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Electrical noise, like taxes, is always with us. Most of the time noise is small and we can ignore it, but there are some measurement circumstances where noise must be dealt with. What can be done to minimize the effects of noise on the accuracy of your measurements? This article will discuss noise and how to minimize its impact on oscilloscope and digitizer measurements.
Noise is basically everything except the signal you are trying to measure. It can include random electrical signals, periodic signals like power line signals, or interfering signals picked up by crosstalk. We will deal with handling random noise which is the most common noise phenomena. Random noise is a phenomenon that is pervasive throughout electronics. It can be measured and analyzed using an oscilloscope or digitizer and an example is shown in Figure 1.
Figure 1 a study of Gaussian distributed noise showing noise in the time domain, statistical domain and the frequency domain. Source: Arthur Pini
The top trace is the time domain view with voltage versus time of the noise signal. Beneath that trace is a horizontally expanded zoom view of the acquired signal. The noise is a series of random voltage values. The measurement parameters read the rms value of the acquired noise trace in parameter P1 and the peak-to-peak value in P2.
The third trace from the top is the histogram of the signal. The histogram plots the number of measured voltage values in a narrow range of voltages called a bin as a function of nominal voltage of the bin. This histogram is an approximation of the probability distribution of the noise values. This is a statistical view of the noise signal. The noise being measured has a Gaussian or normal probability distribution with its characteristic bell-shaped distribution. Parameter P3 records the histogram mean which is near zero. Parameter P3 is the histogram standard deviation. The standard deviation is a measure of the spread of the probability density about the mean. For a signal with a zero mean the standard deviation is equal to the rms value read in parameter P2. P5 is the histogram range, the difference between the highest, and lowest populated bin limits. Gaussian noise is unbounded, that means that both the peak to peak and histogram range values will increase with the total number of measurements. If you report either parameter, you should also include the number of measurements for a complete description.
The bottom trace is the fast Fourier transfer (FFT) of the noise signal. The FFT, like a spectrum analyzer, shows the distribution of the signal versus frequency. The noise spectrum is flat with equal power across the full span of the spectrum. This type of noise is characterized as “white” noise.
There are many other noise distributions encountered in electrical measurements. Figure 2 shows a sub-sample of four different distributions that are commonly encountered.
Figure 2 Examples of four different random noise distributions: gaussian, uniform, sinusoidal, and dual Dirac. The views of each are (left to right) time domain, histogram, and frequency domain. Source: Arthur Pini
The time domain views in the left-hand column are all similar in that they show random sample values. The histograms show the greatest difference. We see the aforementioned bell-shaped distribution of the Gaussian distribution in the top row. The second row from the top are the views of the uniform distribution. As the name implies, the uniform distribution has sample counts that are equally spread across all possible amplitude bin values. This is reflected in the histogram which shows an equal population for each amplitude value. Quantization noise is an example of a uniform distribution.
The third row from the top shows the three domain views of sinusoidally distributed noise. The sinusoidal distribution has a greater number of sample values near the peaks of a sine wave where the rate of change is slow. There are fewer samples near the zero crossings where the rate of change is the greatest resulting in the saddle shape.
The bottom row shows the statistical domain views for the dual Dirac distribution. This distribution is commonly found in measuring time jitter. The distribution shows two distinct peaks representing two possible amplitude centroids.
All the distributions have flat frequency spectra with equal energy spread across the frequency span. This observation is helpful because the noise amplitude can be reduced by bandwidth limiting noise using filters. The frequency response of the filter should pass the frequency of the desired signal with little attenuation while the noise outside of the signal spectrum should be attenuated.
Reducing noise
There are two basic approaches to reducing noise. The first is to use averaging. There are two common types of averaging available in most oscilloscopes: ensemble averaging and boxcar averaging. As we have seen, noise consists of voltage samples with random amplitude and polarity. Ensemble averaging acquires multiple waveform records and averages of the nth sample of each acquisition across all the acquisitions, the noise averages to its mean value improving the signal to noise ratio as shown in Figure 3.
Figure 3 The ensemble average takes the nth sample of each acquisition like those under the cursor and adds them. This sum is divided by the number of averages (N) to obtain the average value which is the lowest trace. Source: Arthur Pini
The figure shows 16 acquisitions where the same samples in each acquisition are added and then normalized by the number of acquisitions to obtain the average value for that sample point. Note that the average waveform, the bottom most in the figure, is smoother than an of the individual acquisitions. The primary downside of ensemble averaging is that it requires multiple acquisitions.
Boxcar averaging is an approach that can be applied to a single acquisition. It consists of averaging n adjacent samples. The number of samples averaged determines the signal to noise improvement. Figure 4 provides an example of how the boxcar average is calculated.
