Day 25: Frequency Dependance

Frequency Dependance

Today we talked about weird stuff that wasn't on our test and that we didn't have homework on. So I have only a cursory understanding of what we did today. Bear with me. Here goes...

We worked on finding poles and zeroes today. This happened when we would have a variable frequency. So it would get faster or slower with time. In order to represent this, we left j and Omega in the equation and go about finding a ratio. We either found H(omega) = V/I, I/V, V/V, or I/I. Once we found that, we would replace j*omega by 's'. Then we could solve for the poles (when denominator equals zero, AKA: asymptotes) and zeroes (where the top equals 0).

Here's another example. In this case, we are asked to find H(omega) = V_0/I_i. We then find the zeroes on top and bottom in order to get the holes and zeroes. In order to find our equation, we are able to use Nodal analysis of the circuit.

Professor mason showed us a code where we able to graph the function we were given. The point of inflection is where the pole is. We can see that it happens at omega = 10^1 rad/s.

Finding poles and zeroes in a RLC Circuit for H(omega) = V_o/V_i.

Signals With Multiple Frequency Components

In this lab project, we calculated the magnitude response of an electrical circuit and used this information to infer the effect of the circuit on some relatively complex input signals. In particular, we will apply signal composed of sine waves of different frequencies and sine signal with time varying frequencies using sweep.

Here is our RC circuit. Nothing spectacular. Just regular stuff.

This is our addition of sinusoids in a single function. You can see the input wave in yellow and the output wave in blue. This is the input and output signal at 500Hz

This is our addition of sinusoids in a single function. You can see the input wave in yellow and the output wave in blue. This is the input and output signal at 1000Hz.

This is our addition of sinusoids in a single function. You can see the input wave in yellow and the output wave in blue. This is the input and output signal at 10k Hz. Although it looks larger than the other 2, it's actually not. I should have included a picture of the scales in these pictures. Unfortunately, I didn't. You may take a point off for my folly.

We then changed the frequency to a sweep, which made it from low to high in a specified time. Chris had his phone in front of mine as I was trying to get my picture. But don't blame Orphan Chris, he doesn't any better. The input signal is in blue, and the output frequency is in yellow.