Sustained sample rate in digital oscilloscopes

Hewlett-Packard Journal, April, 1997 by Steven B. Warntjes

At all but a few of the fastest sweep speeds, the acquisition memory depth and not the maximum sample rate determines the oscilloscope's actual sample rate Peak detection capability, when used correctly, can make up for acquisition memory shortfalls.

One of the most basic specifications in digital oscilloscopes is the maximum sample rate. Oscilloscope users often understand the theory of signal sampling and signal reproduction, but often mistakenly assume that the oscilloscope always samples at its maximum sample rate. In reality, two specifications need to be considered: the maximum sample rate and the acquisition memory behind the signal sampler. At all but a few of the fastest sweep speeds, the acquisition memory depth and not the maximum sample rate determines the oscilloscope's actual sample rate and consequently how accurately the input signal is represented on the oscilloscope display. The deeper the acquisition memory, the longer the oscilloscope can sustain a high sampling frequency on slow time-per-division settings, thus increasing the actual sample rate of the oscilloscope and improving how the input signal looks on the oscilloscope screen.

The digital oscilloscope's peak detection specification is another often overlooked specification. This important feature, when used correctly, can make up for acquisition memory shortfalls. In addition, peak detection can be combined with deep acquisition memory to create unique advantages in digital oscilloscopes.

Digital Oscilloscope Sampling

Basic sampling theory states that for a signal to be faithfully reproduced in sampled form, the sample rate must be greater than twice the highest frequency present in the signal. This sample rate is known as the Nyquist rate.[1] For an oscilloscope, this means that if the user wants to capture a 100-MHz signal, the sample rate should be at least 200 MSa/s. While the theory states that greater than 2x sampling is sufficient, the practicality is that to reproduce the input signal with 2x sampling requires complex mathematical functions performed on many samples. Reconstruction is the term commonly given to the complex mathematical functions performed on the sampled data to interpolate points between the samples. In practice, oscilloscopes that do reconstruction typically have less than perfectly reproduced waveforms because of imperfect application of the mathematical theory,(*) and they may have a slow waveform update rate because of the time it takes to do the necessary computations.

One solution to the reconstruction problem is to sample the waveform at a rate much higher then the Nyquist rate. In the limit as sampling becomes continuous, as it is in an analog oscilloscope, the waveform looks "right" and requires no reconstruction. Consequently, if the digital oscilloscope can sample fast enough, reconstruction is not necessary. In practice, a digital oscilloscope rule of thumb is that 10x oversampling is probably sufficient not to require reconstruction. This rule dictates that a digital oscilloscope with 100 MHz of bandwidth would require an analog-to-digital converter (ADC) to sample the input signal at 1 GSa/s. In addition, the acquisition memory to hold the samples would have to accept a sample every nanosecond from the ADC. While memories and ADCs in this frequency range are available, they are typically expensive. To keep oscilloscope prices reasonable, oscilloscope manufacturers minimize the amount of fast memory in their oscilloscopes. This cost minimization has the side effect of dramatically lowering the real sample rate at all but a few of the fastest time-per-division settings.

The sampling theory presented above assumes that the sampler only gets one chance to "look" at the input signal. Another solution to the reconstruction problem is to use repetitive sampling. In repetitive sampling, the waveform is assumed to be periodic and a few samples are captured each time the oscilloscope sees the waveform. This allows the oscilloscope to use slower, less expensive memories and analog-to-digital converters while still maintaining very high effective sample rates across multiple oscilloscope acquisitions. The obvious disadvantage is that if the waveform is not truly repetitive the oscilloscope waveform may be inaccurately displayed.[2]

Digital Oscilloscope Memory Depth

Now that we understand digital oscilloscope sampling requirements, we can examine how memory depth in oscilloscopes affects the sample rate at a given sweep speed or time-per-division setting. The time window within which a digital oscilloscope can capture a signal is the product of the sample period and the length of the acquisition memory. The acquisition memory is measured by the number of analog-to-digital converter samples it can hold. Typically in digital oscilloscopes the length of the acquisition memory is fixed, so to capture a longer time window (adjust the oscilloscope for a slower time-per-division setting) the sample rate must be reduced.

[sup.t]CAPTURE = [sup.k.]MEMORY/[sup.f]s,