# Gas station without pumps

## 2017 February 27

### Understanding semilog plots

Filed under: Circuits course — gasstationwithoutpumps @ 10:22
Tags: , , ,

I realized in doing the homework grading this weekend that few of the students in my electronics course had any intuitive understanding of semilog plots (that is, plots in which one axis is linear and the other logarithmic).  I had been assuming that providing the following plot

Forward voltage as a function of current for a 1N914BTR diode.

would let students see that the voltage grows approximately with the logarithm of the current, and that means that a voltage difference corresponds to a current ratio. Very few students got that from the picture, the formulas, or the description in the text. They almost all wanted to pretend that the diode was a linear device with voltage proportional to current (i.e., that it was a resistor), so that a 6% change in current would result in a 6% change in voltage.  The whole point of using the diode was to introduce the exponential non-linearity, so this confusion definitely needs to be cleared up.

I was going to try to explain semilog plots and exponential/logarithmic relationships in class today, but my cold has gotten so bad that I had to cancel class today. That means I have another 2 days to figure out how to explain the concepts. If any of my readers can think of ways to get students to interpret semilog plots correctly, please let me know. I think that the relationships are too obvious to me for me to help students past their misunderstandings—I can’t get far enough into their mindsets to lead them out of confusion.

1. Show exponential growth using compound interest on a linear graph. This gives them the exponential curve they’ve seen since algebra/calculus. Then plot the same data on semilog axis. Plot a quadratic function on linear scales, then semilog. Only one data set produces straight line with semilog plot, exponential functions. Poor mans curve fitting…

I kinda think it’s a lost cause with today’s generation. Us old farts used to use semilog plots in lieu of processor based curve fitting algorithms from a library.

Comment by Rich — 2017 February 27 @ 20:01

• I expect that almost all the students have seen exponential curves and quadratics, and all the other things you suggest here, but that many have not bothered to internalize what any of it means—it has all been studying for a test, not for understanding. I don’t know that repeating exercises that they have done in high school that did not result in learning will result in learning this time around.

Comment by gasstationwithoutpumps — 2017 February 28 @ 07:29

2. Here is a start at achieving their mindset. Forget everything – everything – you know about logs.

Seriously. They have no clue because (1) they have never made a graph by hand and (2) they have no idea at all what the log function is doing. Most of them forget everything about logs as soon as they pass a class that used them. And semi-log paper? Magic. It hides some things and exposes others, buy you can’t read it if you can’t plot it.

So my only suggestion is to have them plot the data by hand on linear paper, then have them plot y vs logx and logy vs x. They might notice that 3 is 10^3, 4 is 10^4, etc, if you ask the right questions.

Comment by CCPhysicist — 2017 February 27 @ 20:05

• You are probably right about what it would take to get them to understand semilog plots, though I’m not a great fan of hand plotting as a route to understanding (a lot of tedium that many will get nothing from). In any case,I don’t have the time in the course to spend on something that they are supposed to already know—I can afford at most 10–15 minutes of class on filling this hole. Maybe less,since I was so sick yesterday that I had to cancel my classes.

Comment by gasstationwithoutpumps — 2017 February 28 @ 07:23

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