I understand that If the dipole is fed with coax, one leg is tied to the
outer coax shield.

Regarding the end at the radio -

Is the coax shield "always" tied directly to the radio's chassis ground,
(which is also earth ground for my set) ?

This is almost always the case. The coax shield may also be grounded
at one or more locations between the antenna and the radio chassis
(e.g. where it enters the building), for both RF-grounding and
lightning-safety-grounding reasons.

Or, are the outer and inner coax conductors sometimes fed into an
isolation transformer, and therefore the coax shield would not connect
directly to the radio chassis ?

This can be done (with an isolated "unun" transformer) but it is
rarely done.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
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