Day 16 (Day18 on notes)

Today we learned about second order systems - RLC series circuits and performed a Series RLC Circuit Step Response Lab.

Above we have a RLC circuit in series and derived a characteristic equation based on the second order differential. 

We then let alpha=R/(2L) and omega=sqrt( 1/(LC) ) from our characteristic equation. Based on these individual values, we can determine the response of the RLC series circuit as shown in the bottom of the picture.

Here is a small summary of the equations for the overdamped, critically damped, and underdamped responses along with graphs.

Above we worked on a series RLC example.

Series RLC Circuit Step Response Lab:
The purpose of this lab is to

We had to build a RLC circuit with the values listed above and measure its voltage across the capacitor when a 500Hz 2V square wave for input voltage. We see that our circuit will be underdamped.
On the bottom we had to find a value for C that would make our circuit critically damped but we didn't have components in class to do so.

Above is our circuit.

In the fist picture we have our input voltage and the second picture is the output voltage.

With an exponential curve fit, we get V(t)=0.43*exp(-2340t). This was done manually so we are unsure if the curve fit was done correctly which would explain why our alpha is significantly smaller than our theoretical value.