Wireless Power

I have a number of friends who are seriously worried about my sanity. Not because I sometimes have the greatest ideas for anti-gravitating devices or clean nuclear power. Nah, they are used to that. In this case they worry because I spent last week shouting at my laptop. More specifically, I was cursing the whole internet! I was looking for some insights regarding the 'wireless power' that I read about. I actually found a lot of articles. But they are all more or less identical copies, and they all explain nothing - but that with an impressive amount of words.

After a week or so, I gave up. It then occurred to me maybe one or the other reader of our blog understands more about the technical details, so here is what I found out with a lot of open questions.

The issue is how wireless power for home use could work. That is, we are typically talking about distances of some meters or so, over which we want to transmit energy to power technological devices (say, your cellphone), preferably without roasting every human in the room.

To set the base, energy can of course be transmitted without wires. There are generally two ways how this can work:

One is to use electromagnetic radiation. E.g. your microwave does that. Actually, every bulb does that. The problem with this energy transport is if you want to use it over useful distances you either have a sender that broadcasts the energy into all directions, and a receiver that picks up only a part of it. This means a lot of energy is just lost. Or you focus the sender's radiation on the receiver, which means for moving targets you have to track them. (The microwave is a box that avoids radiation loss by reflection, and you don't want to sit in it).

The other possibility is using inductive coupling. In this case, energy is transferred from a sender to the receiver by using the very near field, and the radiation loss is negligible. This technique works pretty good and very efficiently and is in fact used to recharge many devices. The problem is that it only works on really short distances (say, a centimeter or so).

Neither of both ways sounds very useful for wireless power at home. Now, while I was scanning through these articles, I found out that there are currently two ideas on the market that rely on different schemes.

A) The one has been proposed by a group of physicists from MIT, Marin Soljacic (assistant professor of physics), Aristeidis Karalis, and John Joannopoulos (professor of physics). They have a paper on the arxiv about it: physics/0611063. I could also find these slides from a talk one of them (M. Soljacic) gave. There is a news article on BBC, and the story has been echoed with slight alterations, e.g. here, here, or here.

B) The other one is the technology used by a company called Powercast. They have a website that you find here. It it almost void of any information. They have a form that you can fill out and they send you some pdf-files. These again hardly contain any information (except some general explanation about the allowed limits on power density). If you don't want to fill out the form [1], the pdf's are here: 1,2,3,4. They apparently have presented their device on the consumer electronics show 2007, see e.g. here, here, here, or here (they are all more or less identical).

Let me first comment on A: The paper says they propose an 'efficient wireless non-radiative mid-range energy transfer'. Efficient means there is little energy loss. Mid-range means it potentially operates on the distances that we are interested in. Non-radiative means it doesn't use radiation. The idea that they build up upon is a resonance effect. You know that from your car. Your engine causes vibrations, and if you accelerate their frequency changes. If the frequency of the vibration coincides with the resonance frequency of some parts in your car (say the CDs in the glove box) they will also start to vibrate. This does extract energy from the engine, just that for the car this is a totally negligible (though annoying) effect.

Now the technique of A proposes to use a receiver and sender system that are resonant objects. In addition to that they state that they do not use the radiation field for this. Note that a field can very well be time-dependent (oscillating) without actually having an energy flow to far distances. For the sender and receiver they consider two examples: disks and loops. The paper does hardly contain any calculation, it seems there isn't very much one can do analytically with these boundary conditions. But electrodynamics can be treated numerically without too much complications, so that's what they have done. Figure 2 from physics/0611063 shows how that field would look like for the two disks (sorry, I removed the figure due to copyright reasons, see update note below).

Interesting is also Figure 6 which shows how the field gets distorted by a wall (to the right), and by a by sample (the square) that simulates a human (again, sorry, I removed the displayed figure, please check the paper) . In both cases, there is not too much distortion which is really promising. As they write 'the system performance deteriorates [...] only by acceptably small amounts'.

I was wondering why the 'human' isn't placed between the disks, wouldn't you too? But I have to say I find it actually reasonable. As long as you don't hit the resonance frequency you probably don't distort the field too much. A human body is very unlikely to contain resonating parts. Though I wouldn't want to have a pacemaker in such a room. More generally, one should ask how other technological (and metal) objects affect the field. Also, what does the field look like if sender and receiver are not parallel to each other?

