Today, someone on Freenode ##electronics was asking about wireless communications between AVR microcontrollers with only passive components, so I was interested in the available energy for harvesting and possibilities for low-power RF communication. I started reading about ferrite loopstick antennas and energy harvesting from broadcast AM radio (as suggested by user Bga3 on Freenode ##electronics). These antennas are normally useful up to about 5 or 10 MHz and can be salvaged from old AM radios; more exotic ferrite mixes are viable up to 50 MHz.
As mentioned in Arduino radio and Could you do DDS of comprehensible radio signals with an Arduino?, the usual AM radio band is around 0.5 MHz to around 1.7 MHz. I don’t think the AVR is the best choice for this kind of thing, since it’s fairly power-hungry and slow, but even the AVR should work. The AVR has PWM generation circuits that can generate frequencies up to 8 MHz, so some degree of amplitude modulation at a few hundred kHz should be doable.
The highest power available for broadcast radio station licensing in the US is 50 kW, while there are many 10-kW radio stations around. So let’s suppose you’re located 10 km from ten isotropic 10-kW AM transmitters, which would seem to be a common situation in urban areas. Each contributes about 8 μW/m² of radiation (10 kW spread over a sphere of area 1.26 × 10⁹ m²), for a total of 80 μW/m². But you can’t collect all of that energy because loopstick antennas are inefficient. Still, μW-scale energy harvesting seems like it should be feasible. And of course crystal radios were powered entirely from AM radio waves, and had enough power to be audible, if barely.
Research has been done on designing loopstick antennas to be tunable (Chris Trask, “An Active Ferrite Rod Antenna with Remote Tuning” with a high Q factor by setting up a resonance between the antenna inductance and some varactors.
The ARRL Antenna Handbook chapter 4 talks about loop antennas in some detail.
Zungeru et al. describe several previous RF energy harvesting systems in the μW range.
Xie et al. 2012 report harvesting 82 μW using a 10-meter-long horizontal antenna, even though that was just a dipole, and one with the wrong polarization, at that.
The Xie paper contains circuit diagrams and various plots of output voltages, currents and powers. The circuit was extremely simple! One end of the antenna was hooked up to a parallel-resonant LC tank (with, ideally, infinite impedance to ground at the resonant frequency) with a “multi-stages doubler rectifier” hooked up across the inductor (Figure 4 shows that this is a Cockcroft–Walton generator made out of six 1N60 germanium Schottkies and six 0.1-μF caps), feeding an energy storage capacitor to which the microcontroller is directly connected. They report getting 14 volts out of the damned thing — before the Cockcroft–Walton 6× multiplier! There in Xi’an, there’s apparently a 300-kW station 23 km from their site, but they got more power from a 50-kW station at 8.5 km — that’s where the 14 V came from. (But it’s only 1.2 V without the resonant tank.)
Leon-Gil et al. 2018, “Medium and Short Wave RF Energy Harvester for Powering Wireless Sensor Networks”, CC-BY also used a resonant tank circuit and a Cockcroft–Walton generator to step up their antenna voltage, but this one of 6 stages, using a center-tapped loopstick configuration. (Note that the PDF of the paper is not readable with libpoppler; xpdf can read it.) (They also mention that TV broadcasting stations are up to a megawatt in the US, 20× stronger than AM broadcast stations, but are not available in rural areas.)
Leon-Gil et al. also stacked up layers of ferrite in order to get a giant 60 mm × 60 mm antenna cross-sectional area in a compact volume, because (they say, I trust) the radiation resistance of the antenna is jointly proportional to the square of the area and the number of turns, and, astonishingly, not dependent on the length of the rod. They also point out that diode parasitic capacitances provide an AC leakage path that limits the total voltage available from a Cockcroft–Walton generator, which I hadn’t thought of; these parasitics decrease with back-biased voltage, but need to be small compared to the intended capacitance. They used BAT85 diodes, which specify a 200-mV voltage drop and 5-pF junction capacitance, and found that 10-nF capacitors or larger were needed to avoid inefficiency.
