Every situation is different.? Personally, I would never run my equipment ungrounded, but that is just me.
I wondered how his system was grounded, because it actually sounded like he was getting RF on 80m into the amp, which could cause the issues he has on 80m if the amp wasnt grounded.? I have a copper 1/2" pipe mounted across the back of my desk.? It is grounded directly to the power circuit breaker box ground.? Then all my stuff is grounded to that bar with self tapping screws with one ground wire for each piece of equipment.
