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When terminating coax (e.g. RG-400) that has an outer braid over an inner braid onto an SO-239 chassis mount, do we want to solder both the inner and outer braids together onto the ground of the SO-239? I assume yes.

It's obvious that the inner and outer shields are already coupled together at DC. But I know that AC is a strange beast and sometimes complicates things. I also have the idea that "good" differential current travels on the inside of the braid, and "bad" common mode travels on the outside. Now, I'm pretty sure this happens because the differential currents get "pulled together" and the common mode currents "repel" one another- so it sort of happens on its own.

That being said- would it make sense to cut away the outer shield and only solder the inner shield at the termination? I'm assuming that only the inner shield carries the signal (on the inner part) and that the outer shield is simply a passive shield to help reduce leakage.

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The short answer is yes, both shields must be connected together.

Many other connectors for this already connect the shields for you, providing that you follow the instructions. N connectors (at least the ones I've used) do. The snap-and-seal crimp connectors for my RG-6 (that's all that I use outdoors anymore) does this also.

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