Quantify noise with a DSO
A DSO's time, frequency, and statistics data can help you analyze the noise in circuits.
Martin Rowe, Senior Technical Editor -- Test & Measurement World, 1/1/2002
Electronic devices such as resistors, linear amplifiers, and digital-to-analog converters (DACs) generate noise. When qualifying a component, circuit, or system design, you must measure the circuit's noise to determine how well your device performs. Because a digital storage oscilloscope (DSO) stores digital data, it can perform calculations that tell you if the noise is random or periodic.
DSOs sample data at nearly equal intervals, from which they can calculate frequencies and statistics. You can use a DSO to calculate the peak-to-peak voltage range over a period of time. A DSO can also calculate a signal's rms value, then get statistics based on measurements of multiple sweeps.
Using a DSO's fast Fourier transform (FFT) feature, you can measure a noise signal's frequency spectrum. FFTs reveal whether your noise is truly random (wide bandwidth) or whether it contains periodic (narrowband) signal components. Wide-bandwidth noise usually comes from within circuit components, while narrowband noise usually comes from known sources such as power supplies and microprocessor clocks.
Statistics give you insight into both time-domain and frequency-domain measurements. Besides calculating a signal's mean amplitude and standard deviation, a DSO lets you view a signal's amplitude distribution with a histogram. The histogram's shape can reveal clues about a noise signal's source.
Figure 1. DSOs can calculate statistics such as peak-to-peak, mean, standard deviation, and rms values from the signals they sample. Courtesy of Tektronix.
Figure 2. Noise produces nonlinearities in a triangle wave's histogram. Courtesy of Nicolet Technologies.
Figure 3. FFT analysis can let you see frequencies that you can relate to specific signals in your system. Courtesy of Tektronix.
Figure 4. Taking an average of FFTs reduces the effects of random noise, which makes spectral lines from specific sources more apparent than those in Figure 2. Courtesy of Tektronix.
Figure 1 shows some of the statistics you can get from a DSO. In this example, the scope calculated the average, low, high, and sigma (one standard deviation) for the amplitude measurements in 133 sweeps of 8000 samples each. For those sweeps, the average is 0.4 mV. When that value approaches zero, the overall standard deviation and rms values become nearly identical.
The analog amplifiers, attenuators, and analog-to-digital converters (ADCs) in DSOs contribute random noise to the signals you see when you connect the instrument to a circuit. Thus, before you can measure noise in a circuit, you must measure the noise in your scope and then subtract that amount from your measurements.
When you measure a scope's noise, don't simply attach a probe's ground lead to its tip. You'll create a loop "antenna" that will pick up noise from the magnetic fields of nearby lights, motors, and computer monitors. Instead, connect a 50-Ù load terminator to the scope's BNC input connector. Measure the scope's noise on each channel you'll use for your measurements; you can't rely on the measurements for just one channel because noise levels vary from channel to channel.
A DSO's vertical setting (V/div) also affects the noise that the scope contributes to a measurement. Therefore, use the same V/div setting that you'll use for your circuit noise measurements. Use the scope to calculate peak-to-peak, rms, mean, and standard deviation. You'll need these calculations to subtract from later measurements.
Which measurement?Many engineers prefer to characterize circuit noise with an rms measurement instead of peak-to-peak or average measurements because an rms measurement is repeatable and it provides the best overall indication of a circuit's noise output (Ref. 1). The rms value represents the AC equivalent of a steady DC voltage, and it corresponds to the heating that such a DC level produces in your circuit.
The following equation describes how a DSO calculates noise from a set of samples. If your DSO can't calculate rms values, you can offload your data to a PC and use a spreadsheet to make the calculations using this equation:
where V is the voltage of each sample, and T is the time interval of the measurement. For a 100,000-point acquisition sampled at 1 Gsample/s, T= 100 µs.
An rms calculation finds the deviation from a statistical mean that encompasses 66% of all samples. But about one-third of the measurements will fall outside one standard deviation from the mean. Any of those measurements may exceed the maximum tolerance that a circuit or system can tolerate. You may, therefore, need to measure a noise signal's peak-to-peak difference. When you measure random noise, though, you don't know how long to wait for those rare events that will disrupt system performance. You could wait forever. Unlike rms measurements, peak-to-peak noise measurements aren't repeatable.
You can try to capture a deviant signal by setting the scope to trigger on a voltage that occurs outside the statistical norm or one that's outside a specified window. Then, you just have to wait for a trigger. But if the noise you're looking at is random, there's no way to know how long you'll have to wait.
More than just numbersBesides providing basic statistics, DSO's have other tools that let you characterize noise. Histograms rank high in popularity because they give you a visual image of a signal's amplitude distribution. When you measure the output noise of an amplifier or DAC, noise that confirms to a Gaussian distribution will tell you whether the noise in a signal is truly random. If the noise isn't random, you'll see more than one peak in the histogram plot or you might see a skewed distribution.
Figure 2 shows a triangle wave and its histogram. Although the two traces occupy the same grid, they don't use the same timebase. The histogram plots amplitude (horizontal axis) versus number of bin "hits" (vertical axis). A triangle wave should produce a perfectly flat amplitude histogram. Yet, for the signal in Figure 2, noise causes the signal's peak to flatten, which produces more samples at the highest amplitude bin of the histogram (far right). In addition, noise in the test signal produces nonlinearities that cause the other bins to contain differing values.
You can also get a feel for the noise signal's randomness through frequency-domain analysis. Noise from a source such as a switching power-supply or from a clock often looks random in the time domain. In the frequency domain, though, the spectral lines from these noise sources become apparent. In Figure 3, the time-domain signal (upper trace) appears random, but the spectral plot (lower trace) clearly shows frequency components rising above the noise floor.
The lower the noise floor, the better you'll see spectral lines from periodic signals in the frequency domain. You can reduce a plot's noise floor to a point, beyond which you measure the noise in the scope. Each FFT bin displays all the energy in that bin. If you take more samples for an FFT, you'll narrow each bin's bandwidth, which lowers the total noise in each bin, reducing the noise floor. Unfortunately, more samples per FFT requires more processing time, which slows the scope's response if you're looking at an FFT in "real time."
DSOs also let you take multiple FFTs of the same signal, then create a plot of their average. FFT averages reduce the effects of random noise and enhance the spectral lines of repetitive frequencies. Figure 4 demonstrates how averaging just 12 FFTs produces a lower noise floor, which makes the low-level spectral line from periodic signals lines more visible. More FFT averages will further clean the noise. After about 100 averages, you won't see any additional improvement in the noise floor.
DSOs give you computational tools that let you measure noise in a circuit, component, or system. You can use these tools to characterize noise and determine if the noise is random or periodic. Because you know the sources of periodic signals in your circuit, you can measure their effects on other circuit components or on other systems. Just remember to subtract the scope's noise from the measured noise in your calculations.
| Reference |
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| For more information |
"Measuring Noise: Time, Frequency and Statistical Domain Analysis," Applications Brief L.A.B. 426, LeCroy, Chestnut Ridge, NY. www.lecroy.com/tm/library/LABs/PDF/LAB426.pdf . |
| Author Information |
| Martin Rowe has a BSEE from Worcester Polytechnic Institute and an MBA from Bentley College. Before joining T&MW in 1992, he worked for 12 years as a design engineer for manufacturers of semiconductor process equipment and as an applications engineer for manufacturers of measurement and control equipment. E-mail: m.rowe@tmworld.com. |
