So far in talking about adiabatic circuits we've been talking about
the logic circuits themselves, and have been neglecting the power supplies.
But the power supplies are a very important part of the total energy dissipation
of a system. It doesn't do much good to avoid dissipating energy
within our circuits if we still end up dissipating a lot of energy within
our power supplies.
(Actually, it does do some good, as it can help prevent the circuit
from overheating, but it doesn't help from a perspective of battery lifetime,
or net cost of power.)
We want our power supplies, like our adiabatic logic circuits, to be able to recover and reuse most of the system's energy from one cycle to the next, rather than dissipating all or a large fraction of it on each cycle.
1. It should supply precise, reliable, and consistent voltage levels. Why? Because if voltage levels are different from one signal to the next (or one cycle to the next) it will mean significant voltage drops across transistors when we turn them on, even when we thought we had arranged for the voltage levels to be the same on either side.
2. It needs to produce many different voltage waveforms in different phases. Different versions of fully-pipelined schemes require various numbers of rails from 4 to 36. But as I mentioned last time, you can always get by with at most 12. But, that's still more than the 2 or 4 clock signals that most irreversible processors use.
3. It needs an efficient energy-recovering design. The standard parameter used to characterize energy efficiency in energy-transforming or oscillating systems is called Q, the "quality factor" of the system. Q is essentially the ratio between the total energy being transformed by the system on each cycle, and the energy that is dissipated. In other words, it's the reciprocal of the fraction of energy that is dissipated per step. Obviously we want Q to be as high as possible. If Q of the power supply is only 100, then our adiabatic system can be at most 100 times as energy-efficient as an ordinary irreversible computer that dissipates all of its electrical energy on each cycle. Whereas if Q is better, then we might do better.
Typical Q's attained in typical electrical osciallators are not enormously high, maybe a thousand or so, but I don't know fundamental reasons why osciallatory systems can't be designed with higher Q. Part of the problem is losses through emission of electromagnetic radiation, although this can be alleviated in well-shielded transmission lines.
Q can be as high as a billion for mechanical vibrations of pure crystals at low temperatures, or for moons orbiting planets. Whether mechanical oscillations of solids could be used to generate good fast high-Q voltage signals, I don't know yet. I need to look at characteristics of piezoelectrics.
4. Not only should Q be high for oscillations at reasonable speeds, but we'd like it to scale up, in proportion to cycle time, to levels that are as high as possible. The dissipation per cycle in the logic circuits themselves scales down as frequency is decreased; if it does not also scale down this fast in the power supply, then at low speeds the power supply's dissipation will come to dominate.
5. The voltage waveforms produced by the power supply need to have sections that are perfectly flat, or as near to flat as possible. This is so that voltages across a transistor will match up at the time we turn the transistor on, and so that there are no currents through a transistor when we turn it off.
So in other words, a pure sine wave won't work, because it is only near constant for an infinitesimally short time at the peaks and troughs, and our transistors won't be fast enough to turn on and off during those short times, especially given that they are being driven by a similarly slow signal. It takes several thermal voltages' (26 mV @ room-T) worth of voltage change to significantly change a transistor's conductance.
However, I don't know of any fundamental reason why a resonant waveform with flat components can't be generated; I have a proof-of-concept mechanical implementation which I'll show you later.
6. The power supply should be of reasonably small size (and reasonably inexpensive to manufacture) or else it will dominate the weight and cost of the system to such an extent that we might be better off instead buying a larger battery, better cooling system, etc. A good benchmark is that the power supply should be comparable in size to the rest of the system. (As opposed to, for example, 99% of the size and mass of the system just being the power supply!)
Not only this, but the size of the power supply should not scale up as cycle times are increased, or we will find that we can't practically scale the energy dissipation per operation to the arbitrarily low levels that adiabatic circuits are supposed to allow.
Unfortunately, I don't yet know of any power supply technique that really satisfies all these desiderata to my complete satisfaction. But on the other hand, I don't know of any reason why it's impossible, and if the potential benefits from adiabatic circuits were great enough, it might spur more work and development on power supplies, and they might get better.
