(4/25/2017) Day 17: 1st Order Circuits and Inverting Differentiator

Day 17: 1st Order Circuits

Lab: Inverting Differentiator

This lab will allow my team and I to examine a differentiator circuit and the effects it places on any input voltage.

A differentiatior is essentially an op amp with a capacitor on the input and a feedback resistor.

Prelab

To begin, we had to understand symbolically what the output would be after processing.

Using what we were taught in class, the output would be something similar to this equation:

With a formula to build from, we simply took the derivative of the input sinusoid:

V(in)=A*Cos(wt)

(where w = 2*pi*frequency)

From there we were given actual values to calculate. The values for the circuit were 

A = 1V

R = 680 Ohms

C = 1 micro Farad

Once a frequency was determined, we were set to begin.

Procedure:

 To begin we fabricated the circuit with the specified values used in the calculations

then we input a series of sinusoidal voltages at varying frequencies. This gave us a chance to compare the input/output with the oscilloscope feature of the analog discovery. Important to note here is that the yellow channel (1) is the input and the blue channel (2) is the output.

(All input waves have A = 1V and offset = 0V)

First was a wave at 100Hz 

and its output.

Then at 250Hz...

and one at 500Hz

From these valuable results, we can see first hand the behavior of this circuit and compare it to our theoretical understanding!

Post Lab:

For the post lab analysis we tabulated the results in terms of the amplitudes possible for both the measured (from oscilloscope) and calculated (from the prelab) values.

Last thoughts:

From these results, we can see that the inverting differentiator did indeed take the derivative of the input! Between the two values found for each frequency, the percentage difference was not far off either. The two waves can also be seen to be 0.5pi from each other in terms of phase. Which is the difference between a Cosine and Sine wave.