Measuring Noise with a Teledyne LeCroy Oscilloscope

Overview

Random noise is generated in every electronic component in a circuit. Analyzing random electronic noise requires tools in the time, frequency, and statistical domains. Teledyne LeCroy oscilloscopes have the capabilities you would expect to locate random noise. This application note will show you those capabilities.

Toolset

Random processes are always difficult to locate because the information provided by a single measurement does not reflect the signal characteristics before and after the measurement, that is, the measurement results may not be repeatable. Only through multiple cumulative measurements can the behavioral characteristics of random signals be understood. Figure 1 uses some basic tools for measuring random processes such as noise: the top waveform is the time domain measurement result, which is the change of the noise voltage collected by channel 1 over time. The next waveform is the power spectrum density, which shows the frequency distribution of noise energy. The waveform below is the histogram of the current measured noise voltage waveform, which shows the amplitude distribution of the waveform on the current screen. The bottom waveform is a trend chart of the standard deviation value of 1000 capture results, which shows the change process of multiple measurement results. These analysis tools and measurement parameters are combined to provide a complete tool set for noise measurement.

Time domain measurements

Let's start with the most basic measurements. Figure 2 shows a time domain measurement of a noise waveform that has been bandwidth limited. We can use the measurement parameters to gain some insight into the characteristics of this noise signal. The most meaningful parameters are the mean, standard deviation, and peak-to-peak value of the waveform. Of these parameters, the standard deviation (which can also be described as the AC RMS value) is probably the most meaningful because it describes the effective value of the waveform. The parameter statistics give the mean, maximum, minimum, standard deviation, and number of measurements for each parameter. The small histograms below the parameter statistics table are called histicons and show the distribution of the cumulative measurement results of the parameter values.

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Histogram

Noise signals are generally Gaussian distributed, and the mean and standard deviation of their probability density function (pdf) are very informative. Histograms provide an intuitive way to measure the distribution of parameter values. Figure 3 shows a waveform histogram for channel 1, which shows the number of times the measured value occurs in a small binary interval. This plot provides an estimate of the probability density function of the measurement process, which can be further explained using the histogram parameters. Three histogram parameters are used in Figure 3, hmean, hsdev and range, which represent the mean, standard deviation and range of the histogram distribution respectively. Histograms can be obtained from a single capture as shown in the figure, or they can be the result of the superposition of multiple captures. In both cases, they provide good insight into the characteristics of the process under investigation. In this case, the distribution is nearly Gaussian, indicating that the source of the noise is a random process.

The histogram in Figure 4 looks a bit different. The width of the distribution has increased and there are two main peaks. This is due to the presence of sinusoidal components in the random noise. By observing the shape of the distribution, you may be able to understand what is happening in the process you are studying. It is a good habit to look at the characteristics of the noise distribution before making any measurements.

Power spectral density is
a more common frequency domain analysis of noise. The most common frequency domain measurement is power spectral density, which represents the energy per unit bandwidth, and its unit is generally V*V/Hz. F3 in Figure 5 is the average of the FFT results of the waveform acquired 1000 times on channel 1. Although the oscilloscope has power spectral density as an output type, it uses a logarithmic decibel scale.

We can also select magnitude squared as the output type, with the unit being V^2. The FFT settings are shown in Figure 6.

In addition to the output type settings, the figure also sets the rectangular window function and the Least Prime FFT algorithm. In the FFT settings window, you can see the frequency resolution bandwidth (100KHz in this example) and the effective noise bandwidth (ENBW) of the window function, which is 1 for the rectangular window. [page]

The averaged FFT output needs to be normalized to the effective FFT bandwidth. In addition, there is another scaling issue that must be considered. In Teledyne LeCroy oscilloscopes, the FFT output is read as a peak value rather than an RMS value. To convert to an RMS value, the FFT magnitude must be multiplied by 0.707 and the magnitude squared by 0.5. We also normalize the FFT value to unit bandwidth (1 Hz) by dividing it by the effective bandwidth of the FFT. This is achieved using the Rescale function in Figure 7. The Rescale function allows the user to normalize by multiplication, addition, or subtraction. In this example, we multiply by 0.5/100E3 = 5E-6. The factor of 0.5 is mentioned earlier. The other factor is the inverse of the effective bandwidth, which is delt(f) times ENBW in Figure 6. If a window function other than rectangular is selected, the value of ENBW will be greater than 1.