They reported 1.5 volts at the input to their Cockcroft–Walton generator and 8 V at its output, providing about 60 μW into a 1-MΩ output impedance — quite impressive for the 100-mm-long antenna they’re using, 100× shorter than the wire in the Xie paper! They report a 3.2% antenna efficiency.
They report that using the center-tapped Cockcroft–Walton configuration doubled their output power over what they describe as a “half-wave” configuration, but I suspect that this is because they were only using half of their winding when they were testing the “half-wave” configuration. In a Falstad simulation, I see in-phase current and voltage both positive and negative in the configuration they describe as “half-wave”, so I think their description is erroneous.
Dyo et al. at the University of Bedfordshire wrote “Design of a ferrite rod antenna for harvesting energy from medium wave broadcast signals” in 2013 (doi: 10.1049/joe.2013.0126). They used an 8-stage Cockcroft–Walton generator made out of Schottkies driven from a loopstick antenna with an LC resonator tuned to a local 150 kW radio station at 909 MHz; in simulation they generated over 1000 μW, up to 9 km away, but apparently they only tested it by powering a 3 μW clock. Their paper is the only one of the ones I’m summarizing here that has a decent review of the existing work in the field, including the Xie et al. paper.
They point out that actually the length of the rod does matter, and the peak for a cylindrical rod is when the rod is 20 times as long as its diameter; its effective permeability rises almost linearly from aspect ratios of 1 to 10, half of the ideal aspect ratio of 20, nearly doubling its value; it gains another 10% going from 10 to 20.
They report a cost-optimized antenna design: they ended up with a 10-mm-diameter ferrite rod that was 200 mm long (a size you might find in a normal AM radio), with 50–500 turns of litz wire wrapped around the middle of it, depending on how weak the signal was — weaker signals needed inverse-proportionally more turns to get the same output voltage. For a sufficiently weak signal, the coil’s self-resonant frequency falls low enough that the design is no longer viable.
Strangely, their optimization results table reports that wire length s varied from 67 meters to 787 meters. These are consistently about 45× the wire length I calculate via nπD, where n is the number of turns and D is the diameter. This seems to be a result of their using 45-strand litz wire.
How much power do you really need to harvest in order to have a usable computer?
I’ve written a fair bit on low-power computers in Keyboard-powered computers, Low-power microcontrollers for a low-power computer, and Notes on the STM32 microcontroller family, and just today I encountered the oversold-as-low-power Renesas RL78 microcontroller line, although that was disappointing in the end. The summary is that you can get useful amounts of computation at around 1 μW, which is a bit smaller than the self-discharge current of a CR2032 coin cell, which contains about 2.2 kJ. Understanding Capacitor Leakage to Make Smart Things Run Longer explains that you have to be careful to ensure your bypass capacitors don’t have more leakage than that if you’re designing, say, a passive IR sensor designed to run for ten years maintenance-free from a coin cell, but that you can do it by using capacitors rated for 10× higher voltages than you need, which will be larger.
Linear regulators dissipate the voltage difference between the input voltage you get and the output voltage you want; this is wasteful if there is a large difference. Below I suggest using a buck converter so that your power usage is the same regardless of the input voltage — this works by drawing current less of the time when the input voltage is higher. But buck converters require a minimal quiescent current to remain stable, which is also wasteful. A possible solution is to use a linear regulator in sleep mode, then turn on the buck converter when waking up.
Xie et al. used 1N60 germanium Schottkies. Germanium diodes are a bit exotic nowadays, but the 1N60 is specified to have a threshold voltage of only about 250 mV. Schottkies in general have high leakage currents, and Taitron lists their 1N60P as leaking up to 50 μA, which would be disastrous for this application, but apparently they didn’t observe such high leakages. Regular junction germanium diodes, on the other hand, have a threshold voltage of around 300 mV, and would be ideal.
Aside from low-leakage capacitors, low-self-discharge batteries, avoiding power supplies with high quiescent current, low-leakage diodes, and using low-power chips, it seems like the main trick to low-power design is to use a low duty cycle — keep your chip asleep most of the time. This means you can’t be running either a radio or any other kind of ADC at high speed all the time. With typical wakeup times of 5 μs in modern microcontrollers, though, you could reasonably wake up 1000 times a second and still keep the duty cycle below 1%.
