How I arrived

People take pretty twisty paths in life to get where they are now. I am no exception. When I was in the US Navy I was enrolled in the AEF (Advanced Electronics Field) under Electronics for a 6 year hitch in exchange for over a year of schooling. As a young undergrad, what could be better than getting paid to learn electronics? And they treated me pretty good, I got instructor duty, class leader, and most importantly, the #1 scorer in my classes throughout A School, And then (inexplicably) came C school, where the 4 year ETs went off to OCS, no, not Officer Candidate School but Over the Choppy Seas and the rest of us got to get up to speed on the latest in Radar. Problem was, I was designated an ET-N (Communications in some unknown militaryspeak dictionary), but at the time the Navy was updating the Comm school, so I went to Radar school instead. I eventually kicked ass and graduated 2nd in a class of 19, which wasnt bad. But by the strangest coincidence I retained my ET-N classification, so my next school was a Crypto school which is a communication function and, at the time, Crypto was all digital which, being a Radar guy was no sweat for me, but the the Communications guys (ET-N) who where coming in from the fleet were totally unprepared for digital and they did poorly. Meanwhile I ate it up, it was super easy for me! I took a second class there and got #1 on both of my classes at Mare Island, California. Then off to my duty station, which has a big Sonar site. So here I am, a Comm ET with Radar training at a Sonar site. OK, fine I guess. I did great, solved a lot of problems and did some things I could tell you about, but then I would have to kill you.Anyway, fast forward to my work with Nextest, pretty much my last job in the ATE biz. I sold a Nextest tester to HP in Boulder, Colorado. Yep, I sold a tester to a company that made testers, but the manager I spoke with couldnt afford an Agilet 83000 so he decided a Nextest Lightning was the way to go. I agree. They bought it and Marvin from the applications group in the Philippines came to Boulder to get the project going. Marvin did a fantastic job, but one day I got an email from him.How can I measure Duty Cycle without a Time Measurement Unit?Because the Nextest Lightning didnt have a TMU and the customer (HP) started saying they made a mistake choosing to buy the Nextest tester, and perhaps should have bought an Eagle or something else with a TMU. To prevent them from canceling the order and shipping the tester, and Marvin back to us, Steve Holder and I worked on it in our office in Tigard, Oregon using a digital pin to capture a square wave from a pulse generator. We came up with a solution that should work great we decided, it measured the duty cycle of everything we could throw at it, so we sent it off to Marvin hoping to hear good news the next day. But the news wasnt good, according to Marvin, it was way off, and we had no ideal why. We asked Marvin to send the captured wave in a file and we did an FFT and the spectrum looked like this:And thats fine, a 1% duty cycle rectangle wave would have both odd and even harmonics. But look closer, and ignore the obvious aliasing. The highest signal here is the 4th harmonic? In any square/rectangle wave shouldnt the fundamental be the largest signal? Makes sense right?Well, no, thats not right. We were using hearsay from other engineers about the rules for harmonics AND we were not capturing coherently. Now, I am not a prude that says you must always capture coherently, but I understood the dangers, or so I thought. Lets zoom into that spectrum and look at the fundamental (1st harmonic) and the 4th.It may not shock you to hear that in my capture, I captured 14.25 cycles of the fundamental (as seen in the upper pic) and exactly 57 cycles of the 4th harmonic since 4*14.25 = 57, which thanks for the FFT, shows up in bin 57. Yeah, this FFT stuff is hard man, I have to remember the number 57 for the span of two seconds! How will I ever survive?Now look again at a closeup of the spectrum:So the reason that the 1st harmonic (the fundamental) is smaller than the 4th harmonic (by a lot) is because bin 14 had to share the fundamental energy with bins, 13, 12, 10, 9, and 15, 16, 17, 18, etc, etc. But every signal drop of energy was contained in bin 57 since the 4th harmonic was accidentally captured fully coherent, so that bin, the 4th harmonic was taller than the fundamental bin, even though that should never (almost ever) happen.What we did was devise a solution using the Bunneman function and it worked great! Disaster avoided, customer happy, and I sold a tester to a tester company, which was a great feeling! But think about it, I would have never figured out how harmonics worked if I had relied on non-coherent sampling where you clearly do not get a proper read-out of the amplitudes as I showed here. Even if you window it, you cant get past the damage that non-coherency does to your measurements. Nobody in the world figured out harmonics simply because they were doing non-coherent captures and then trying to rely on the results, like I did in the beginning of this exercise. That stupid mistake almost cost me one of my most important sales: The sale of a Nextest tester to another tester company, HP.Matt Mahoney, you were a great man. Thank you for pushing coherent capture so I could make a discovery like this. I wish I had met you in person, but here is a secret: My accomplishment is greater.