05-05-2016

Lab: Step response of LRC in parallel and series circuit
I. Introduction:
After many exposures to natural response of LRC circuits in parallel and series on Tuesday, today Professor Mason lectured us about step response, the step response is actually natural response except that we add one independent in the circuit, which would add another term when we solve for second order differential equation

Given some constraint conditions, we were asked to find out the circuit here was under damped, critically damped, or over damped

Here are some constraint condition to solve for the problem, since we have parallel LRC, we have di/dt=V/L

Here we have a critically damped condition, the second term has an extra compared to the third term.

II. LRC step response lab:

1. Pre-lab: 

Given the setup above, we were asked to find the change( shoot) of the voltage and current across the capacitor and the inductor. We focused mostly on the right part of the circuit which has LRC in series.

Here is the setup of our circuit, we used the channel 1 and 2 to measure the voltage and current across the capacitor and the inductor

Here is the pictures of our graphs, the orange is the voltage of the input, the blue one is the voltage across the capacitor. 

Here is the zoomed-in graph of voltage across the resistor

Here is our setup of every circuit, there was slightly different numbers between our lab and the theoretical yields, this could due to the fact that we have +-5% in our lab components.

III. Conclusion:
For this lab, we spent much our understanding the behavior of step response LRC circuit, which just adds one more term to the natural reponse LRC circuit, the rest are the same. We also spent some time understood the step response LRC by doing the lab, the lab was almost the same we did on Tuesday except we just needed to add one more voltage indendent source.