But I think the Israelis have built things like this... At least I've read an article or two to that effect. In other words, to send a pulse through a detonator and make it go off, the emp device doesn't have to be powerful enough to fry all the electronic contraptions around it. In effect, you're just tickling all the electronics in a given neighborhood, not frying them.
That's not an EMP weapon, it's an RFI generator.
Basically, the principle is that you generate a strong enough radio signal to induce current in nearby wires. If those wires happen to be attached to an electrically triggered detonator, you get a "prematurely detonated" Palestinian.
The same sort of thing happens whenever an F-16 flew too close to a radio tower in Europe - the induced currents and RFI interference shuts down the computerized fly-by-wire system and causes the servos to get weird inputs.
Real EMP weapons *start* at about the size of a Uhaul truck and are *very* obvious.