If you can hear a radio station around 10 μW/m², then it ought to be able to broadcast a signal around 100 μW and be audible on radios in the same room. Of course this requires a duty cycle of 1% or less if you’re only harvesting 1 μW. This suggests that you can probably use the same antenna for harvesting and transmission — you perhaps must switch off the harvesting circuit during transmission, but that will only reduce the power harvested by 1% or so. You might want a shorter winding, or a center tap, to reduce the antenna’s impedance, improving its efficiency at low voltages.
You could try the Xie et al. circuit or the Leon-Gil circuit without the resonant tank (thus receiving all frequencies indiscriminately) or perhaps with a few different parallel tanks in series to ground (thus, I think, receiving just those particular frequencies). Perhaps a better idea is to use an RF transformer on the input side to step up the antenna voltage to a more reasonable level; with a loopstick antenna this can be effected simply by having MOAR TURNS on the antenna, as Dyo et al. did, but only up to a point, so a transmission-line transformer or two to step the voltage up might be a reasonable option.
Stepping up the input voltage with a transformer should allow the use of regular signal diodes (which reportedly leak about three orders of magnitude less than Schottkies) or even special low-leakage types (which leak about three orders of magnitude less than regular signal diodes).
I had a silly idea that maybe you could get a variable multiplication factor out of a Cockcroft–Walton generator, and thus a sort of analog MPPT circuit, by adding some more diodes to it, bypassing the later stages when the output storage capacitor voltage is low. Such diodes are relatively harmless but turn out not to be useful — they never conduct, even though their voltage drops are lower than the voltage drops of the chains of diodes they bypass. That’s because all the capacitors in the Cockcroft–Walton generator charge simultaneously and discharge simultaneously, across cycles. (Within a single AC oscillation, they charge and discharge at different times.) The Cockcroft–Walton generator already gives you a variable voltage multiplication factor out of the box!
I think the effect is that if you load a Cockcroft–Walton generator’s output so that it never approaches its maximum possible voltage, you in effect decrease its impedance. Assuming the input voltage is large compared to the sum of the diode drops, if you load it so heavily that only the output capacitor ever develops any charge, it becomes effectively a long diode, a half-wave rectifier; then, if you let it charge, its AC impedance gradually increases toward, ideally, ∞, because there is no purely capacitive path through it — all the paths through it go through the diodes.
I don’t understand why it was that the Leon-Gil experiment needed 0.01-μF capacitors; calculations based on capacitor impedance suggest that even a much smaller capacitor should have been sufficient, given the 1-MHz frequency and the total output current of about 6–8 μA (62 μW ÷ 8 V, or 8 V ÷ 1.5 MΩ).
The Cockcroft–Walton generator’s distributed capacitance works as energy storage; you can draw it down in a balanced fashion by temporarily drawing a larger current from the output. A buck regulator running from the Cockcroft–Walton output could efficiently handle a wide range of input voltages and thus enable efficient circuit operation from very low amounts of stored energy up to very high amounts.
As the capacitors become fully charged, the power factor shrinks — there is only current at the very peak of the wave. This suggests that, in the absence of resonance, higher output can be maintained from a Cockcroft–Walton generator that isn’t fully charged. For example, with a multiply-by-six configuration — six diodes and six capacitors — if the input voltage is a 10-volt-peak AC wave, and the output voltage is 30 volts (feeding, say, a buck regulator producing a 2.0-volt power supply for a microcontroller), then whenever the wave is over 5 volts, the power supply will draw charging current, thus harvesting energy in phases from 30° to 150°, then 210° to 330°, ⅔ of a full cycle. If the output voltage is allowed to rise to 40 volts, it will only be charging for 54% of the cycle, and if allowed to rise to 50 volts, only 37%.
(I’m not sure if this depends on how the capacitance is distributed throughout the circuit.)
The above was observed simulating the circuit with a source with 500 Ω of internal impedance (because a more realistic amount made it charge very slowly, as you’d expect). Upon simulating with low source impedance, the charging current peaks happen right after the input voltage crosses zero, and indeed at first have periods of time where the circuit returns power to the source — as you would expect from a capacitive load. This ceases once the output voltage has risen to the input peak voltage plus the combined voltage drops of the capacitors.
