Interesting.??
Mine doesn't do that (tested in SSB mode on both a QMX and a QMX+ into a dummy load).
Sometimes at the instant of pushing the PTT key, the SWR indicator does jump up, but then goes back down and doesn't continue to change.
Testing instead into an antenna, which shows 1.3:1 on the Hardware test / Test SWR function, I see the swr indicator go up one or two 'bars', which is correct, based on the operational manual's definition of an increment of 0.2 per 'bar'.
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So I'm wondering what is different in your setup that changes the behavior?? It's almost as if you are looking at ALC or mic AGC rather than SWR, but I don't think it is supposed to be able to do that.
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Stan KC7XE.