Several factors recently conspired to have me dust off an idea I've thought of occasionally for many years. First, I've been having Twitter conversations with some electronics hobbyists in Japan, and even though I gave up on hobby electronics in disgust and discouragement a number of years ago, I'm starting to think that maybe that field is worth another look. Second, I downloaded Qucs. It's an electronics simulation package with a graphical interface that works under Linux, and it's the first such I've found that is actually capable enough to make designing things on the computer a realistic possibility for me. Finally, my current job is ending at the end of the year. The positive side of that is that now I can do whatever I want (if and only if it doesn't require the involvement of any persons other than me); the other side is that my life and my career plans are not going well, I don't see much hope of things getting better soon or ever, and having other things to think about would be nice.
Whatever the reasons, it has come to pass that I'm thinking a lot about this idea I first had many years ago: what about a pipe organ in which the pipes are fluorescent-light tubes?
Understand that I don't just mean a conventional organ (maybe an electronic one with no actual pipes) decorated with lamps in place of the pipes. I mean one in which the special electrical properties of gas-discharge tubes - in particular, their negative resistance - is a meaningful part of the way it makes music.
Part I: Negative resistance, you say?
At first blush it might seem that the idea of negative resistance is obviously nonsense. Doesn't that equate, basically, to perpetual motion? Indeed, if you go looking on the Net for information about negative resistance, it's quite notable that at least in the hobby realm, many of the people writing about negative resistance are clearly cranks. I've spotted a number of negative resistance articles on the same Web sites that carry articles about zero point energy, VLF radio, homemade lasers, and so on. You know the type. There are certainly people who might take a look around my Web site, see some of the other things I write about, and conclude that it's no surprise I too would be writing about negative resistance.
Nonetheless, most people in electronics are reasonably comfortable with the idea of imaginary resistance - that's just what we usually call reactance, right? - and if you're going to allow Z to be an imaginary number it seems like it would be very strange for negative, but real, numbers to be forbidden. The key to what makes imaginary resistance meaningful is that it's talking about AC, not DC, and that's the first clue to how negative resistance could also be meaningful.
Next, look at a battery. You've got a potential difference of let's say 12V across it, and there's a current flowing too (let's say 1A - it's feeding a 12 ohm resistor), but that current is flowing from negative to positive; the direction of the current relative to the voltage through the battery is the opposite of the direction of current through the resistor. Compute R=E/I, 12V/-1A=-12 ohm. The battery is exhibiting a negative resistance at DC; and most of us don't think batteries break the laws of physics. They add energy to the circuit not because of thermodynamic violations but because they're consuming energy somewhere else, in internal chemical reactions. That's the second clue to how negative resistance could appear: it could be coupling energy from somewhere else into the part of the analysis where the negative resistance appears.
Putting these together: it may be reasonable to talk about negative resistance if we are talking about AC, and it may be reasonable to talk about negative resistance if we are talking about a device that adds energy to the circuit. The energy has to come from somewhere, but there do exist places it could come from. These can even be seen as two sides of the same coin, because in the case of AC, it could well be that a device has negative resistance at AC and positive resistance at DC, adding AC power to the circuit by converting DC power. It could be an amplifier or an oscillator, and most of us are willing to believe in those.
Before going further into the theory of negative resistance, let's think about the venerable neon tube relaxation oscillator. You may have built one of these as a kid, if you grew up in the era before everybody's parents started freaking out about these kinds of voltages.
The usual theory of relaxation oscillators - the "lies for children" version - is an hysteretic theory. "Hysteretic" is today's vocabulary word. It refers to things that exhibit hysteresis, which is the phenomenon whereby it takes more of something to start something than would be needed to keep the thing going once started. For instance, thermostats are usually hysteretic: the temperature has to go above let's say 23 degrees before the air conditioner turns on, but then once on, it will remain on until the temperature drops to 21 degrees. Mechanical devices that exhibit backlash are hysteretic. The hysteretic theory of neon tubes teaches that there is a relatively high starting voltage - typically about 70V for the ubiquitous NE-2 glow lamp - and the lamp remains off, with a high resistance, until the input reaches that voltage. Then it suddenly turns on, and draws as much current as it can until the voltage drops to a relatively low maintenance voltage, typically 50V in the case of the NE-2, at which point it turns off.
Consider what happens in the relaxation oscillator above. Most of the time, C1 is charging through R1. The neon lamp is switched off and effectively uninvolved in the circuit (it has a high resistance, something like 100Mohm). The time constant for this RC circuit is 1Mohm times 0.1uF = 0.1s. However, when the capacitor charges to 70V, the lamp suddenly switches on. When it's on, it draws current very fast - much more current than the 120V power line can supply through R1's high resistance. So nearly all the energy to light the lamp comes out of C1, whose voltage drops very fast. When C1 drops to 50V, which happens almost instantly, the lamp switches off again, and C1 starts charging again through R1. We get a sawtooth waveform in the voltage across C1, as shown in the simulation result.
