4/28/2015

RLC Circuit in Series

For this lab we built a RLC circuit in series. Using the Analaog discovery we supplied a step function into the RLC circuit. This is a second-order circuit and after a few calculations we found the circuit to be under damped due to  α < ω 0 .

Results

Above are our calculations. Although not shown on the board, for under damped i(t) = e^(-at)(B1coswt+B2sinwt) 

Graph of Response

The circuit was supplied a 2V step function at a frequency of 100Hz.

Summary:

Today we analyzed second order circuits. Second order circuits contain two circuit elements which in this case are capacitors and inductors. They are know as second order circuits because their response is described by differential equations involving second derivatives. The response of a second order circuit also includes a dampening where; if α > ω 0 the circuit is over damped, if α = ω 0  the circuit is critically damped, and if α < ω 0 the circuit is under damped. Each case has a unique equation that can be used to describe i(t). Our lab emphasized the testing of an RLC circuit where the measured and expected results are compared. For our circuit, we predicted that it would be under damped and our graph of the results supported our expectation, which was the gradual loss of the initial stored energy. α determines the rate at which the response is damped.