Measuring energy

One day I was hanging around the Fremont offices of Credence and sauntered by a classroom in the training area. The door was open and the class was on Mixed Signal, so I stuck my head in to see if I recognized anyone. Living and working in Oregon is so great, but I missed my friends in San Jose, so I was always looking for a way to catch up. I did see several people I knew and they recognized me. While the trainer was lecturing, one of them piped up and said, "Hey, I bet Dan knows the answer to that question!" Now my interest was piqued. The question written on the corner of the white board was this: "Why is Glitch Energy measured in nanovolts per second?" I laughed. It's not at all obvious what this nV-s thing is, I'm sure they don't teach it at MIT. I replied, "It's not nanovolts per second, it's nanovolt-seconds, it's the product of voltage and time. Come on, it's energy!"

I got a nice thank-you for that, and I was glad to help out. I don't remember where I picked that tidbit up, probably from revamping the Credence DSP library manual that was seriously in need of an update back in the day. And it's not obvious if you pull out your little black Pocket Reference manual or check the Wikipedia entry for energy. Electrical energy is measured in Joules and is equivalent to Watt-seconds, not Volt-seconds. But in DACs, amplifiers and other electronic components, we can't measure Watt-seconds, because the current is virtually nil, and we don't really know how much current will be flowing when the signal gets to its final destination. It might be a video signal going to a CRT (back in the day), or it might be an audio signal going to a set of earbuds, or it might be going to a rock concerts 80,000 Watt speaker array, so it's not fair to call it energy in the mathematical sense, and yet it's not fair to not call it energy either, since it represents energy that is, thus far, unrealized.

That is why I never refer to energy in Joules. In Glitch Energy, and in Distortion, I always refer to energy in Volt-seconds or more commonly microvolt-seconds. It's the area of a waveform that is different from what it is supposed to be, like in the graphic above. Here I show how much energy is removed from the peak of a sine wave with various degrees of distortion. A 1% distortion removes 0.8558 uV-s of energy from a 2Vpp sine wave@1KHz. A 2% distortion removes 2.414 uV-s and a 4% distortion removes 6.83 uV-s from the same peak. We know from a previous article that when you remove a portion of a sine wave, the harmonic signature exactly mirrors the harmonic content of the feature that was removed. Once we measure the area of the distortion, we can figure out how different distortions cause different harmonic signatures. You can't understand a physical law until you quantify its parameters, and that is what I did when I researched and wrote Distortion. I own this physical law, because I created the tools to understand it.

When I struggled with how to quantify the distortion, I invented a new parameter I called Total Distortion Energy, or TDE for short and proposed using it instead of THD. THD is a seriously flawed measurement based on idiot assumptions about how harmonics work, and thus far, every single scientist, professor, engineer and author has gotten it wrong on harmonics (and I really enjoy beating them up for that). TDE quantifies the total potential distortion energy in Volt-seconds. not in Joules, partly because, again, we don't know what the final current is going to be, so we don't know how many Watts this signal will end up driving, but also, in the case of TDE, it is potential energy, not real energy. A distortion anomaly does not announce itself to the world by saying "Hey, look at me!" Oh no, distortion hides, and that is why we have to do things like THD tests (ridiculous as they might be) or TDE tests, which are very similar to linearity tests done on a DAC or ADC. Kind of like a rock stuck in the tread of your tire, hidden in the wheel well of your car. You won't know about it until you start driving. Then that "thump thump thump" will tell you that something is wrong. Pull over, and it may be hard, or even impossible to find, because without motion, just like in an amplifier without a signal applied, all is well. Apply a signal again and you see the "thump thump thump" that we call harmonic distortion. Drive faster, the frequency changes, just like the harmonics increase in frequency as you increase the frequency of the stimulation sine wave in your THD test. But pull over, get out your voltmeter and you'll never find it, because it takes an activation signal to tease out the evidence of the anomaly.

So when you are reading my book, please don't go on a rant that Dan doesn't know what he's talking about, that energy is in Joules, not this uV-s crap. If the bloody thing needs a name to make you engineers happy, call it Prestons, my middle name (and the last name of the leader of the wagon train that got my family down the Oregon Trail). I've got Bullard-this and Bullard-that plastered all over the place, and Dan's Rules are 30,000 views strong, so you can't use my first name either. Or just stick with microvolt or nanovolt-seconds. Just don't call it nanovolts per second or you'll sound like one of the myriad of idiots out there with a degree who still spell dB as db.