Does the GFI trip before it gets keyed on an antenna?
Had a friend that would trip a GFI breaker in his house when he used his linear on 80 meters. Changed some ground connections and the problem went away for him.
If it trips as soon as you turn on the power, this suggests one of two things. First, a bypass capacitor in the amplifier chassis can do this if it got damaged by a surge, or if someone replaced with the wrong capacitance value. There should be a disc capacitor from each side of the AC line cord to the amplifier chassis. Leakage current from a capacitor that was damage by a surge, or was replaced with the wrong capacitance value can do this.
Second, a leaky power transformer can do this as well. Unplug the power transformer and try powering the amplifier by itself. Won't run anything but the cooling fan, but if the fault is in the RF chassis, you'll still trip the GFI. And if the transformer is at fault, you'll only trip it with the transformer connected.
And if it only does this when it is keyed and showing RF power, that makes it a RF problem in the GFI. Whole 'nother range of things to try for that.
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