But okay, I thought, great. So far I can make sense out of this. But this is the static configuration, in which case there is not really a sender or receiver. It's just two coupled systems. But to describe the realistic situation, one disk (loop) has to be the source that 'powers' the other one. The above figure is perfectly symmetric, so it can't describe this situation.

In particular the question is where is the energy flow localized in that case? I mean, energy is a locally conserved quantity. It has to get from the sender to the receiver somehow. My naive guess would have been, it takes place in that cylindrical part of space whose end-caps are the sender and receiver - this intuition relying on the simple fact that photons like to travel in straight lines. I was looking for something like the Poynting vector of that field, but couldn't find anything. The only 'explanation' I found was from Howstuffworks, which says:

"Electricity, traveling along an electromagnetic wave, can tunnel from one coil to the other as long as they both have the same resonant frequency. The effect is similar to the way one vibrating trumpet can cause another to vibrate."

This, excuse me, is simply bullshit [2]. We're talking about a classical system, energy doesn't just 'tunnel' somewhere. The vibrating trumpet transfers its energy via air molecules. Try it without air, you'll see. (You also find the tunnel-explanation in the BBC News article). In this article at physorg, you will find the statement 'Most of the energy not picked up by a receiver would be reabsorbed by the emitter' which doesn't make sense to me either. Photons don't just turn around and fly back if they were not absorbed.

The reason why this puzzles me is that their paper considers as an example a 'useful extracted power' (p. 15) of 10 W (p.16). Now I would expect this power to be transferred between the two loops, that is, it for a diameter of 30 cm, it is distributed over a surface of roughly 1000 cm². Distributing the power over a surface that large does of course significantly lower the power density relative to that of a cable. But still one finds a power density of 10 mW/cm² (The FCC limit e.g. in the frequency range 30-300 MHz is 0.2 mW/cm²). One can of course make the loops larger, just that - if you ask me - already a diameter of 30cm doesn't appear so very handy to me.

In addition to this, I have tried to recall how these resonance effects work. In the symmetric configuration (none of both is a source), there is a phase shift between the oscillations of both coupled systems, and energy is transferred periodically from the one to the other. On the average, this does not lead to an energy flow. In case energy is 'used' on one side, an average flow will take place. However, the energy of the total field is typically significantly larger than the fraction that is transferred. I am not sure I understand all the details, but it seems to me that indeed the extracted energy is only a small fraction of the total field. Then, the power density of the total field is even larger than the above estimate, even though a large part of it does not lead to an effective energy flow, but just goes back and forth [3].

I looked at the slides from the talk, and it seems to me that the configurations examined there indeed have a source and a receiver. But since I didn't hear the talk I am not sure, and again I couldn't find anything about the energy transfer. So I wrote an email to the guy who posted the paper on the arxiv, Aristeidis Karalis. He kindly explained:"Think of two penduli connected with a spring. If you move one, energy will be moved to the other and then back and so on. The energy stays in the system and does not leak out. It just jumps from one to the other back and forth." I am not sure I can make more sense out of 'jump' than out of 'tunnel'.

I repeated my question on where the energy flow takes place, but it seems I exhausted his patience at some point (well, I know, I can be really annoying). Interesting is also what he wrote regarding my question why the human sample wasn't placed between the plates:

"The system of dielectric disks is more affected from extraneous objects than the system of loops. I initially made calculations for the 'human' between the two disks, and the numbers were still viable but worse. Therefore, I chose the positioning presented in the paper, because for application where humans are present most probably the loops would be used, while for applications where disks would be used (e.g. optical regime) the materials have much smaller indices and losses."

But as I said above, I actually believe that a human wouldn't make a big distortion because it's unlikely to hit the resonance frequency.

I then looked who's who on this photo, and I thought maybe it would be more helpful to ask Dr. Marin Soljacic. So I wrote him an email, but he didn't reply - at least not yet[4]. And this is where this story ends.

