# Electromagnetic charging

I'm building a circuit that uses a really low voltage and current. I thought that instead of using a standard battery it would be nice if I could use a rechargeable battery and charge it with electromagntic waves (2100MHz or 850MHz). I may use a LC circuit and set it to the right resonant frequency. If I set it to 2100MHz I will need:

1pF and 0.0057438 MicroHenrys

That may work, but how will it be possible? If I used 100MHz it might work but I don't know how efficient it will be and what will be most efficient? I would like to achieve 3V at 1-2mA at a distance of 20-30km.

• I don't think you can get a reasonably fast charger working on electromagnetic waves. Simply not enough energy in them. – user17592 Jun 12 '13 at 12:43
• 2ma-1ma , 3v is that too much? – D.christian Jun 12 '13 at 12:47
• Ambient EM energy or driven by a charger? For ambient you could try 50Hz and pick up energy from nearby mains. – pjc50 Jun 12 '13 at 12:57
• it is ambient, but what do tou mean "nearby mains"? – D.christian Jun 12 '13 at 13:01
• Did you calculate how long it's going to take to charge your battery with 2mA? – user17592 Jun 12 '13 at 13:21

What you describe is theoretically possible, but very inefficient, and probably not feasible. Proof:

$3V$ at $2mA$ is $6mW$. This is how much power you need to receive to make your thing work. The question is this: how much do you have to transmit?

If you have a $1W$ transmitter attached to an isotropic radiator (such things don't exist, but we will address that later), then for any sphere centered on that radiator, there is $1W$ of power. But, this power is spread out over a sphere of increasing area as we get farther away. This is the inverse square law. Knowing this, we can calculate the field strength from your $1W$ isotropic radiator at some distance $r$, by taking that $1W$ of power and dividing it by the surface area of a sphere. At $20km$, the field strength from your $1W$ isotropic radiator is:

$$\frac{1W}{4 \pi (20km)^2} \approx 199pW/m^2$$

Let's just say on your device you have made an antenna that can collect all the RF energy passing through a square meter. You will then receive 199pW, which isn't anywhere near the $6mW$ you need. In fact, you need about thirty thousand times more ($6mW / 199pW \approx 30151$). You could invest in a $30kW$ transmitter, but that's probably not what you had in mind.

You can make this system more efficient by sending less energy into space where your receiving device isn't. That is, you can use a directional antenna. We need an antenna that is 30151 times stronger than an isotropic radiator in the direction of the receiving device. That is, we need a gain of $10 log(30151) \approx 45dBi$. (more about dBi) You could get about that from a very directional antenna, like one with a large parabolic reflector.

So, if you can have a big, directional antenna, you can aim it at your device (hard, because the antenna is so directional), and your receiver can collect all the energy in a $1m^2$ area (probably not possible, if you want it to be small), you could power your device with a $1W$ transmitter. You are still not very efficient:

$$6mW / 1W = 0.6 \text{% efficient}$$

and all of those assumptions are pretty generous. By the time you take into account other inefficiencies in the system, the practicalities of making these devices small, aiming the antenna, etc, RF power transmission doesn't sound so great.

How about a solar panel? The sun is also an isotropic radiator of electromagnetic energy, and it's far away, and suffers from the same inefficiencies. But, it's free, and transmits at a power of about $383YW$, (solar luminosity) with the field strength being as much as $1kW/m^2$ at Earth's surface (Earth's insolation).

• Interesting read. – Rev1.0 Jun 12 '13 at 18:25

A company called PowerCast have various solutions for RF energy harvesting. There is a power calculator here for their products if you have Microsoft Excel:

http://www.powercastco.com/power-calculator/

However for example plugging in 850MHz at 100W EIRP (probably the rough power of a mobile basestation) to get to your target of 3mW you need a 6dB antenna (not something tiny) and need to be around 7 meters away after conversion losses from their products, which have no doubt had a lot of design work put in. Have a play around with the numbers but you'd need to be pretty much standing under the tower to get 3mW.

Perhaps this is only tangentially related, but it may provide the solution your'e looking for. I came across some TI some chips meant for wireless power. The ICs handle some of the hassle of having tiny intermittent amounts of power needed to charge a battery, etc.

check out Page 6 of this document from TI for wireless power/energy harvesting: http://www.ti.com/lit/sg/slyt420/slyt420.pdf