It seems like a little input series inductance would do some good for the circuit’s power factor and power dissipation — with 7 100-nF capacitors and 7 300mV Schottky diodes at 500 kHz, it charges more than twice as fast (for the first 25 cycles, which get it to about 5× the input voltage) with a 2.2-μH inductor in series with its input. Probably better to err on the low side there with a 1-μH inductor or an 0.47-μH, though — the asymptote at low inductances (or low frequencies) is just the situation described above, while the asymptote at high inductances or high frequencies is that zero energy gets into the circuit.
Suppose the input voltage source has very low impedance; what limits the power it can supply? I think it’s just the amount of charge that gets loaded into all the capacitors each cycle, so it’s proportional to frequency and proportional to the square of the input voltage — it’s just the impedance of the straight capacitive path to the output, plus a diode. (Except if the output voltage is lower than the instantaneous input voltage, when its impedance is the Vf of the the string of diodes.)
I think this means that the Cockcroft–Walton generator is a good approximation to the circuit I was trying to find in Constant current switching capacitor charging! Suppose you limit the output of a six-stage device to 50 V (with a “zener” avalanche diode or whatever). Then it will transmit power with reasonable efficiency from the input to the 50-volt output for an input AC voltage anywhere in the range of about 10 volts to 50 volts (peak), and furthermore for an output DC voltage anywhere in the range from just below the input peak voltage up to those 50 volts — it’s like a transformer that dynamically changes its turns ratio according to the current draw! Like, uh, a switchmode power supply. More stages will increase the diode losses but, for a sufficiently high output voltage, will reduce the required input voltage.
It isn’t exactly an MPPT circuit, since its impedance starts too low (though, unlike a simple rectifier charging a storage cap, not near zero), rises to the maximum power point, and then keeps rising; but all of the input energy is either dissipated in the diodes or stored in the capacitors, and with a little input inductance, it even avoids wasteful inrushes.
Disregarding diode capacitance, you can model the basic characteristics of a Cockcroft–Walton generator as follows.
Vₒᵤₜ ≤ N(Vᵢₙ - Vf)
Pf = NVf Iₒᵤₜ
Pᵣ = VₒᵤₜIᵣ
Pₒᵤₜ = VₒᵤₜIₒᵤₜ = ∫VᵢₙIᵢₙdt/Δt + Pf + Pᵣ
Vf is the forward voltage drop of a diode at the low currents we’re dealing with here, around 600 mV for a 1N4001 or 300 mV for a Schottky. Pf is the total power loss from the diode voltage drops for forward current; Pᵣ is the total power loss from diode leakage resulting in reverse current; N is the number of stages, each containing a diode and a capacitor; Iᵣ is each diode’s average reverse current. Vᵢₙ above is variably the peak voltage of the AC waveform (in the first inequality) and the instantaneous voltage in the integral.
The first thing to notice here is that if Vᵢₙ < Vf, the circuit won’t work at all, regardless of how many stages it has, and that’s why so many of these papers use Schottky diodes; and if Vᵢₙ > Vf, it will, again regardless of the number of stages — and that’s how the humans first split the atom.
Second, the forward power losses in the circuit are proportional to the number of stages. So if you have six 600 mV stages, they’re going to drop 3.6 volts; if your output voltage is 3.6 volts then you are going to lose half of your energy inside the generator. You should probably use less stages. The reverse or leakage losses, though, actually decrease with the number of stages, for fixed input voltage, output voltage, and load current, because the diodes leak less when that fixed output voltage are divided across more stages. (This seems to contradict results in the Leon-Gil et al. paper, so I may have gotten something wrong.)
So, with few enough stages, the losses will be dominated by reverse losses, and you should use low-leakage diodes; and with enough stages, they will be dominated by forward losses, and you should use low-Vf diodes, even if they could leak more.
