I'm putting the finishing touches to a proposal that I hope allows me to teach a short course at the local high school this summer or autumn for seniors who plan on entering the sciences. It's a course I've wanted to do for 20 years, drawing on info I've pulled together over 40 years, and I'm confident it'll provide the typical student with new perspectives.
That's because I know from observation that even some with years in the technical fields and academia have long forgotten how to address basic topics ranging from technical terminology to helping their students understand a problem in the simplest way.
Who understands the everyday words we use? I'll find that out first, providing some terms that are appropriate to analog design. One key term is “linear.” The graph of the equation for a straight line is y=mx + b. When that graph is representing a linear system such as an amplifier, we usually use the x-axis for the input signal and the y-axis for the output signal. We usually consider the system to be linear only if the line passes through the origin. Or put another way, y=mx + b is linear only if b = 0.
Now, 25 years ago, I explained this to a class of graduate students and their professor, none of whom accepted it. Even after I drew a line that crossed the y axis at 5, thus defining a machine that delivered an output (an offset) with no input!
I'll be providing a few more math examples. How about symbolic division? Everyone divides a numerator by a denominator to secure a quotient expressed by a number. But most don't realize that the quotient can be letters or symbols (i.e., resulting from a direct division of letters by letters), which sometimes comes in quite handy.
Another important area for students is “dimensional analysis.” Your dimensional analysis may be correct but yet the equation you've derived might not be. I'll give numerous examples.
I'll cover some circuit applications. Few people seem to notice that a power supply rectifier/filter and an AM diode detector (for recovering the audio from an RF carrier) are basically the same circuits and can be analyzed similarly. Moreover, they say they know oscillators, but couldn't fashion a simple proof to show that oscillation initiates from the system's inherent noise.
I'll be asking students to bring meaning to an audio-amp spec that has 0.1 percent THD in the context of our inability to hear distortion in the music below 5 percent. I'll also be asking why efforts to match an RF power amp to its load (to secure efficiencies up to 90 percent) is not at odds with the maximum power-transfer theorem (50 percent efficient). Surprisingly, this topic was a subject of intense debate among engineers in a respected radio magazine a few years back.
I haven't yet read a clear, simple explanation in an elementary textbook of the counter-EMF phenomenon in a resistor-inductor circuit. The words most often used, “equal and opposite,” tend to lead to true confusion at some point relating to the “instantaneous” applied-minus-back voltages. Some authors are just beginning to address it, and contributors to the various web fora are still creating ingenious constructs to explain what they think happens.
Taking a step back, there's the matter of “convention,” which apparently runs afoul of energy conservation principles when electrons “flow” from the negative terminal of a battery through a resistor, do work, and yet come out of the resistor at a higher potential. Now the so-called “field-dynamics” explanations say energy flow is opposite in direction to that of electron migration — but it's a bit of obfuscation, I think. Some recent texts imply electron flow is from the plus terminal through the resistor and then to the minus terminal. But plus or minus may be more than just about declaring a “convention.” Let's illuminate.
I could provide many more examples. But my initial goal this summer will be getting young people to inspect the ground floor before they even think of “high technology.”