"Do you find a high degree of correlation between your (assumed) K3 and KAT500 
SWR readings across various levels of SWR? "

I don't have a K3.  I do have loads of recorded data that would allow 
comparison of KPA500 SWR and LP-100A SWR and a more limited set of data that 
would allow comparison of KAT500 SWR with LP-100A SWR.  I have not performed 
either comparison but, as a general observation, it's obvious that the LP-100A 
is far more useful at low power levels or for mismatches that would give low 
reflected power.  At high power levels there is quite good agreement between 
the LP-100A and the KPA500 for power and SWR.  Since I know that, I look mainly 
at the LP-100A data.

I did a quick test on 20 m.  For an antenna system load that my LP-100A reports 
as SWR 1.09 with  Z of 52.7 ohm at 4.3 deg it took about 70 W output power for 
my KAT500 to change from 1.00 to 1.11 SWR.

To look at this another way - until the meter moves off the peg it isn't 
telling you much about the signal being measured.  All it's telling you is that 
you need a better meter.

I'm not saying there is anything wrong with the KPA500 or KAT500 SWR metering.  
You just need to know how it behaves and what it is useful for.  I expect the 
same applies to the K3 SWR meter.

Andy, k3wyc

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