1 Fish 2 Fish Reactive Fish 2nd Order Reactive Circuit (Blue Fish)

2nd Order things today! The only hard part of these suckers is solving initial conditions.  Everything else (damped response included is solved by a known second order equation.  So we're going to do a quick review of them from my book, and then study Ideal Autotransformers instead! Autotransformers are some nifty little circuit elements with Theoretically Infinite Impedance. They're a 3 prong component, and they can be used to get large step up or step down magnitudes.  I'm curious why the book didn't talk about their non-ideal maximum gain; I'm now curious whether the max would be significantly different from that of other transformer types. Ideal Transformers have no losses.

LAB: Series RLC Circuit Step Response
So we set up a Series RLC circuit with:
R = 1ohm  <-- We had problems with our calculations until we realized the actual circuit resistance is ~2.5 ohms
L = 1mH
C = 100 uF
We did calculations for the predicted values of alpha, natural period, and driven period, see below.:

And our measured quantities, with appropriate calculations.  See the top box for the measured quantities, and the bottom box for the predicted current response over time.  The current response was generated by the math above.

Our vastly series RLC circuit; Wires: Yellow is square wave, Red and Orange are probes, Black is ground.

And lastly, the voltage response of the capacitor over time! We used 2V Square wave driven at 2Hz, to allow plenty of time for 5*Tau to pass between Oscillations.  At 2Hz, we require 5Tau to be no longer than 1/4 seconds.  We show in our calculations that we expect Tau (1/alpha) to be (1/500) seconds, which is much smaller than 1/4s.  It turned out that we could have gone for a significantly higher frequency input square wave, as the the circuit had realistically 1.5 additional Ohms resistance beyond the 1Ohm resistor.  The effect of a higher resistance is a higher alpha, which scales inversely with Tau.  Our measured Tau was .0004s, about 5 times quicker than the expected .002s expected Tau.

Pi pip Cheerio, Jesus visited me after class today, and I discovered we like many of the same shows.  He might bring the new Rick and Morty card game that I've heard a little about to game night Friday! Scooooree