But anyway, I'll now show the basic power supply ideas that people have come up with so far.
You should know that an inductor is an electrical element that essentially imparts a momentum to a current running through it. The strength of an inductor is characterized by its inductance L.
In the circuit shown, initially transistors T2 and T3 are off, and T1 is on, holding the voltage level to 0 (ground). Then T1 turns off and T2 turns on, connecting the node to this Vdd/2 level over here. Current begins to flow through the inductor, and because of the momentum imparted to it, it continues to flow after the node has reached Vdd/2 (like a pendulum reaching the bottom of its swing), and finally only stops flowing then the voltage is close to Vdd. (Exactly how close depends on the precise inductance and other characteristics of the circuit; if L is high it can be very close.)
Then, T2 turns off and T3 turns on, clamping the node voltage to the Vdd level. (There is a small dissipation here if the node wasn't already exactly at Vdd.)
This is great, it produces a nice waveform with flat tops and bottoms and gently sloping (though not perfectly diagonal) transitions. But there are the following problems:
1. To scale up the transition time (and scale down the energy dissipation), one needs to increase the inductance (analogous to inertia) of the circuit, which generally requires a larger inductor. So the power supply cost tends to increase as we scale down the dissipation of the circuit, an unfavorable relation (violates criterion 6).
2. There is dissipation in turning the various transistors on and off, especially since (a) they must be large devices in order to carry the whole power-supply current load with low resistance, so their capacitance and thus CV-squared energy is large, and (b) we have to turn them on and off relatively quickly compared to the transition time of the output signal.
We can save some energy by driving those transistors adiabatically as well, but this will not be so efficient because (a) the adiabatic transistion time will be shorter, and (b) one then has to design a the power supply for *that* adiabatic signal. You can imagine a nested series of ever smaller, faster adiabatic supplies, each driving the MOSFET of the next-larger supply, with the smallest transistors driven non-adiabatically, but the total per-cycle dissipation of this whole stack of power supplies I think still does not scale down as fast as f, violating criterion 3.
One good idea I have seen proposed to improve this situation is to use MEMS (micro-scale lithographed) electromechanical relays as the switches, rather than MOSFET transistors. MEMS switches are good because their ratio of on-conductance to switching-energy can be much higher than in MOSFETs (by factors of as much as 10-100, perhaps more). (See the table of MEMS switch data on the reading list.) The advantage is due to the fact that a turned-on relay makes a direct, low-resistance, metal-to-metal contact, as opposed to the fairly resistive transport of charge carriers in semiconducting material. The MEMS switches' top speed is lower, but that does not matter so much in these low-frequency adiabatic settings.
But it turns out it's actually not necessary to have inductors at all. One can instead have N different constant-voltage power supplies at a succession of levels between 0 and Vdd, and connect the output to them in turn so that it is charged up in a succession of N steps, each of size Vdd/N. Each step has dissipation (CVdd/N)^2, so the total dissipation of N steps is CV^2/N. The steps take fairly constant time (determined by the RC constant of the circuit) independent of their size, so to scale dissipation down by a factor of N, one needs merely scale the total transition time up by a factor of N, by proceeding in N steps rather than 1.
It may seem inconvenient to require N different DC power supplies, but actually one can get by with only 2 input levels, 0 and Vdd - the rest will be spontanously generated by charge sharing as one goes through the cycle, assuming you have some fairly large (compared to the load) tank capacitors on the intermediate lines.
Again, like the inductor approach, this approach suffers from the fact that you have to turn these N power transistors on and off fairly rapidly, and there will be dissipation is doing so.
And again, people have proposed using MEMS switches in place of MOSFETs here to reduce that dissipation. But still, the scaling is not quite ideal. The size of the circuit still grows as the transition time increases, and the dissipation does not quite scale down as quickly as desired due to the switching overheads.
Unfortunately, in real transmission lines, the impedance increases with frequency, and so high-frequency components of the signal will be retarded more, travel slower, than low-frequency ones. So, any non-sinusoidal wave shape will rapidly degrade.
