# Gas station without pumps

## 2014 April 11

### Impedance, finally

Filed under: Circuits course — gasstationwithoutpumps @ 21:32
Tags: , , , ,

I finally got a chance to cover impedance in class today.

I started with complex numbers and Euler’s formula ($e^{j\theta} = \cos(\theta) + j \sin(\theta)$), showed them how the amplitude and phase terms could easily be factored out to make a phasor, then had them develop the formulas for impedance of resistors and capacitors.  For capacitors, I had to guide them a bit, but they came up with $Q=CV$, $i = dQ/dt$, and taking the derivative of the voltage.  That actually went a bit smoother than I expected, and almost everyone in the class was participating.

I then had them come up with the circuit for an RC filter (they only know one circuit, the voltage divider, so this was pretty easy). They used the voltage divider formula to get the gain of the filter, and I showed them how to plot it by hand (a Bode plot).  The filter we started with was a low-pass filter, so I challenged them to design a high-pass filter.  This is an easy task, and they almost instantly suggested swapping the resistor and capacitor.  They derived the formula for the gain of that filter, and I showed them the how to draw the Bode plot for it also.

Note: we only do amplitude Bode plots in this class, not phase.  For what they are doing, the phase response is not very important.  I did let them know that there were more advanced classes where the phase response was carefully determined, and that filter design got a lot more complicated than simple RC filters.

I covered in class almost exactly what I set out to do, and the students came up with most of what I wrote on the board, so I felt that the Socratic questioning I used to guide them worked fairly well.  I’ll probably have to give them some design exercises soon, to see if they actually understand the material or were just nodding along with their classmates.

This weekend I’ll grade their second design reports (for the microphone lab), and try to rewrite the week-4 labs, which will be characterizing polarizing and non-polarizing electrodes.  I have a bunch of other stuff to do this weekend also (mow lawn, do state taxes, read a thesis proposal, read a chapter of a thesis, replace the rear wheel on my bike, rewrite the designing courses to tech design talk, write a letter of recommendation for a former student trying to get a green card, feed the cats and the fish, … ). I may have a bit less time than usual this weekend, because I’m cooking for myself—my wife and my son have gone to an admitted-students weekend at UCSB.