Figure 1: Maintaining the maximum sample rate over more timebase settings is possible with long memory |

The maximum time window that a digital oscilloscope can capture at a given sampling rate is:

Time window = memory length / sampling rate

where acquisition memory length is the maximum number of samples that can be captured in the data acquisition memory. Because the acquisition memory length is of a finite amount, the only way to capture longer time windows is to lower the sampling rate (Figure 1). For example, an oscilloscope such as the Teledyne LeCroy WaveSurfer 3000 with 10 Mpoints of memory and a sampling rate of 500 Msamples/s (2-ns sampling period) can capture a total time window of 0.02 seconds at that sampling rate.

Figure 2: An example of an undersampled CANbus signal |

Some digital oscilloscope users would believe that the analog-to-digital converter (ADC) in their instruments determine its sampling rate. The ADC determines the maximum sampling rate, but don't discount the role played by the length of the acquisition memory. A long acquisition memory allows you to maintain high sampling rates at longer capture times. As much as 1.5 Gpoints of memory is available in Teledyne LeCroy's state-of-the-art LabMaster 10 Zi-A oscilloscope. This allows for a capture time of 6.25 ms with a sampling rate of 240 Gsamples/s!

Let's say your oscilloscope contains a modest 2 million sample points of memory per channel. In the example given above, a full 4 ms can be captured at 2 ns/sample using 2 million points. At the end of the day, an oscilloscope that gives 2 million points to 4 ms worth of signal capture will give you 40 times better timing resolution, a much better view of the signal, and more usable bandwidth than one that spreads the same signal over 100,000 points.

#### Using Long Memory to Spot Signal Anomalies

Figure 3: A 1-GHz clock modulated by a 31-kHz SSC |

Figure 4: At lower right, zoom trace Z3 shows a single output pulse from a motor drive's inverter |

#### Long Memory and the Frequency Domain

Resolution in the frequency domain is determined by two factors: the frequency span being measured and the number of points within that span. Nyquist's theorem determines the measurable range of frequencies: from DC to one-half of the sampling rate at which the data was captured. A Fourier transform of an array of N time-domain data points produces N/2 frequency-domain points within the range of frequencies from DC to the Nyquist frequency. Thus, the frequency resolution (Δf) of the FFT is:

__(1/2) sampling rate__

(1/2) number of points input to the FFT algorithm

Figure 5: This screen capture of an FFT uses only 12.5 kS, resulting in broad frequency peaks |

However, simply capturing the points isn't the whole answer. The oscilloscope must have enough processing horsepower to compute the FFT on a long data array. Some oscilloscopes that have appeared on the market limit the FFT processing to some number of points that may be far fewer than the number the instrument is able to capture. The result is an FFT with greatly reduced frequency resolution.

Figure 6: The same FFT shown in Figure 5 now comprises 1.25 MS, clearly revealing two frequency peaks |

Stay tuned for more on how you can best make use of your digital oscilloscope's deep acquisition memory in future posts.

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