Series RLC Circuit Step Response Lab

Series RLC Circuit Step Response Lab

Overview: In this lab we modeled and tested series RLC second-order circuits. In the first part of the lab, the step response of a circuit wass analyzed. Then, in the second part the same circuit was modified to be critically damped, and then once again its step response was analyzed.

Design: 

We designed the following circuit to test the step responses:

R was set to 1.1 ohms

L was 1 microHenry

C was 470 nanoFarads

Below are our calculations, predicting the damping ratio, resonance frequency, and damping frequency:

*From the picture above*

Alpha = damping ratio = 4.5 *10^5 Hz

Omega = resonance frequency = 1.543 *10^6 Hz

Omega d = Damping frequency = 1045 Hz

Alpha/Omega = Damping ratio = .292

Construction and Execution: 

The circuit was fed a 2V step function at 100Hz, allowing the circuit to stabilize between each step. 

Results:

 ^^^^ Triggered response of one step ^^^^

^^^^ Close up view of the oscilloscope window ^^^^

^^^^ best fit line applied to voltage peaks of the system ^^^^

The best fit exponential line gives an alpha value of ~12, which is wildly inaccurate, but then so is the fit line, so that is being excluded from our results. That being said the rest of the results are as follows:

Experimental Omega = 1.543*10^6 Hz

Experimental Omega D = 8.70 * 10^3 Hz

Experimental Damping Ratio = .292

Analysis: 

The corrupted experimental alpha value really impacted our ability to do a successful analysis. As you can see, the inaccurate experimental Omega D hints at something having gone incorrectly with our initial or post calculations. However, the graph looks accurate, so perhaps there is an error involving the inductor, which may not have a negligible amount of resistance. That would seriously impact our results, since the amount of resistance being used in a mere .9 ohms. Also there is other system resistance which could be throwing off the accuracy of our calculations.