Becker and Knight's suggested solution is to modify the transmission line to make the low-frequency components travel a longer distance! They do this by inserting an "RF trap" or impedance discontinuity in the line at selected points; these traps selectively reflect high-frequency components of the signal, whereas the low-freqency ones proceed to the end of the line. When the reflected waves return, they arrive back at the central waveform-generation point at the same time, recreating the input signal. With 1 trap one can maintain a 2-component waveform. By inserting more traps, one can increase the number of component waveforms and in theory get arbitrarily close to the ideal trapezoidal waveform.
Unfortunately there are several problems:
1. With only a small number of traps, the waveform is not quite ideal; not flat where we need it to be. To decrease dissipation asymptotically to zero, one would need to increase the number of distinct wave components and thus the number discontinuities in the line which would presumably increase its cost roughly proportionally, an undesirable scaling.
Perhaps one could alleviate this problem using a transmission line with a continuously graduated impedance profile, by modifying the width as you go down the line.
2. As you slow down the frequency (to increase the energy efficiency of your logic) you have to make the line longer. This is unfavorable scaling.
3. As a result of #2, the total resistance of the line increases as you lower the frequency, so the total dissipation per cycle does not quite scale down as fast as desired. (It scales with square root of frequency rather than frequency.)
A potential solution to that problem is to use an evacuated cavity rather than a solid conductor for the transmission line. I think this makes it harder to store significant energies though. Not sure; I'm not an RF expert.
Sigh, all these approaches seem to hint at an ideal supply but don't quite make it! One worries, is it perhaps the case that the desiderata stated earlier are impossible to achieve simultanously, for some fundamental physical reason (rather than just an inadequacy of our engineering designs)?
See the slide... The basic idea is a bunch of mechanical parts moving with low friction - they must be on near-frictionless (well lubricated?) bearings. The basic energy storage element is this rotating flywheel. It can run at speeds as low as desired. This neglects static friction, but we could potentially have contactless bearings using superconductors and magnetic fields, for example, so that static friction would be virtually nonexistent. Actually, there will also be some quantum lower limit to angular momentum, but if the wheel is large, this is infinitesimal.
Energy dissipation from friction in all these mechanical components scales down as desired, in proportion to frequency.
As the wheel rotates, a knob on it slides along this vertical track, moving the track left and right, this moves another knob in an S-shaped track so that that (second) knob moves up and down with the desired waveform; that knob in turn slides horizontally in another track, moving that track up and down, this in turn moves a charged plate of a capacitor up and down, generating a voltage on the opposite plate that varies as desired.
Electromagnetic radiation energy losses from the moving plate scale down with frequency, as desired.
So anyway, this does the job, in principle. Whether this or some micro-scale version of it would ever actually be cost-effective as a power supply, I don't know - I rather doubt it. The point is to say, "Hey, look, the idea of a good adiabatic power supply isn't forbidden by some fundamental principle! Here's an approach that has the properties we want - aside from constant factors."
Whether a good practical supply will be invented is yet to be seen. Given only leaky, high-resistance CMOS devices, adiabatic circuits may not have enough applications where they are more cost-effective than ordinary circuits in order to make investments in adiabatic power supply research desirable. We will see; I have applied for a summer fellowship at JPL to look into the feasibility of using adiabatic systems on spacecraft, where present bulky power and cooling systems may contribute a lot to launch cost; we might alleviate this via low-power circuits. We shall see if there's any advantage.
However, in the longer term, we will see later in the course that for large computing systems built from nano-scale components, reversible operation (if we can achieve it) offers ever-increasing performance advantages over conventional operation as we build larger and larger systems. So at some point, some form of adiabatic computing scheme will become necessary, and at that point $ will be poured into designing good energy-recovery power supplies.
In whatever reversible technology we end up with, I think that the qualitative requirements will be similar, although the waveform might not be over voltage levels but rather some other energy-storing parameter such as magnetic fields or even mechanical forces.