Turning the backlight off makes the spurious term go away when probing :)
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There is a soft menu button that turns off the backlight and pressing this makes the spurious vanish on the probe (that feeds to another spectrum analyser).
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Also if I do a screen grab via Excel and GPIB (with the backlight ON) the 60kHz spurious is present on the spectrum from the baseband input. But if I grab the screen with the backlight off the baseband spectrum is clean on the grabbed screen image in Excel. A huge improvement.
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I guess I can live with this when grabbing screen plots as (hopefully) I can add the 'backlight off' command to the excel routine.
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So screen grabs will look much better. I'll have a look for the backlight command in the programming guide...