Are stranded wire center conducter coax cables as good, worse, or better than solid copper center conductor?
The only thing that will usually have stranded center is RG-58, used for ring networks in computer systems. Remember, you can't push a rope and if you use F connectors, the center needs to be rigid. Even for BNC and RCA compression fittings, the center needs to push into a tip and if the cable is stranded, it won't. I have used literally thousands of the F-Conn RCA connectors and they work well, without being particularly expensive. They make a wide variety, including mini the kind for installing BNC and RCA plugs on the mini cables.
The benefit of solid copper is flexibility, more than anything. Coaxial cable usually has a plastic foam dielectric (the white or colored soft plastic that the center runs through) and it can compress. If it compresses, the distance from the center to the shield decreases and noise, interference and reduced frequency response result.
BTW- cabling has a recommended minimum bend radius, which is 4x the cable's diameter. This means that laying cabling over the crisp edge of framing, metal ducts, brackets and anything else will result in the bottom cables being kinked and problems will arise from this. Wire management supplies are in the electrical department of all hardware and big box stores- use them and your installation will be more reliable.
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