I picked up a neat little Radio Shack mobile magnet mount antenna for a great price (free) recently. I took it home, and couldn't find any model numbers or information on it. Despite it looking a lot like a dual band 144/440 antenna I have, I found it actually was a CB antenna. It seemed like too good of an antenna to junk, so I took a stab at converting it to the 2m VHF band.
I opened up the base and found an odd circuit board with a spiral pattern leading to the center. My ohm meter showed a dead short between the tip and ground of the PL-259, so it looks like that's some matching circuit to get the antenna to a reasonable SWR on the 27mhz band.
I first tried moving the tap around a bit, but couldn't get a match or enough movement in the SWR curves to get it resonant on 2m. Since the antenna was a few inches short of a 1/4 wavelength on 144mhz, I bypassed the base circuit and fed a lead directly from the coax to the whip. It's not pretty, but it worked and now the antenna was resonant a little above 150mhz:
First I drilled a hole in the circuit board and fed the center coax connector through. A short piece of solid copper wire connects from the coax to under the main bolt holding the antenna whip.
A 1/4 wave whip is similar to a 1/2 wave dipole - it needs a second half counterpoise for the ground. This is normally done with a car body or the metallic base for a mag-mount antenna. Mag-mounts don't have a direct electrical connection to the car, but there should be enough coupling between the antenna and metal to get it to work.
I had fairly decent SWR curves, but they weren't particularly sharp. With some antennas, this can mean it's acting more like a dummy load than a radiator.
I decided to avoid using the circuit board for anything, and instead cut a 19" wire length to server as a 1/4 wave ground. This is coiled up under the circuit board and should couple into the metal below:
The antenna was still a little high in frequency, with a resonant dip up over 150mhz. To bring it down, I added a short brass rod to the end. I first filed off the paint to bare metal, then placed the rod next to it and tightly wrapped a few turns of braided copper wire. Finally I heated the whole thing with a really big soldering iron and let the solder flow over the wire, rod and whip:
The antenna now resonated down around 135mhz, so I started trimming the new rod. I had to trim a few inches to get the frequency right so the dip is in the middle of the 2m band: