Day sixteen - Exam Day, Day seventeen - Series RLC Circuit Step Response 5/2/2017

Hey guys, today we talked about the second order differential equation, which is RLC circuit. From the name of the circuit, we can know that this circuit consists of three elements, resistor, inductor, and capacitor.

In order for step response to occur, we first assume that certain voltage source is applied to the circuit before.

For RLC circuit, there are some values we have to find first.

They are the very important values we have to find in order to solve the problem.
It is important to remember that the v and i are correspond to the capacitor voltage and inductor current.
In addition, there are two convenient ways to find the v(0) and i(0), which are using the facts that the voltage across the capacitor can not rapidly change and the current across the inductor can not rapidly change.

Lab

Pre-Lab

This is the differential equation, damping ratio, natural frequency, and damped natural frequency of the circuit in the lab.

Lab Result

This graph is showing we have successfully implement this lab. We can see the transient and steady state parts of the Vout.
Our estimated rise time of the circuit is 1.241ms. Note that the rise time of the circuit is the time between the point where the Vout increases rapidly to the point where Vout meet the first steady state voltage.
Our estimated overshoot time of the circuit is 3.5ms, and our estimated oscillation frequency is 42.58 microsecond (23485Hz) .
Here is the way we find the rise time and overshoot.

At the beginning (in transient), the DC gain is 2.383.

Summary:
From today's lab, we have experienced the step response of the RLC series circuit, in our special case, the Vout is a under-damped response. One point to note is that even the Vin is still connected to the circuit while connecting data from Vout, the transient and steady state response can still be attained. Look at the Vout graph we have, the overshoot of Vout is larger than our input voltage, which means that we can use the step response to create a sudden, huge amount of voltage output, such as car ignition system. Very important point is to note that the sudden changing voltage is caused by the sudden application of a dc source. The solution of the equation must have both transient and steady-state response.