The leakage currents in the diodes depend on the reverse-bias voltage, and the reverse voltage across any diode varies interestingly. It is always less than the peak-to-peak voltage of the AC input, but it varies during the cycle, and in a way that depends on circuit load. If the circuit gets fully charged, all the diodes are always reverse-biased or anyway not forward-biased enough to conduct any more, and so they see the full AC waveform with just enough DC bias to make it never quite conduct, or conduct just enough to compensate for reverse-biased-diode leakage; so, for example, if you’re using 600-mV diodes and the input is a 10-volt-peak (7.1 V rms) sine wave, each diode sees a reverse-biased voltage oscillating between -19.4 V and +0.6 V.
When the current isn’t fully charged, the diode sees a sine wave that’s clipped: the negative bias is more moderate, so when the voltage tries to rise above its threshold, it starts conducting and clips the peak off the voltage wave; and the wave’s trough voltage gets clipped by the diodes that conduct during the opposite half cycle.
Since diode leakage currents increase, very roughly, exponentially with the reverse-bias voltage, probably nearly all of the leakage will happen at the trough of the wave, and the wave spends nearly half of its time there. So, for example, if you have a 6-stage circuit whose output voltage is currently 24 volts, each diode has -8 volts across it half the time. So if each diode leaks 25 nA at a reverse bias of 8 volts, the whole circuit will leak about 12.5 nA and 0.3 μW. (This is a normal number for a silicon signal junction diode.)
Here’s a Falstad circuit for simulating a 7-stage Cockcroft–Walton generator:
$ 1 5.0000000000000004E-8 1.8479586061009856 56 5.0 50
v 432 416 432 576 0 1 500000.0 2.0 0.0 0.0 0.5
d 432 336 528 176 1 0.3
c 432 336 624 336 0 1.0000000000000001E-7 -0.07696510389787246
c 624 336 816 336 0 1.0000000000000001E-7 -0.07127146119106348
c 816 336 1008 336 0 1.0000000000000001E-7 -0.06854028985446714
c 528 176 720 176 0 1.0000000000000001E-7 -0.06854028985446775
c 720 176 912 176 0 1.0000000000000001E-7 -0.07127146119106291
c 912 176 1104 176 0 1.0000000000000001E-7 -0.07696510389786876
d 528 176 624 336 1 0.3
d 624 336 720 176 1 0.3
d 720 176 816 336 1 0.3
d 816 336 912 176 1 0.3
d 912 176 1008 336 1 0.3
d 1008 336 1104 176 1 0.3
c 1104 176 1104 576 0 1.0E-7 0.12035737918464492
w 1104 576 432 576 0
w 1104 176 1216 176 0
w 1104 576 1216 576 0
g 432 576 432 624 0
r 432 336 432 416 0 500.0
x 239 377 407 380 0 12 internal source impedance
r 1216 576 1216 336 0 100.0
s 1216 176 1216 336 0 1 true
x 1262 461 1289 464 0 12 load
o 7 512 0 290 320.0 0.4 0 -1
o 2 512 0 290 320.0 0.4 0 -1
o 16 1 0 35 0.15625 9.765625E-5 1 -1
o 0 1 0 35 9.353610478917778 0.005846006549323612 1 -1
o 16 64 0 35 0.3125 9.765625E-5 2 -1
Something in the neighborhood of 6 stages is probably optimal for this purpose, and a maximum voltage of 50 volts is probably also a good idea (to avoid needing high-voltage components), so you should probably step up the antenna voltage to about 8 volts (with an RF transformer, if necessary) and maybe limit it with a small zener for safety. (Or build the damned thing out of zeners.)
Since the available energy may vary over one or more orders of magnitude depending on location, radio stations starting up and shutting down, time of day, ionosphere propagation, nuclear warfare, and so on, it’s probably worthwhile to have some kind of overvoltage protection across the antenna. It likely only needs to be able to dissipate milliwatts of power, so a couple of back-to-back small “zeners” (avalanche diodes) might be adequate, and maybe a MOV or two for nearby lightning strikes or hydrogen bombs or something, plus some inductance before the Cockcroft–Walton generator to prevent spikes too fast even for the MOV from making it through.
Above I suggested transmitting AM audio at 100 μW or so for the sake of communicating to humans using ordinary AM radios, which has been done on a battery. But suppose we only want to communicate with other energy-harvesting nodes?
