# EMP strong enough to kill devices in an area >20 meters diameter

I'm writing a scifi short story and i would like to have the facts right. The question is:

Is it possible to create strong enough EMP to fry devices (cell phones, etc.) in an area of diameter around 15 - 20 meters using only generally available stuff (car battery, purchasable electronics)? Or it would have to be a real weapon like described here http://science.howstuffworks.com/e-bomb3.htm ?

• It's always hard to say "generally available stuff" – you see, half of engineering is always building your own tools. (That part of engineering actually is pretty close to, or even cooler, what MacGyver does). – Marcus Müller Aug 5 '17 at 8:33
• Here is a small one... youtube.com/watch?v=uOAnAjpXqc0 and a big one.. youtube.com/watch?v=Aj54FcI7_dE Its basically the same... just a matter of scale. – Trevor_G Aug 5 '17 at 15:14
• Does a lightning belong to generally available stuff? – Curd Aug 5 '17 at 17:39

Let's do a bit of rough gathering of numbers:

1. Fry is a pretty relative term. Damaging a sensitive device that is actually designed to receive energy from electromagnetic waves is certainly much easier than to damage e.g. a fridge. So, let's stick with *intentional receivers. That mostly means phones, but maybe also things like drones, gate openers, intercom systems, and any other thing that communicates wirelessly.
2. Purchasable who can purchase what for which price? If you're the Pentagon, meh, you can buy pretty much anything that is technically possible on this earth. If you're John from the third floor who's never dealt with electronics design, you might not even figure out where to buy 1m of cable. Somewhere in between are people that actually design electronics. So, let's assume we're dealing with someone who's got access to the internet, sufficient knowledge, but needs to keep a low profile, so he won't be buying large quantities of explosives or the like.
3. Real weapon this bodes bad for your storytelling: Of course, whatever you build is a real weapon in the end. Much like an IED is a real weapon.

So, let's stay with phones:

GSM phones are known to work well with a field strengths as high as $80 \text{dB}\frac{\text{µV}}{\text{m}}$, which is 10-2 V/m. So, to damage a phone reliably, let's assume you'd want to have 100 times that field strength. That's 1 V/m of E-Field strength!!

So, we take the field strength $E$ and relate it to the transmitted power $P_T$:

$$E = \frac{\sqrt{30P_T G_T}}{r}$$

With $r=20\,\text m$ being the radius of the sphere around the transmitter where this field strength is observed (i.e. the distance phone–EMP device) and $G_T$ the antenna gain, ie. a measure for how much the transmitter "focuses" the energy in one direction. Since you were talking about radii, let's assume it doesn't focus at all, but sends in all directions equally, so $G_T\equiv1$. Solving for the power leads to

\begin{align} P_T &= \frac{E^2r^2}{30G_T}\\ &= \frac{1^2 \frac{\text{V}^2}{\text{m}^2}\cdot 20^2\,\text{m}^2}{30}\\ &= \frac{400}{30}\text{W}\\ &\approx 14\,\text{W} \end{align}

Note that this is the power to distribute only over frequencies that the receiver actually picks up. So, when you'll build a 14 W transmitter that works exactly at the frequencies that a GSM phone uses, it will damage these – but not things that work at other frequencies!

But accepting that restriction, we can state that yes, whilst not trivial, it's certainly not hard for someone with microwave design experience or good instructions and access to standard components (that being oscillators/frequency synthesizers, and power transistors) that can be freely purchased online, as well as copper-clad board and patience, to build something like that.

If your question is: the protagonists lives in a house and needs to build such a device out of things he can find or buy at a supermarket: nahhh.

Your best bet would be to take a microwave oven, and remove the casing. Tadah, high-power, lethal, electronics-damaging microwave gun. Dangerous as hell. Wouldn't recommend doing. Of course, there's enough folks on youtube that don't effing care. These two dimwits have the disadvantage of living in a war zone, so they really have limited access to electronic components:

• Good answer, Marcus. Check the last bit of "So, when you'll build a 14 W transmitter that works exactly at the frequencies that a GSM phone uses, it will damage these – but not things that work at these same frequencies!" Should that be "but not things that work on other frequencies"? – Transistor Aug 5 '17 at 9:17
• Nice to see that you did not include the instructions otherwise some Darwin Award candidate would be testing it already... – Solar Mike Aug 5 '17 at 9:31
• 14W at low microwave just is not that dangerous, and I would expect it to stop the phone working due to interference and blocking, but at only 20dB overload I would not expect the receiver to be damaged. For this you want pulsed power, and lots of it, doable if you know what you are about, and don't mind using the sorts of tubes that need a few kV on the plate, even doable solid state if you have real money, but it is proper engineering, not a 14W signal jenny. – Dan Mills Aug 5 '17 at 10:04
• Microwaves and Wi-Fi/Bluetooth both work at 2.5GHz. So at least most consumer electronics are exactly tuned to your improvised microwave oven weapon. – Sanchises Aug 5 '17 at 10:41
• @Transistor ... you write one small answer, then make a bike ride to france to get cheese, baguette & cidre, come back, just to find that you've spotted a mistake in my answer :) yes, indeed, will correct that. – Marcus Müller Aug 5 '17 at 15:44

Let's try a different angle of attack: energy.

ESD tests use a 100pF capacitor charged to 2kV. This is 200µJ of energy delivered to the victim.

Now, let's perform a remote ESD test. Suppose the device has an antenna of area $A_1 = 1cm^2$.

We transmit an amount of radio energy E from an omnidirectional antenna $r=20m$ from the device.

This energy spreads on a sphere of 20m radius, which has a surface of about $A_2 = 4\pi r^2 = 5000 m^2$...

The amount of energy received by the target's antenna will be:

$E \frac{ A_1 }{ A_2 } = 2.10^{-8} E$

In other words, if we want the device to receive to receive 200µJ at a distance of 20m (assuming it has a perfect antenna) we have to transmit 10kJ of energy.

Now, devices are suppposed to pass this test. Crashing the CPU is allowed for consumer electronics, but no permanent damage should occur. So we're probably going to need a lot more energy.

Anything that burns 100 kJ in a millisecond is basically a bomb.

This means we need the victim to have a much better receiving antenna. However, the motherboard inside a cellphone is tiny, and it has multiple ground planes and lots of decoupling capacitors. It won't make the antenna we need.

Now, if the cellphone user has earbuds plugged in, then it's a different story. We now have a 1m long piece of wire, which would make a very decent tuned antenna. Just find the right frequency and fry it. If you manage to push the E-field enough and get the frequency just right to exploit any resonances, and the user is wearing both earbuds, you might also fry them a little bit.

Conclusion: EMP doesn't fry electronic stuff directly. Instead, it induces currents into the big efficient antennas that are available (like wires and cables) and uses that to fry whatever is connected to the wires.

This can happen in real life. Lightning is basically a huge amount of current flowing vertically, and it emits the associated EM fields. Any conductor loop large enough, close enough, and in the right orientation can pick up some pretty nasty stuff. Devices which sit at the intersection of two networks (like mains+ethernet, or mains+telephone) are quite sensitive to this. DSL modems at the intersection of 3 networks of long cables, this is why the early modens tended to blow up their ethernet ports in lightning storms.