Day 16 - 2nd Order Circuits

Topics Discussed

On day 16 of the ENGR 44 course, we discussed 2nd order circuits. We discussed heavily the importance of understanding the initial conditions of RLC circuits and how they can be used to determine the behavior of these circuits. We also discussed source-free circuits and the tools and equations that can be used to uncover how these circuits behaved. We did a multitude of problems focusing on whether a system was damped, over damped, or critically damped. (Fig. 1) Additionally, we did some practice with source free circuits with granted initial conditions. (Fig. 2). We further derived some expression that we would commonly use throughout these types of problem. (Fig. 3)

Fig. 1

Fig. 2

Fig. 3

Series RLC Circuit Step Response Lab

In lab today, we investigated the voltage response of an RLC circuit when inputting a square wave voltage. We intended to find the alpha, tau, natural frequency, damping ratio, and other various pieces of information relative to our circuit. We first drew up a schematic for the circuit and found the according pieces of information that would be used as our theoretical values. (Fig. 4) Once this was complete, we proceeded to create the actual circuit. (Fig. 5) 

Fig. 4

Fig. 5

Upon completion, we ran the circuit and proceed to analyze the voltage response. (Fig. 6) We drew up several experimental values and compared them to what was originally expected.

Fig. 6

Summary

Upon completion of the lab, we were drawn to one value in particular that stuck out, which was our measured/experimentally calculated tau. We had originally expected a much shorter period for a single oscillation but found one to be relatively 1/4 of a second. This may have been accounted for in the additional resistance of the circuit, which would have increased our alpha and thus decreased our tau.