Originally posted Apr 22, 2014
Simplicity and synergy—sometimes physics breaks your way
Elegance, like beauty, may be in the eye of the beholder. And I doubt that non-engineers would find the classic spurious measurement setup to be elegant. Nonetheless, I think the traditional approach to measuring CW spurs near noise does qualify as elegant and it’s impressively simple and effective.
One of the main tasks of spectrum analysis has always been to find and measure spurious signals. It can be a difficult job when spurs are close to the noise floor, a situation that causes problems with both measurement accuracy and speed. I summarized the problem graphically in Oh, the noise! Noise! Noise! Noise and described how measurements of both the signal and the signal/noise ratio (SNR) would be affected when SNR was small.
Fortunately, the laws of physics sometimes break our way, and this is one of those times. The practical averaging technique available in early spectrum analyzers had two significant benefits: It both accurately represented the CW spurs that engineers were searching for and—wonders!—itreduced the apparent magnitude of the noise that was spoiling the measurement.
How can an averaging technique improve accuracy and effective SNR? The traditional averaging technique for spectrum analyzers was a narrow video bandwidth (VBW) filter, smoothing the video signal that represented the magnitude of the detected signal. Because the video signal was usually log-scaled, the VBW filtering performed an average of the log of the signal magnitude. In The Average of the Log is Not the Log of the Average I described the two approaches and noted that VBW filtering was accurate for CW signals but not for other signals such as noise. In Log Scaling: Useful But Sometimes Tricky I explained the downward bias that comes from video averaging noise and other time-varying signals.
It all comes together in the classic—and elegant—spurious measurement setup where the averaging of a VBW no wider than one-third of the RBW accurately represents the magnitude of CW spurs and reduces apparent noise power by about 2.5 dB, as shown in the figure below.
The results of power averaging (center) and log averaging (right) on a signal with 1 dB SNR are compared to a no-noise measurement (left). Log averaging substantially reduces the effect of the noise and dramatically improves the accuracy of the measurement.
For the 1 dB SNR case shown in the figure, the decrease in measurement error is dramatic, falling from 2.54 dB to 0.63 dB!
It’s a fortunate coincidence for the common and demanding measurement situation in which small signals must be measured near noise: The simple, easily-implemented averaging technique is also the one that better separates the signal from noise and improves measurement accuracy.
Of course, other factors and tradeoffs are always involved. The VBW averaging technique is not accurate for non-CW signals. Also, narrow VBW filters may reduce measurement speed significantly because sweep rates are related to the narrower of VBW and RBW settings.
For a more thorough discussion of this topic, including a quantitative analysis of the errors, see page 24 of Application Note, Keysight Spectrum and Signal Analyzer Measurements and Noise.