Electronic – why is it bad if a coax cable (used for antenna cable) has multiple paths to ground

The antenna is used to pick up an electric field (not the same thing as a radio signal). It can be any length but I'd expect that the further away from the ground plane of the circuit the "stronger" a field you will get.

The "optional" 1Mohm resistor is really ought to be included otherwise you risk damaging the FET through electrostatic discharge.

The most likely explanation is the new UHF connector you fitted.

UHF or PL259 connectors aren't really suitable for 450 MHz as the 50 Ohm impedance is not maintained through the connector.

Here is a site that describes some experiments, on a pair of connectors the vswr was about 2.3:1. Another site has some graphs showing up to 2.5:1 for various combinations of UHF connectors.

Why did the VSWR change? I can think of a few effects.

First, it's possible your UHF connector, and your soldering, wasn't as good as the original. These connectors vary in quality, it's likely that the antenna manufacturer chose a fairly good one.

Second, the mismatch of the connector will interact with the mismatch of the antenna, which might actually make it slightly better, or worse. It's possible that you were unlucky, and went from a match-improving location, to a worse one.

Cable loss also improves VSWR, so in the absence of any other factors, shortening a cable will increase VSWR slightly. At UHF, a 1 m change would only account for 0.1 VSWR though.

Finally, if your antenna mount isn't well grounded, the coax cable itself might be part of the antenna. Changing the length will change the antenna performance. This isn't ideal, you should ground the mount properly with its screws... If you have a magnet mount, then this might also be happening. It's easy to tell - while measuring VSWR, just move your hand along the coax, starting from the radio. If the VSWR changes, then you are part of the antenna.

What to do about it? You can probably ignore it, and suffer very little impact. The additional loss is well under 1 dB. A radio for 477 MHz with a UHF connector can't expect an SWR of 1.5:1 anyway. 1.7:1 sounds like a reasonably good match for a mobile antenna.

If you want to fix it, the simplest is probably to join the coax where you cut it. You get back the better connector, and most of the old length. It is possible to join coax, but you need to be careful. Here is my method:

1. Cut the coax cleanly by rolling it under a sharp knife.
2. Prepare both ends: Cut off about 20 mm / 3/4" of outer jacket, without damaging the braid.
3. Carefully fold the braid back slightly, trying not to destroy the weave.
4. Cut about 3 mm / 1/8" of the dielectric.
5. Now tin each of the inner conductors, and solder them together lying side to side. Just let them touch, don't twist them or make a mess. Be quick and use a cool iron, otherwise the dielectric will melt. It melts anyway, so be careful not to stress the plastic until it cools.
6. Insulate the joint with tape. First take a piece of tape 3 mm wide and wind it several times around the bare wires. Then wrap one layer of 10 mm wide tape over the top.
7. Now fold the braid of one side down over the joint. Use a piece of very fine wire, hair thin, to tie it down, if it doesn't lie flat.
8. Fold the other braid down, it will lie over the first braid. It will overlap only about 3 mm. Smooth it down and possibly tie it down with thin wire or cotton.
9. Gently solder it in a few places. You're not looking for a massive shiny solder joint, as you'll destroy the dielectric or melt through the tape if it gets so hot. Just tack it in 5 places, letting it cool each time.
10. Insulate the whole thing with more tape. Watch out for short spikes of braid that penetrate the tape...

The goal of the above procedure is to keep the cable as coaxial as possible through the joint, and to keep the region of incorrect impedance as short as possible.

You should also try tweaking the antenna length - see this answer for some ideas of the procedure.