Spark gap logic

Kragen Javier Sitaker, 02020-09-20 (updated 02020-12-16) (25 minutes)

Thinking about Marx generators last night, I realized that their traditional elements — two-electrode air spark gaps, capacitors, resistors, and a high-voltage, low-current DC power supply — are probably sufficient to implement universal sequential digital logic, It may be limited to a few kilohertz, but air-gap flashbulbs can produce microsecond-level discharges when cooled by a quartz heatsink, so faster speeds might be achievable.

A Marx generator is a simple sort of RC relaxation oscillator used as a source of high-voltage pulses when efficiency is not important. A series of capacitors in series, separated by similar-sized spark gaps, are charged through a resistive network connecting their anodes and another connecting their cathodes, which, as long as little current flows, respectively maintains the anodes at similar voltages and maintains the cathodes at similar voltages, so the voltage across each spark gap is nearly the negative of that across each condenser; once this voltage rises to a high enough level, the air in the gap experiences avalanche breakdown with a large current and effectively connects two capacitors in series, immediately overwhelming the breakdown of the adjacent spark gaps. This very rapidly produces a chain reaction and a very high voltage, which, as I understand it, then discharges on a timescale primarily limited by the self-induction of the elements of the system, commonly nanoseconds to microseconds.

(Ordinary electrostatic discharges, like from walking across the carpet and touching a doorknob, have rise times in the range of a nanosecond or so, so the rise time will not be the limiting factor in performance; the recovery time will.)

Without the voltage gain, you can build such a relaxation oscillator with a single RC timing circuit with a spark gap in parallel with the capacitor. Paschen’s curve has a minimum at one atmosphere at 327 V and 7.5 μm, tailing off to linear growth at 3.4 MV/m, so, for manual work, it might be expedient to work with some 4 kV and gaps of 1 mm. You can easily adjust the period of this oscillator by changing the RC time constant, although the arc ignites at somewhat imprecise times due in large part to the irregular availability of free so-called “seed electrons” at the cathode, provided by photoelectrons or background ionizing light and other particles.

(Common neon-sign transformers provide 2–15 kV RMS at 18–30 mA, according to Wikipedia, a much less frequently lethal current than the typical 500 mA of a microwave oven transformer.)

In particular, it’s straightforward to make a triad consisting of a “primary oscillator” running at, say, 500 Hz; a “reference oscillator” at half that frequency, say 250 Hz; and a “bit oscillator” also running at 250 Hz. (At 1 mm the arc should ignite around 3.4 kV; with a 4 kV power supply, that should take about 1.9RC, and the remaining voltage after the arc extinguishes should be small; so, to get 250 Hz, a 4-ms period, we could use an 10MΩ resistor and a 210 pF capacitor, a 1MΩ resistor and a 2100 pF capacitor, and so on, although the resistors will start to get rather hot at lower resistances.)

In isolation these three oscillators will tend to drift relative to one another, but I think this can be remedied. If we use another capacitor to couple the voltage spike from the triggering of the primary oscillator into the reference oscillator and the bit oscillator, we can advance the timing of the reference oscillator and the bit oscillator so that they run at exactly half the frequency of the primary oscillator, if they were running slower. The voltage spike early in the charging process won’t be enough by itself to fire the spark gap, but when the capacitor voltage is already nearly high enough to strike a spark, it will easily overwhelm the dielectric strength of the air in the gap.

Now the phase relationship between the reference oscillator and the bit oscillator is quantized at either 0° or 180°, so the phase of the bit oscillator stores a single bit of data.

For reliable storage, it is essential that the free-running frequency of the reference and bit oscillators be slower than or equal to that of half the primary oscillator; otherwise, they may spontaneously fire early, resulting in phase drift and eventually a bit error. Various expedients are available: the use of a slightly larger resistance or capacitance, of course, but also a slightly larger spark gap that will never fire without the excess stimulation provided by the primary oscillator; or a resistive network that charges the capacitor up to only a fraction of the power supply.

It is worth mentioning at this point that a cascade of two or three low-pass RC filters before the spark gap, rather than a single one, can provide a more desirable voltage waveform at the spark gap — one that remains lower for a longer fraction of the cycle, thus widening the voltage safety margin against early firing.

Now that we have a reliable way of storing a bit, we have the problem of constructing digital processes that evolve in time rather than merely remaining stable, by coupling two or more bit-storage devices. And in particular we want to be sure we can achieve chaos or instability, known in the world of digital logic as “fanout” or “amplification”. The example of the Marx generator shows that this is definitely achievable.

One easy way to achieve amplification, though stepping outside the framework of the Marx-generator parts mentioned above, is step-up transformers.

Air-gap flashes pass a lot of charge between the main electrodes at, typically, 20 kV, to produce the bright flash, triggering this with a quartz-insulated “ignition tube” electrode at a much higher voltage like 70 kV, but a much smaller amount of charge due to a lower capacitance. The higher voltage provides initial ionization in the gap, which triggers the discharge of the lower-voltage but higher-energy arc.

This provides energy gain, but not voltage gain — a high voltage is used to switch a lower voltage. A direct way to attack this problem is by using a pulse transformer to step up voltages, so that a spark at a relatively low voltage can produce a lower-current pulse at a much higher voltage, used to trigger other gaps.

But, as we have seen above, more indirect routes are also available.

For example, if a 3400V spark gap has been charged up to 3000V, then a 700V impulse will trigger it to conduct, discharging the 3000V down to perhaps 50V or 150V. This impulse can be coupled in via a small capacitor, requiring a correspondingly small amount of charge and energy. This can be facilitated by a small resistance between the spark gap and the 3000V-charged capacitor — in this way a 700V impulse coupled in thru a coupling capacitor need not charge the 3000V capacitor, only the capacitance of the spark gap itself, which will typically be in the picofarads. If we suppose the spark gap is 10pF and the pulse has a rise time of 1μs, a few hundred kilohms would suffice, a number not normally considered a “small resistance”, but it’s one or two orders of magnitude smaller than the other resistances discussed above.

Another more indirect route is used by the Marx generator itself: rather than using a small coupling capacitor to trigger the discharge of a larger storage capacitor, we can couple the triggering pulse through the large storage capacitor itself, suddenly increasing the voltage on its other end by a factor of up to 2.

A third possibility involves resistive networks. By charging a small capacitor (to ground) through a resistive network from two or more other capacitors (to ground), its voltage can be brought rapidly to a weighted average of their voltages, and if a spark gap is in parallel with it, it will either discharge repeatedly through the spark gap, or not, according to whether its terminal voltage is greater or less than the spark gap’s breakdown voltage. The pulses thus generated can be used to trigger other, higher-energy spark gaps (and their time of occurrence can be synchronized with the primary oscillator by coupling in a little of the primary oscillator to them), or the resulting larger current draw on the “input” capacitors can be sensed.

A particularly interesting possibility here is the use of such a threshold device as a phase detector. Given reasonable waveforms on two bit oscillators, their instantaneous sum will rise above some threshold for a while each cycle if they are in phase, but for a high enough threshold, not at all if they are out of phase. This provides us with the operation XNOR; combined with negation and access to the reference oscillator, we can construct in some sense all boolean functions.

This same sort of threshold device may be of particular interest as a display pixel, glowing or not according to whether its voltage reaches the threshold and thus provokes repeated discharges. Low-pressure plasmas, xenon, and mercury vapor coupled with phosphors may be useful in boosting visible light output for a given power level.

A fourth possibility is to interrupt a continuing arc, ballasted for example by a resistor or the self-inductance of the wires, with a voltage pulse that temporarily robs the spark gap of the tens of volts necessary to continue conduction. This, however, seems much more precarious and sensitive.

Encoding bits directly as voltage levels rather than oscillator phases seems like it would be more challenging, if feasible at all, unless you are spending the enormous amount of energy required to keep a spark gap in a state of continuous arcing, or find a way to employ glow or corona discharge like an old Dekatron, which I suspect would cost significant speed. So I suspect the phase-encoding approach, although less simple, is probably more practical.

The above falls short of being a fully worked out design for digital sequential logic using spark gaps, resistors, and capacitors, but I think it amounts to a convincing argument that it’s practically doable, though only over a fairly narrow voltage range in the normal atmosphere (400–4000V); it might be easier to debug something closer to the middle of that range, like 1200V, than designs near the limits, like the 4000V I was considering above. Reducing the pressure or substituting a friendlier gas like argon (127V at 10μm) might help.

Sources of deviation from designed behavior include:

Another crucial question about such devices is to what degree they can be miniaturized and sped up. Near-kilohertz discharge rates should be straightforwardly achievable, but neon-tube logic topped out around a kilohertz due to the relaxation time required for the gas to deionize.