Some work has been done on passive signaling using Wi-Fi for sensor motes and even passive sensors, analogous to Theremin’s masterwork, The Thing. As I understand it, the mechanism is that if you have an antenna tuned to a particular frequency feeding into a load (such as a Cockcroft–Walton generator), you absorb some energy at that frequency; if you disconnect the load, the radio waves reflect from the antenna (perhaps with a phase shift) instead of being absorbed. So someone in the vicinity listening on that frequency can detect that you’ve turned the antenna off.
Suppose it’s possible to get reasonable antenna efficiency across a wide range of frequencies, like the whole AM band, as would be ideal for energy harvesting, and so you can be absorbing tens of microwatts as the Leon-Gil experiment did, or even more. To a nearby observer “tuned” to the same set of frequencies, temporarily disconnecting your harvesting input would be precisely as observable as beginning to transmit noise at those same tens of microwatts. In effect, this amounts to a time-domain radio transmitter with 100% efficiency — “111% efficiency” if your power supply is 90% efficient. This is probably an order of magnitude or more better than you could do by actually transmitting a signal, but the range will be very limited, because you can’t concentrate power harvested over time at a particular moment.
If you want to transmit, say, four meters, by failing to absorb 50 μW and instead reflecting it isotropically, your lack of signal will be noted as 250 nW/m² at that four-meter range (assuming far-field radiation, which isn’t actually correct — at 1 MHz, where the wavelength is 300 m, energy can bounce back and forth between the nonlistener and the observer of nonlistening some 37 times per oscillation, so I think the near-field coupling can be stronger than this). This is about 320x lower than the “background noise” we’re assuming of 80 μW/m², although it seems likely that Leon-Gil et al. were more strongly irradiated than that. This is a SNR of -22 dB and accordingly requires at least 22 dB of coding gain to establish communication; each additional factor of 10 in distance adds another 20 dB.
(Unfortunately I don’t know how to calculate near-field electromagnetic coupling to a reasonable degree of precision; I’m pretty sure it’s stronger is all.)
The Shannon–Hartley formula is that the channel capacity in bits per second is C = B lg (1 + S/N), where B is the bandwidth in Hertz, S is the signal power, and N is the (additive white Gaussian) noise power. So in this case it’s 1.2 MHz · lg (1 + 1/320), which is basically 1.2 MHz · 1/(320 ln(2)), or about 5.4 kbps. In theory, this drops by a factor of 100 with every factor of 10 in distance, in the limit: 54 bps at 40 meters, 0.54 bps at 400 meters, 0.0054 bps at 4 km. I think this is hit harder by the near-field effects, though — you get terrible antenna efficiency with an antenna that’s a tiny fraction of a wavelength in length (it reabsorbs almost all of what it emits, in a sense), so the situation is orders of magnitude worse.
Down here in the power-limited regime, it doesn’t really matter whether your signal is spread over 100 kHz or 1 MHz or 10 MHz — if you spread it over ten times as much bandwidth, you also get ten times as much noise, which compensates to within a small rounding error. But if you narrow the signal to, say, 10 kHz, you start to see an effect: 10 kHz · lg (1 + 1/2.7) ≈ 4.6 kbps — you’re entering the bandwidth-limited regime. This is counterproductive from the point of view of power efficiency — you get less bits per joule that way.
The power input circuit I simulated above generates very substantial harmonic distortion (though less so with a bit of PFC inductance) — the sharp current edges from the diodes turning on are potentially quite noticeable, and I think the strongest signals would probably be the second and fourth harmonics.
Suppose you have something like the above setup and you want to periodically measure the energy in the radio spectrum, perhaps because you are trying to decode a signal sent by another such node. You have to be careful because the total amount of signal is small enough that the normally-negligible bias currents of analog inputs could consume a significant fraction of your harvested power! A low duty cycle might be adequate.
The voltages, however, are large enough that you probably want to divide them down — the original input voltage can be as high as 8 volts and you want to divide it down to, say, 1.1 volts or less. Maybe you could use some kind of capacitive divider that you then rectify and analog-filter the output from, with a multi-megohm resistive path in parallel with it to prevent unequal leakage in the capacitors from introducing a DC bias.
