Dave,
It's possible to generate EMP from something other than a nuclear weapon, but not effective over more than half a km or so. You can search for the ATLAS-1 EMP "Trestle" here in Albuquerque. I know you want it to be nuclear-based EMP, but thought I'd introduce a non-nuclear source for EMP.
Generating EMP on a scale large enough to effect a city, or large portion of a big city, from a LEU (<20% U-235) will be hard to make realistic. If you have something that's 20% HEU, that means it about 80% U-238, which is fissile, but it's not fertile. To fission U-238, you need the 14.1 MeV neutrons that come from the tritium-deuterium fusion reaction. We're now talking about a thermonuclear device, or a fission-fusion-fission device. This is a state sponsored type device, not an improvised device fabricated from acquired fuel assemblies.
Authoring a realistic EMP device given your desired details and the science as we know it today would be a stretch. But...this is a fiction novel, 50 years from now, so create a "new technology" that makes it all come together. EMP is a byproduct of high gamma and/or neutron flux stripping electrons out of the atmosphere, the kind of flux that comes from a 1 megaton or bigger weapon. That size weapon has to be a thermonuke because the largest implosion device was...umm...it was smaller. Again, with fiction, you can change these details. Your creativity would need to lead you to an external neutron source that generates those high energy neutrons to induce the fission in your fuel which is mostly U-238.
I hope this provides some help. I'm sure it wasn't the easy answer you had hoped to find, but it's not always that easy. EMP was another one of those things that was accidental and unanticipated. For that reason, this anomaly isn't so easy to generate on a large scale without the bright-white flash followed by the rising mushroom cloud.
Chris