# Low SNR Measurements: How Close to Noise is Too Close?

Blog Post created by benz on Sep 22, 2016

Originally posted Sept 25, 2013

Understanding when the errors will become a problem

In this space, we’ve already talked about how the universe may be noisier than you think and described how noise adds something to all signal measurements. The Grinch’s distaste for noise was understandable, but it’s hardly a strategy for making better measurements—or for handling holiday stress—so now is a good time to quantify the errors associated with measurements made close to noise.

As engineers, we do our share of careful calculations; however, good engineering is also based in part on effective rules of thumb. Is there a minimum signal-to-noise ratio (SNR) for adequate accuracy in power measurements? Stated another way, how close to the noise floor must a signal be before the error from the noise, inevitably measured along with the signal, becomes too great?

In this case, a reasonable rule of thumb requires more than just a single number—but not too much more. For the typical case of measuring a CW signal near broadband noise, this little table should do:

These are the measurement error values—always positive—resulting from signal measurements made near broadband noise. The error is shown versus actual SNR and not apparent SNR.

The first entry in the table makes intuitive sense: if the actual signal power matches the noise level, the analyzer will read the combined power in its resolution bandwidth and the result will be too high by a factor or two, or 3 dB.

As SNR improves, things become more interesting. For example, with SNR at 5 dB the signal will usually be very distinct from the noise. In addition, the measurement may seem reliable even though an extra 1.2 dB of positive error is present.

At 10 dB SNR, things look even better and some engineers (not us, of course!) will accept a marker reading as it appears. However, the added error power of 0.41 dB is more than twice as large as the basic error figure of the best modern spectrum or signal analyzers.

As a matter of fact, you need an SNR of 15 dB to reach a measurement condition in which the added error power is comparable to the best error figure of a high-performance signal analyzer. If you want to make measurements that let you reasonably disregard the added power from broadband noise, you’ll need an SNR of 20 dB or better in many cases.

Alternatively, the broadband noise can be separately measured or modeled and then subtracted from the signal. This will increase accuracy and effectively improve dynamic range. The process is performed automatically in the Agilent PXA signal analyzer and called Noise Floor Extension (NFE). More on that in an upcoming post.

As we’ve seen before, noise is often more troublesome than we expect, and the amazing accuracy of some of today’s signal analyzers can make it a factor that might not otherwise be noticed.

To wrap this up, here are a few things to remember about these measurements and the table:

• The signal measurement error due to the power added by broadband noise is always positive. Although noise voltage may cancel signal voltage at some points in time, the noise is uncorrelated with the signal and the powers will add.
• The table applies to measurements of CW signals and broadband noise. Modulated signals require different measurement approaches.
• The table doesn’t apply to the traditional spurious measurement setup that uses a peak detector along with significant video averaging (i.e., video bandwidth is much less than resolution bandwidth). This setup reduces the apparent noise level and its effects.
• The table lists error versus actual SNR rather than apparent SNR. The difference is described in Oh, the noise!