If your device is powered by energy harvesting from AM radio, the average bit rate you can achieve via active signaling is necessarily lower — the power you would have passively reflected must instead be harvested an used to power a radio transmitter, which is typically less than 20% efficient. However, you can save up that energy and transmit it in bursts, possibly in a frequency band where this is a legal thing to do, and possibly at a predetermined hour so that the intended destination node will be listening. (Sort of like FidoNet “mail hour”: whatever its other hours of operation, you would leave your FidoNet node turned on during your zone’s “mail hour” so that other nodes could call it and deliver its waiting mail.) So if you’re harvesting 50 μW, you could save up 4.3 joules in a day, and transmit, say, 300 mJ of radio energy during a single second, thus transmitting at 300 mW — a million times stronger than the passive near-field communications numbers above, and thus in theory able to transmit a thousand times as far.
(Elaine Chao explained to me that she wrote such a time-domain multiplexing system for the Motes project at Berkeley — as I understand it, each node listened in a particular fairly-coarse-grained time slot, and transmitted in the time slots of the nodes it wanted to talk to.)
Saving up 4.3 joules requires somewhere to put it, though. If you try to put it in ½CV² with V ≤ 50 V, you need C ≥ 3400 μF, which is a hell of a lot of capacitance — and, in particular, the electrolytic capacitors that are the best bets for this kind of massive capacitance are leaky as shit.
It’s clear, though, that long-distance communication needs either some kind of highly directional reception, a better power source, extremely infrequent communication, much bigger antennas, or all of the above. Frequency bands like the one I’ve been talking about are ideal for over-the-horizon communication because of skywave propagation.
(As mentioned above, though, the 20× larger energy available from TV stations is a potential better power source, and their higher frequencies would avoid the need for bulky ferrites; PV cells are another possibility, as a 21%-efficient 10 cm × 10 cm cell can generate 2.1 watts in full sun — that’s 2,100,000 μW, enabling four orders of magnitude higher communication bandwidth.)
The field strengths we’re talking about here are far too low to saturate our ferrite cores. Some research has focused on optimizing the core shape to gather more flux, for example by using a barbell or hyperboloid shape, but it seems likely to me that a ferrite core that branches out at both ends in a fractal branching pattern, something like a pair of sprigs of parsley or a pair of antlers, would have a better flux-gathered-to-weight ratio than such solid shapes. Fabricating such shapes has not been practical in the past, but you ought to be able to do a reasonable job with a ferrite-filled plastic system, carrying powdered ferrite or even powdered iron in a small amount of something like ABS or PLA.
PVC plumbing pipe is a durable, shock-resistant, sunlight-resistant, waterproof, and visually unremarkable package into which you could stuff even a fairly thick ferrite rod and attach the device to the side of a building; you could reasonably expect it would stay there for many years. To seal the package entirely hermetically, you could seal plugs in place some distance inside the ends of the pipe, using, for example, silicone, epoxy, or PVC glue.
As a larger-scale alternative to using a ferrite-core loopstick antenna, you could use a just-plain-loop antenna, with a coil of wire running around a larger area than is feasible to fill with ferrite; it, too, could be sealed in PVC pipe, perhaps in a square shape. Loop antennas have nulls perpendicular to the loop plane, so a reasonable orientation might be horizontal, since very few high-powered AM radio transmitters are near the zenith; for example, you could run the loop around the perimeter of a roof. By enclosing, for example, 100 m² of loop area, you can increase the received (or conditionally received) power by 5½ orders of magnitude, minus the one or two orders of magnitude you lose from not having the ferrite. This could boost the power available to such a system up near a watt.
Since the circuit’s coupling to the environment is magnetic, shielding it is not practical, so it could reasonably be embedded in concrete, even underground. The skin depth δ = √(2/ωμσ) is around 16 meters in rock, according to David Gibson’s “AM Radio Reception in Caves”, so even several meters of earth or concrete would barely weaken it. So burying the loop antenna in a ditch, perhaps armored with concrete, is another option to increase the durability of the device.