With the component values and simulation assumptions I used, this circuit runs at about 30Hz. Note that's a fair bit faster than the RC time constant of 0.1s would suggest; we're only charging and discharging over a range of 20 volts out of the 120V supply, so it takes less than one time constant to complete the cycle. The actual frequency of operation depends not only on RC and the supply voltage, but also the high and low voltages of the lamp, which in turn depend on the temperature, individual variation, amount of ionizing radiation in the environment (even visible light, but especially UV), wear on the electrode sufaces, and for some lamps it also depends on the decay of radioactive ingredients used in the lamps' manufacture to guarantee a minimum level of ionization. People who actually build these circuits usually build them for a lower repetition rate, like 1Hz or less, to produce visible flashes from the lamp. It's possible to push the frequency up through most of the audio range; it starts to get shaky past 1kHz and with an NE-2 the upper limit is probably about 10kHz, but it's highly variable. I've seen people claim to have achieved as much as 100kHz with neon lamp relaxation oscillators but I'm not sure I believe that.
At this point we should at least be able to believe that some sort of plasma discharge (I've sneakily changed the focus of discussion from fluorescent light tubes to neon glow lamps) could be used for audio in some way. But what about negative resistance?
When it comes to negative resistance in relation to neon glow lamps, the cranks will usually show you a hand-drawn, unscaled, and fundamentally incorrect E-I plot very much like the one below. It nonetheless illustrates some important principles in an easy-to-understand way, so I'm going to stick with the tradition even though this plot is a lie.
This is a plot of voltage versus current. For most ordinary components (i.e., pretty much just resistors - everything else is more complicated), you can understand what the component does by considering how much current it draws at different voltages. The three magenta diagonal lines illustrate the E-I curves of pure resistors with different values. All of them express Ohm's Law, I=E/R, for different values of R (called Z on the diagram, but let's pretend we didn't see that). A high-value resistor produces a shallow line: current increases slowly with voltage. A low-value resistor produces a steep line: current increases rapidly with voltage. And a resistor with a value somewhere in the middle allows current to increase at a rate somewhere in the middle.
I was just talking about rates of increase, and that should have raised a flag. For simple resistors, we can just divide the actual value of the voltage by the actual value of the current and get the resistance and we'll be done. But we could also compute the slope of the curve. That is the derivative: R=dE/dI. For simple resistors, it's exactly the same as E/I. But what about things that aren't?
The dark blue curve on the diagram is supposedly the E-I behaviour of a neon glow lamp. In the lower part of the curve, below point A, it is turned off. It approximates the "high Z" magenta line - behaviour equivalent to a high-value resistor. When the voltage rises past the limit set by point A, it can turn on. Then it switches to the upper part of the curve, above point B. In that state it approximates the behaviour of a lower-valued resistor, as long as the voltage remains above the limit set by B. If we could bias it into the neighbourhood of point X, and it might appear, especially to a crank, that that should be possible, then we would have a situation where although the actual values of voltage and current resemble those for a medium-value resistor (the magenta line through X), nonetheless the derivative of voltage and current is negative.
That's how we can get away with calling it "negative resistance." Elementary thermodynamics is satisfied because E/I is a positive number. We're not getting energy for nothing. But because dE/dI is negative for the neon bulb in this part of its curve, and that quantity was exactly the same thing as the resistance E/I in the case of an ordinary resistor, we have something that behaves in some meaningful sense kind of the same way that we'd expect a resistor with a negative resistance to behave.
Before going on to next installment's discussion of the actually correct E-I curves, let's look at one more version of this incorrect one. This is supposed to illustrate how the relaxation oscillator works.
When the capacitor is at its low-charge point (50V in the example circuit), we're sitting at the lower left corner of the cyan dashed arrow loop. As C1 charges, we climb the lower limb of the blue curve, in the direction of the cyan arrow, to reach point A. At that point the lamp turns on, we jump to the upper limb of the curve, and then as the capacitor discharges (this part is much faster because of the high current) we slide back down the curve to point B. Then the lamp turns off, we jump back down to the lower left corner, and the cycle repeats. This seems to explain the observed behaviour of the relaxation oscillator quite well. By the way, a diamond-shaped cycle on a state diagram like this is pretty much the universal signature of hysteresis. You've probably seen something similar before in physics class, in a discussion of magentization - another example of an hysteretic phenomenon.
It's also quite clear from this diagram how to get the glow lamp to do interesting things for us: we just have to bias it into the negative-resistance region of the curve, the vicinity of X. I haven't yet exactly gone into just what interesting things we could do with a glow lamp biased into that region, but given all this buildup, it seems reasonable to assume that once we achieve it, it will turn out to be something wonderful and strange.
Hey, did you ever try to balance a light switch midway between "off" and "on"? How well did that work for you?
Next installment, coming soon: a less misleading theory of neon glow lamps. In the mean time, you can download a package of Qucs files including the circuits from this article. I'll update the package to contain more stuff as I post additional installments.