Day 16

Series RLC Circuit Step Response

Here we are testing RLC circuits in a series which results in second order differential equations. We can analyze and test the step response of these circuits. Here we can test can theoretical values derived from equation that we did in last with actual experimental equations. The types of behaviors we are looking for are damping ratios and natural frequencies. We can also design any circuit to behave in any of the three functional modes of overdamped, critically damped, or underdamped. We can do this without changing the frequency or DC gain of the circuit.

Pre-Lab

Here we have calculated a certain RLC circuit which came out to be underdamped. This is where we use Euler's Method to replace the complex general solution with cosine and sine.

Here we are further playing with the differential equations to relate V(out) with V(in) for the circuit. Many calculations were performed such as damping ratio, natural frequency, damped natural frequency, DC gain, and any frequency of oscillations we would expect to see in the step response of the circuit.

This is the output of the under damped circuit. As you can see it has a forced response which limits the amplitude and we can see it dip off gradually as it reaches zero. This is the graph you would expect to see by adding the cosine function and sine function together.

Once again, we have some more sexy circuit pics

Overall, this lab wasn't too difficult where we saw the behavior of a simple RLC circuit in a series and were able to see how it function depending on the ratios between alpha and omega.