Intuitively I would expect higher-ionization-energy gases to recover faster — this is why air-gap flashes use air (primarily nitrogen) instead of the more efficient xenon, because it gives submicrosecond recovery times, and N₂ (1503 kJ/mol = 15.58 electron volts) is close to optimal here, though, e.g., hydrogen (1488 kJ/mol = 15.43 electron volts) is close. SF₆ (≈15.8 eV) may also be worth considering. Perhaps also higher pressures accelerate the recovery time, accounting for the difference between the millisecond recovery time of an ordinary low-pressure xenon camera flash and the 10μs cited for xenon in Wikipedia’s air-gap flash article. Electric-discharge machining routinely uses hundreds of thousands of sparks per second in, typically, deionized water, which is pumped through the spark gap at a high flow rate; typically this uses several hundred volts to initiate the spark and an average of tens of volts and several amps during cutting.

Both higher pressures and higher ionization energies would tend to promote miniaturization.

So, because both air-gap flashes and EDM routinely have submicrosecond recovery times, I think submicrosecond recovery times are probably feasible, putting this kind of logic in the performance range of 1960s CD4000-type CMOS.

Nanosecond-scale recovery times would probably be more challenging and would probably require mechanical removal of the ionized dielectric; for example, if the spark gap is 10 μm wide, it the electrodes can very reasonably be 10-μm-diameter rods with holes in their center for coolant flushing. For the coolant to travel the 5 μm required to clear the still-ionized material from the interelectrode gap in, say, 100 ns, it needs to be traveling at 50 m/s, Mach 0.15, and slightly faster passing through the hole, which is probably achievable; waterjet cutting machines achieve many times that speed through holes in that size range, and the use of a gas would decrease the viscosity far below what a waterjet must withstand. This amounts to a volume flow rate of under 10 microliters per second, again, plainly within the bounds of feasibility. We can conclude that active dielectric flushing is a practical way to increase spark-gap logic operational frequencies well into the megahertz, though probably not to 100 MHz.

What about energy usage? If each spark gap has a capacitance of 10 pF and discharges at only 500 V, it contains 1.25 μJ in its electrical field at discharge time, which will be almost entirely dissipated by the spark; at 1 MHz discharge rates this amounts to 1.25 W. We might thus suspect that active coolant flushing of some sort is necessary to prevent the electrodes from entirely vaporizing, quite aside from its potential utility for accelerating recovery times.

However, the minimal capacitance of a spark gap of 10 μm diameter and 10 μm spacing can be approximated with the infinite-plate formula C = εA/d, which gives some 70 attofarads in this case, five orders of magnitude smaller, so in fact the spark-gap capacitance will not be the limiting factor in such cases, even using a high-permittivity dielectric like water.

This in turn suggests an electrical energy cost on the order of 10 picojoules per bit operation, comparable to modern CMOS, although of course that doesn’t account for the energy cost of pumping all that dielectric through the gap. Also, such low energy costs per operation probably require much higher operational frequencies — for RC = τ = 2.1 ms as above, you’d need a 30-teraohm resistor, which would normally be called an “insulator”. So 1 nJ is probably achievable but 10 pJ may not be.

Conductive-mesh spark-gap electrodes may be a more effective way to deliver light, dielectric, and coolant to the spark gap, permitting as they do the use of spark gaps with electrodes much larger than their interelectrode spacing without diminishing the fluid flow.

Over timescales not too long compared to the relaxation (deionization) time of a dielectric, it may be feasible to use a flowing fluid as a delay-line memory. An input spark gap in the center of a tube of, for example, rapidly flowing atmospheric-pressure xenon, produces a series of plasma blobs which are rapidly carried downwind, still glowing; some 10 μs later, an output spark gap also in the center of this tube detects their presence by virtue of the discharges they ignite at well below its usual breakdown voltage. A partial vacuum behind a hole in one of the electrodes of the output spark gap sucks these blobs into the interelectrode gap. To minimize the time-domain degradation of the memory waveform, this entire stream of memory plasma is kept well away from the walls of the tube by the xenon flowing around it, which ideally would be in inviscid flow so that even the curl of the flow field remains close to zero. Operated at 10 MHz such a tube could store at least 50 Manchester-encoded bits; gases that relax more slowly than atmospheric-pressure xenon could afford larger capacities and less-demanding operational frequencies.

