5/2 Series RLC Circuit Step Response

Before, we considered the circuits with only one element (a capacitor or a inductor), and the circuits are first-order.
Today, we talked about the circuits with two storage elements which is known as second-order circuits because their responses are described by differential equations that contain second derivatives.
The main idea of this kind of problems is to get the value of  v(0), i(0), dv(0)/dt, di(0)/dt, i( ∞ ), and v( ∞ ). By determining these value, we can solve the problems easily.
Next, we talked about the source free series RLC circuit.
 
By determining  α  and ωo, we can see what type of this circuit is.
1. If α > ω 0 , we have the overdamped case.
2. If α = ω 0 , we have the critically damped case.
3. If α < ω 0 , we have the underdamped case.
We did a example of the source free series RLC circuit.


Series RLC Circuit Step Response
Pre-lab

This is the prediction of differential equation, damping ratio, natural frequency, and damped natural frequency of this lab.

The picture below is the basic set up for this lab.

The graph below is the result for this lab.

The  rise time of the graph is 1.241ms.
The overshoot is 3.5ms.
The oscillation frequency is 23485Hz.
Out estimated damping ratio, natural frequency and damped natural frequency is in the pre-lab.
Our estimated DC gain is 2.383 (in the beginning of the transient).

Summary

From today's lecture, we learned the source free series RLC circuit and the source free parallel RLC circuit. By determining α and ω 0 , we can determine which case the circuit is. From the lab, we learned how to determine the rise time, overshoot time, and the oscillation frequency. And from the graph, we can see that there is a sudden change when we apply the voltage to the circuit. An automobile ignition system takes advantage of this feature. By creating a large voltage (thousands of volts) between the electrodes, a spark is formed across the air gap, thereby igniting the fuel.