze the output voltage, which was a derivative of the input voltage with respect to time.

Design: We designed the following circuit to execute the experiment:

The resistor was equal to 470 ohms, and the capacitor was 470 nF. 

For 1V sinusoidal input voltages, we used three different settings:

V1: frequency = 1KHz

V2: frequency = 2KHz

V3: frequency = 500Hz

Because the circuit is an inverting differentiator, it was expected to have the following output:

Following that logic, the expected output values were as follows:

Construction and Execution:

We then constructed the circuit just as the schematic above outlined:

R was measured as being 465 ohms

C was measured as being 424 nanoFarads

^^^^ View of the constructed circuit from the side ^^^^

 ^^^^ view of the circuit from above ^^^^

 ^^^^ Up close view of the circuit ^^^^

Results:

The results are as follows:

 ^^^^ Oscilloscope results from V1 ^^^^

Vout = ~1.4 Vin, and is phase shifted

  ^^^^ Oscilloscope results from V2 ^^^^

Vout = ~2.45 Vin, and is phase shifted (notice the change of vertical scale for Vout)

 ^^^^ Oscilloscope results from V3 ^^^^

Vout = ~.65 Vin, and is phase shifted

Analysis: 

As the data suggests, the overall effect was relatively predictable; the only frequency which had any truly inaccurate results was V2, and it wasn't terribly inaccurate. Unfortunately, the source of that additional error is unknown, and further investigation would be necessary to pinpoint it. It may have just been a fluke. Regardless, this experiment still clearly outlines the behavior of forced inverting differentiator circuits.