05-03-2016

Lab: Series RLC circuit step response

I. Introduction:

Today, we spent some more time to review the inductor and capacitor behave in circuit. Recall that the voltage of the capacitor in DC circuit, in the infinite time, will be the same as the voltage source, thus open circuit. For the inductor, in the infinite amount of time, it will behave like a wire, thus short the circuit

We did some review about the RL and RC circuits

Solving for differential equation, given the RLC circuit

s represents the variable associate with time. Here we solved for s using the quadratic and many algebraic steps

After many derivation, we let the alpha to be damping frequency and w_o to be our natural response frequency, which equivalent to the spring and gravity lab we did back then in 4A

given the RLC circuit, we have to find the damping frequency and natural response frequency, since the delta (b^2-4ac >0) we say that the circuit is overdamped

Some more practice to solve for s, in this case have underdamped, which gave us the imaginary solution.

III. Series RLC circuit Step Response:
This lab will emphasize modeling and testing of a series RLC second order circuit. The circuit will consist of RLC in series, we will measure the voltage across the capacitor

Here is the osilatiion in RLC circuit, this happened because of the bouncing between the capacitor and inductor (the inductor letting more current go through while the capacitor prevents over the time)

Here is our setup of the circuit

Here is our analysis for the pre-lab. There are a total of 3 cases, underdamped, damped, and overdamped

Here is our derivation to find out the two solutions of s

After we found s, we could go back and obtain two more equations to solve for A1 and A2

III. ConclusionFor today lab, we spent most of our time to study the differential equations of RLC circuit. There are a total of three test cases, when the circuit is underdamped (imaginary solution), damped (one real solution), and overdamped (two real solutions), we did the RLC circuit step response to test a series of RLC second order circuit.