Figure 4 Finding the mean value of 7 samples adjacent to the cursor marked sample point. Source: Arthur Pini
Boxcar averaging is the running average of a fixed number of samples adjacent to the selected sample. The vertical cursor marks the nth sample. The blue measurement gates are set to restrict the measurement of the mean value to a range of 7 samples centered on the cursor. The mean value of those 7 samples, P4, is the value of the boxcar average at that point shown in the trace annotation box for the zoom of F6. This operation is repeated for each sample in the boxcar average. Luckily, the boxcar math function accomplishes all this automatically to produce the bottom waveform shown in the figure.
The second approach to reducing noise is the decrease the bandwidth of the signal acquisition. This technique utilizes filters which are selected to pass the desired signal but attenuate as much of the noise spectrum as possible.
Figure 5 provides examples of these approaches using ensemble averaging, boxcar averaging, and bandpass filtering.
Figure 5 Comparing the effect on the signal-to-noise ratio of ensemble averaging, boxcar averaging, and filtering. Source: Arthur Pini
The top trace is the acquired 10MHz sine waveform serving as a reference. The left column is the acquired waveform. The center column is the horizontal expansion or zoom of the acquired waveform. The noise appears as the raggedy areas on the sine wave. The rightmost column is the FFT of the acquired waveform. The sine wave appears as a vertical spectral line at 10 MHz. The noise is spectrally spread horizontally over the entire span of the FFT at a level of -65dB.
This ensemble average is taken over 256 acquisitions. The zoom trace is very smooth with barely discernible evidence of the noise. The FFT has the same vertical spectral line at 10 MHz. The noise level, indicated by the baseline, has been reduced by more than 20 dB with the averaging process. The baseline has decreased to lower than -85 dB from the raw acquisition where the baseline was about -65 dB.
The third row from the top shows the effect of boxcar averaging 7 samples. Looking at the zoom trace in the center column, the effect of the noise is reduced but not as much as it was for ensemble averaging which is averaging more samples. The FFT shows a reduction of the baseline accompanied by scalloped shaping. Boxcar averaging adds n samples together with equal weight and can be thought of as a simple digital filter. The scalloped shaping is the frequency response of that filter. Obviously, the noise is not attenuated as well as the previous example because fewer samples are being averaged. The signal-to-noise ratio can be improved by increasing the number of samples averaged which decreases the effective bandwidth. This has to be done carefully, if n is increased too much such that the number of samples encompasses a major portion of the sine period, it will begin to attenuate the sine wave.
The bottom row shows the effects of applying a narrow band pass filter to the acquired signal. The bandwidth of the filter is 500 kHz centered on 10 Mhz and it attenuates noise outside of that bandwidth. The FFT shows a good reduction in the noise except near the filter center frequency where the attenuation is much less. Like boxcar averaging, filtering can be applied to a single acquisition.
How does this work in an actual measurement? Figure 6 compares the results of noise reduction on a 40 kHz ultrasonic range finder.
Figure 6 Comparing noise reduction techniques of averaging, boxcar averaging, and bandpass filtering on a 40 kHz ultrasonic range finder. Source: Arthur Pini
The top trace is the raw waveform, the transmitted pulse occurs 1 ms into the acquisition. The echo at 3.35 ms is slightly above the noise level. All three techniques increase the signal-to-noise ratio, and the echo is clearly visible above the noise floor. A simple visual comparison shows that the bandpass filter provided the best signal-to-noise enhancement. Averaging and boxcar averaging performance can be improved by increasing the number of acquisitions or number of samples, respectively.
What is the result of applying the bandpass filter to the signal? Let’s compare the results of the original acquisition and that using the band pass filter. Figure 7 compares the two waveforms.
Figure 7 Comparing the results of the raw and the band pass filtered acquisitions using gated x@max parameters to calculate delay times for the echo. Source: Arthur Pini
The delay between the transmitted pulse and the echo is calculated using the x@max parameters which measures the time at the maximum value of the waveform. The x@max parameters are time gated to isolate the transmitted and echo pulses. Parameter math calculates the time differences for each processed waveform. P3 shows the time delay for the raw acquisition and P9 is the bandpass filtered acquisition. The blue parameter markers show the x@max locations. The range of the delay measurement (difference between maximum and minimum values) for the raw waveform is 2.45 ms. The range for the band pass filtered waveform is 50.5 ms. Assuming a velocity of sound as 344.44 m/s at room temperature, the nominal distance measured using the mean delay is about 0.79 m. The uncertainty in the distance measurement is 0.845 m for the raw waveform (basically unusable). The band pass filtered waveform has a distance uncertainty of 0.0174 m (about 0.7 inches). Obviously, noise reduction is a useful tool.
These noise reduction techniques are very useful in assuring accurate measurements. Keep in mind that they work best if the signal inputs to the instrument utilize the full dynamic range of the device. This maximizes signal to noise ratio even before applying noise reduction techniques.
Arthur Pini is a technical support specialist and electrical engineer with over 50 years of experience in electronics test and measurement.
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