Please note that we have applied the normalization function to convert the floating point FFT result to integers. After normalization, the vertical units of the FFT in F2 are V^2/Hz. We can confirm that the normalization is correct by integrating the area of ​​the FFT waveform. In Figure 5, the area parameter Area is used to calculate the area of ​​F3, and the gate function is used to limit the area measurement to within 40MHz because the bandwidth is limited when measuring noise. The average value of the area of ​​waveform F3 measured in parameter P7 is 23.26m. This is consistent with the average value of the square value of waveform C1 shown in parameter P8, which is 23.23m.

As shown in Figure 5, placing the cursor on F2 can directly read the power spectrum density of that point. In the figure, the cursor is at 10MHz, and the power spectrum density is 689.49 pV^2/Hz at this moment.

The parameter statistics include the minimum and maximum values. If you want to view the change process of parameter values ​​captured continuously for multiple times, you can use the Trend function. Trend plots the parameter values ​​of each measurement from left to right in the order of measurement. In the example shown in Figure 8, F4 is the trend chart of parameter P1, which reflects the change trend of the standard deviation of the waveform of channel 1. Each capture will get a standard deviation value, and F4 displays the successive results of the measurements in order. The Trend waveform can be measured and analyzed as any other waveform.

Derived measurement parameters

Another noise parameter of interest is the crest factor, which is the ratio of the peak value to the effective value of the waveform. The crest factor determines the dynamic range of the peak variation in the signal. Although there is no bipolar "peak" parameter in the oscilloscope, we can "create" such a parameter value by using the absolute value of the signal in channel 1. Flip the negative values ​​to the positive region of the waveform, and then use the maximum parameter to get the maximum of the positive maximum and negative maximum values ​​captured in each capture. Note that this method works because the signal has a zero average value. We can use parameter math to calculate the crest factor. The parameter math settings are shown in Figure 9, and we calculate the crest factor to be parameter P4, which is the ratio of P3 and P1. The measured results are shown in Figure 8, and the average result is 3.6. F6 in Figure 8 shows the histogram of parameter P4. Its distribution is not Gaussian. This is caused by the nonlinear process related to the absolute value and maximum math operations.

Measuring single point noise using nbpw

Another way to make a single-point measurement of noise is to use the narrow-band power (nbpw) method in the optical field. nbpw measures the power at a certain frequency by calculating the discrete Fourier transform of that frequency. The output unit is dBm. This method is not very convenient for measuring noise. We prefer to use the noise power spectral density in linear units of V^2 /Hz. Fortunately, Teledyne LeCroy oscilloscopes can embed algorithms to perform more complex operations on parameters to obtain the required measurement results. This is much more complex than the simple proportional parameter of the crest factor in Figure 9. The measurement result is shown in Figure 10.

Measuring single point noise using nbpw

Another way to make a single-point measurement of noise is to use the narrow-band power measurement (nbpw) method in the optical field. nbpw measures the power at a certain frequency by calculating the discrete Fourier transform of that frequency. The output unit is dBm. This method is not very convenient for measuring noise. We prefer to use the noise power spectral density in linear units of V^2 /Hz to measure. Fortunately, Teledyne LeCroy oscilloscopes can embed algorithms to perform more complex operations on parameters to obtain the required measurement results. This is much more complex than the simple proportional parameter of the crest factor in Figure 9. This measurement result is shown in Figure 10. [page]

Figure 12 shows the VB code used to recalibrate the nbpw parameters in this example.

Figure 12 VB code for parameter calculation, converting the nbpw result from dBm to V^2/Hz

The code algorithm converts each nbpw measurement from logarithmic to linear scale (V^2), reads the captured data length, and then calculates the effective resolution bandwidth of the FFT. Next, the algorithm uses this value to obtain the power spectral density in units of V^2/Hz.

Pseudo-random sequence length

If you are investigating a pseudo-random sequence noise source, you can easily measure the sequence spacing using the optical correlation function of a Teledyne LeCroy oscilloscope.

Figure 13 uses the autocorrelation function of waveform C1 to show the results of this measurement. The peak point generated by the autocorrelation function corresponds to the repetition period of the pseudo-random pattern. In this example, parameter P7 measures the pattern period to be 131us. This is consistent with the sequence length of 16384 clock cycles at a clock frequency of 125MHz.

Figure 13 Using the autocorrelation function to determine the length of the pseudo-random sequence

Teledyne LeCroy oscilloscopes have all the necessary tools for noise measurement in the time, frequency and statistical domains, providing great flexibility and powerful analysis capabilities for engineers familiar with this type of measurement.