A big part of the difficulty in getting a handle on random processes is rooted in randomness itself. No given measurement is necessarily related to the one before or the one after. So learning about a noise problem requires cumulative measurements and trends.
The image shows the basic tools offered by an oscilloscope for measuring random processes such as noise. At upper left is an amplitude time plot of the input on channel 1. At lower left, a power spectral density plot shows the frequency distribution of noise power. And on the right is a histogram of the individual noise-voltage measurements. The histogram gives us the distribution of the amplitude values of the individual measurements. These analysis functions, combined with measurement parameters, comprise an all-domains suite of noise measurement tools.
On top of the basic functionality, the oscilloscope provides measurement parameters with which we can derive insight into the characteristics of random noise. Things like the mean value of the waveform (P1 in the screen capture), the standard deviation (P2), and the peak-to-peak value (P3) are all key parameters in understanding the problem at hand. Of these measurements, the standard deviation, which we may also call the AC RMS value, is probably the most useful as it describes the effective value of the waveform.
In the frequency domain, the most common noise measurement is the power spectral density (PSD), shown at lower left in the image. Power spectral density is usually measured in units of V2/Hz and represents the power per unit bandwidth. Because noise is generally spectrally spread, the noise power in a band or range of frequencies can be determined by integrating the PSD over that range of frequencies.
The histogram gives an estimate of the probability density function of the process being measured. This data can be interpreted by using histogram parameters. The image shows three histogram parameters: hmean (P5), hsdev (P6), and range (P7). These are the mean, standard deviation, and range of the histogram distribution, respectively.
With these tools at your disposal, there’s really no need to scratch your head over noisy signals. Having the right tools makes quick work of characterizing noise so you can move on to more important matters in your design or debug work.
|Figure 1: Time, frequency and statistical domain tools for noise analysis|