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2m and wired smoke detectors

As they say, the only dumb questions are the ones you don't ask. [grin]

If anything, putting a common mode choke (ferrite bead(s) on the coax, or coiling the coax) will improve things. It will keep the antenna from pushing RF down the coax shield. In my attic j-pole I coiled the extra coax in a foot diameter coil right at the antenna. Putting a few clamp on beads also works well at VHF frequencies.

What exactly is a common mode choke? How can it filter both 2m and 440 frequencies at the same time?
 
What exactly is a common mode choke? How can it filter both 2m and 440 frequencies at the same time?
A choke is basically an inductor. It lets DC current through, but the higher the frequency the more it tries to block it (higher impedance).
(impedance Z = 2*pi*freq*inductance)

A common mode choke is simply where both the outbound and return wires go through the hole in the bead or get wrapped around the toroid together.

Picture a normal radio setup with transmitter, coax and antenna. Clamp a ferrite bead around the coax. The transmitter's outbound current in the center conductor makes a magnetic field in one direction and the return current in the shield makes an opposite field. The 2 fields cancel and the bead doesn't know any current is flowing. Now, at the transmitter end, short the center and shield together and connect to the transmitter's center pin (don't really do this). Both the center and shield will have an AC current in the same direction. The bead will try to block that.

Real world example: In theory a ground plane vertical (vertical stick with a few horizontal sticks at the bottom) won't put RF on the coax's shield. The ground plane rods are ground, just like the coax shield. The vertical's voltage goes up and down at 144MHz but the horizontal radials should hold still. In practice, those ground radials flail up and down some too. A common mode choke blocks that from going back down the coax.
 
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