Then let me summarize what I think about A. If there really is very little energy loss, then it seems to me this energy flow has to take place around the axis between sender and receiver and is roughly distributed over a surface of their diameter. If the efficiency of that is indeed almost independent of the sender's and receiver's relative positions and orientations, this means it is somewhat like an automatically working tracking mechanism. The problem is then that the energy density shouldn't be too high between sender and receiver. (Or you'd want to make sure you don't get in the way.) I am not too good with numbers (famous for loosing factors of 10⁶ or so). So I don't know - given the limits on the power density are fulfilled - how long would it take to charge the average device [5]?

Now to B: In essence the idea is using a broadcaster that operates in 900-MHz range with acceptably small power density. They call that the 'omnidirectional power beacon' and it 'will recharge devices within about a 1-meter range' [source]. This energy can be received by a device they call 'power-harvester'. Since there are constraints on the allowed power density, the field can not be too large which means one can only use it to power really small devices. As they say:

"We have a technology that's here today, with FCC approval, that sends RF signals through the air to power very low- power devices directly or to recharge battery-powered devices," said Powercast vice president Keith Kressin. "Our wireless systems can recharge batteries in any consumer device smaller than a cell phone, from up to a meter away." [source]

It seems they actually have working products, and had a demonstration that impressed many people last month. I have to say though, I don't think I would want to work in an office where LED lights start gleaming through energy they extract from the radiation field around me. No matter if you tell me the limits are compatible with what the government demands.

"You can forget their orientation, forget the use of coils; just watch the LED get brighter the closer you place your device to the Powercaster."

This technology seems to have been developed mainly by Dr. Marlin Mickle and collaborators from Pittsburgh. I checked some of his publications, to find out how efficient this power transfer would be. I found a lot technological details about antennas, but not what I was looking for (I could not access all of the papers). If you do better than I, please let me know.

Besides me feeling uneasy with sitting in that power transmitting field, my problem with B is that I am afraid there might be a considerable loss into radiation. In particular, unlike this article from the Alternative Consumer says, this can hardly be very 'green' . The Alternative Consumer essentially repeats Powercast's information sheet that says nice things like 'Powercast Reduces High-tech Waste' because 'Continuous recharging of batteries via the Powercast Wireless Power Platform has the potential to reduce the huge waste stream of batteries to a mere trickle'. Indeed, instead of rechargeable batteries you then use the power-beacon and -harvester, and instead of transmitting power with negligible loss via a cable you radiate it generously into your apartment where most of it goes byebye to outer space.

In addition, I wonder what happens if the guy in the apartment below me installs a 'power beacon' it his ceiling. And my neighbor to the right. And to the left...

To summarize: I wouldn't buy neither A nor B.

Update, April 17th: Yesterday, I sent an email to one of the authors of physics/0611063, Aristeidis Karalis, asking whether it is okay that I display the figures from paper. He replied that the paper is in the publication process and asked me to remove the figures. I was kind of afraid that would happen. So, I am sorry for the inconvenience, but you'll have to look at the pdf-file.

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Footnote 1: You can fill in the address fields with x, it works. They sent only the requested files and no spam.

Footnote 2: The use of the expression 'tunneling' is most likely due to a misunderstanding. The electromagnetic field configuration of the proposed system makes use of the Whispering Gallery modes which have an exponentially decaying tail. From the solution of the wave-equation this is similar to the tunnel-effect in quantum mechanics. Just that in electrodynamics the amplitude is that of the electromagnetic field and not - as in quantum mechanics - a probability amplitude. The typical 'tunnel effect' in which a particle 'jumps' through a classically forbidden region has nothing to do with the above described resonance.

Footnote 3: As Stefan pointed out in this comment, the ratio between the transferred power and that of the total field is of order 1000, which means the total power density would be in the kiloWatt range - far above the allowed FCC limits.

Footnote 4: Yes, I checked the junk folder. I found it indeed possible that PI's highly efficient filter discards MIT-senders as spam.

Footnote 5: As my husband just taught me, with a power of 1.5 W it takes 2 hours to charge a common battery of type AA. That is, the transmitted power they considered is very realistic to applications, and going below it makes the scenario considerably less appealing. To meet the limits on the power density, you either have to wait 100 hours, or increase to diameter of the loops to a meter or so.

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TAGS: WIRELESS POWER, ENERGY, PHYSICS