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If you measure a power with a large bandwidth the more accurate is the power meter (about 0.05 dB vs. 0.5 dB of a spectrum analyzer). But with the power meter you measure only a large bandwidth power (so if there are very high spurious, your measurement can not be correctly). With the spectrum you can also see the frequency, see if there are spurious or oscillation, set the resolution bandwidth close. Also the dynamic range of the spectrum is higher than the one of the power meter.
I think that the Power meter is more accurate on power measure, but in some case such as measure a signal with PAR, the spectrum analyzer is more better, this is my opinion.
As far as the accuracy is concerned, power meter is best, as it is used to
calibrate the spectrum analyzer.
But, sometimes, you may not know what you are measuring with the power
meter. Spectrum Analyzer will show you the frequency domain contents
of what you are measuring.
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