ignition noise

I have an '00 Intrepid and an '02 Stratus, and whenever I try to use a
battery operated CB radio (for trips) or a "ham" radio, whether with
internal or external antenna, I get lots of ignition noise when the car is
running. It's not a "whine" but more like a speed-intensive "pop." The
noise is present even when running of the power outlet. Shut off the
engine, and the interference is gone.

Wondering what I could do to eliminate the noise. Would running the units
directly off the battery (or in my case the positive and negative terminals
in the engine compartment) help.

Thanks for any clues.