Somewhat surprisingly for a digital-logic device that can plainly be constructed by hand from Victorian-era materials, the above dimensional figures strongly suggest that microscopic realizations of this family of devices might be not only feasible but even practical, particularly with higher pressures and modern insulators like teflon (as opposed to sealing-wax and gutta percha). With adequate plumbing, they might be capable of speed rivaling modern solid-state electronics, or at least 1980s solid-state electronics. Spark gaps of under a micron should be effective at a megapascal or so of gas, or perhaps at atmospheric pressure with liquid dielectrics.

Another amusing application of such relaxation oscillators might be as microphones: below the Paschen minimum, even a very small change in the electrode spacing should produce a very large change in the breakdown voltage of the spark gap and consequently both the frequency and the breakdown voltage of a free-running RC oscillator. (I’m not sure if it also increases the jitter.) Above the Paschen minimum, it should produce a smaller, nearly linear, but still fairly reliable change in these variables.

The oscillation period also depends, of course, on the resistance and capacitance, and in many applications it may be more practical to modulate the capacitance rather than the spark-gap size. 3 mm of ordinary glass ought to provide about 30 kV of dielectric strength, or fifty times that if fused silica instead; the 2 cm² of a finger touch, coupled with the relative permittivity of around 5 for glasses, gives a capacitance of about 3 pF, which may be a detectable touch. Lower voltages and thinner materials may be a more practical way to detect human touch, or simply mechanical deformation of air-dielectric capacitors through levers.

DTIC document 633669 from 1991, “Hydrogen spark gap for high repetition rates”, reports 10-μs recovery times to 17% for a 1.4 MPa 2.5-mm “unblown” hydrogen spark gap and 100-μs to 42%, about an order of magnitude faster than air; this is attributed to hydrogen’s high thermal diffusivity. That is, by “undervolting” the gap to 17% of its normal breakdown voltage (some 120kV), they can trigger discharges at 100-kHz rates, or 10 kHz at 42% of its normal breakdown voltage. Recovery to 90% takes about 1 ms for hydrogen and 10 ms for air, “dominated by the cooling time of the hot channel” rather than its deionization. It also points out that narrower gaps permit closer gas contact to metal surfaces, thus cooling the gas more rapidly, as well as lower inductance and resistance, and that the gas requires some time to recover its density after being rarefied by thermal expansion. They were working with three-electrode trigatron-type devices and report that “the recovery time varied little from millijoules to kilojoules of transferred energy”, though it would be unsurprising if the picojoules I contemplate above did result in significant variation. (Hopefully the smaller energies would also result in longer electrode life than the hundreds of shots at which they reported substantial electrode wear.)

Above I haven’t considered inductance, but of course at high enough speeds at a given length scale, inductive impedance will dominate resistance. Decreasing the length scale also helps with this.

The related DTIC document A636361, “A laser-triggered mini-Marx for low-jitter, high-voltage applications”, describes an interesting way of triggering spark gaps with ±700-ps 2σ jitter — by using ultraviolet light to ionize SF₆ in the spark gap (in this case by a frequency-quadrupled Q-switched Nd:YAG laser) it is possible to ignite a plasma in a precharged spark gap, which then activates a Marx generator with rise times in the range of 2 ns. There are a variety of ways that such spark gaps can detect light, ranging from the reduced jitter from photoelectric seed electrons to this sort of ionization-induced ignition-voltage reduction, and of course a traditional Geiger counter is nothing more than a spark gap arranged to detect ionizing light and other particles.

A low-voltage way to try out some of these ideas is to replace the spark gaps with transistors, or perhaps diodes, in reverse avalanche mode, as in Look Mum No Computer’s Super Simple Oscillator, which uses two unspecified terminals of a 2N3904 in parallel with a 10μF capacitor. Another, better-explained variant of the design uses a 2N4401 with the emitter toward Vcc and the collector toward ground, in series with an LED and in parallel with a 3300μF (!) capacitor. (Thank you very much to Hideki and splud on ##electronics for linking me!)

Folklore says red LEDs suffer reverse avalanche discharge around 5V and often survive it, so they might be an alternative to the transistor or spark gap. Their lifetime might be limited in this application, or it might not. Probably something like a 1N4001, or any ordinary rectifier or small-signal diode, would have an inconveniently high breakdown voltage, which increases the chance of damage to the diode, as well as power consumption and electric shock risk.

In either case you’re depending on properties of the components that are not specified by the manufacturers because they’re irrelevant to their usual uses, so consistent results from component to component may be hard to obtain.

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