Design Feature: August 3, 1995
Ideally, a digital scope samples continuously at a very high rate, so that it never misses anything. In other words, the scope should never stop sampling and should sample so fast that the sample rate is not an issue. Fig 1a shows this ideal situation.
Practical DSOs have a finite sample rate; moreover, they pause after each acquisition to process the acquired samples for display on the screen (Fig 1b). The scope's sampling system determines the sample rate; faster sampling systems cost more. The time that the scope takes to process the acquired samples and prepare for the next acquisition is called dead, or blind, time. The dead time depends on the required amount of data processing and the computational power of the µP or ASIC that crunches the data.
Fig 1b shows the dead time as relatively short--about the same duration as the acquisition time. The actual situation is usually much worse; the dead time can be orders of magnitude longer than the acquisition time. Another way to quantify this behavior is as a duty cycle—the ratio of acquisition time to total time. The duty cycle, which varies greatly among scope models and also depends on the scope's sweep speed, can be surprisingly small—sometimes less than 0.0001% when a scope with a long dead time operates at a fast sweep speed.
Another way to represent dead time is via the display-update rate, expressed in samples/second or waveforms/second. Think of the display-update rate as a measure of how efficiently a scope converts its maximum sample rate into displayed points. For example, the HP 54600B, a 100-MHz-bandwidth scope with a very fast display-update rate, has a maximum sample rate of 20M samples/sec but a maximum display-update rate of 1.5M samples/sec. So, when operating at its fastest sample rate, even this very fast scope can convert only 7.5% of the possible samples into displayed points. Scopes with slower update rates take an even smaller percentage of the possible samples. Digital scopes don't always operate at their maximum sample rate, however, particularly on the slower sweep-speed settings, so the efficiency is often higher.
On most scopes, the dead-time/display-rate performance changes with time/division setting. Using the HP 54600B as an example, on slow timebase settings, the time/division that the user selects limits the display-update rate. For example, at the 10-msec/div setting, acquiring the samples takes 10 divx10 msec=100 msec. The HP 54600B processes these samples to the display essentially in real time, so the duty cycle approaches 100%.
On faster time/division settings, the scope dead time becomes significant. For example, on the 100-µsec/division setting, the time to acquire the samples is 1 msec. The dead time is approximately 1.3 msec, so the duty cycle is 1 msec/2.3 msec=43.5% (Ref 2). Again, this scope has a fast display update rate. Many scopes have much lower duty cycles.
How fast does the sample rate need to be? Even though the Sampling Theorem (Ref 3) states that the sample rate should be greater than twice the scope bandwidth, practical considerations can make you want an even higher sample rate. On the other hand, various repetitive sampling techniques can enable a scope to acquire a waveform, despite using a sample rate lower than the Nyquist rate (a sample rate equal to twice the highest frequency component present in the signal). These techniques work only on repetitive waveforms, however. In an ideal sense, you'd like to make the sample rate so high that you can forget about it, but doing so is expensive (Ref 4).
To get a handle on how sample rate and dead time affect scope measurements, divide all the waveforms in the world into three main categories (Ref 5):
Some waveforms might not fit easily and cleanly into one of these categories, but these waveform categories help you understand how sample rate and dead time affect the quality of a measurement.
Understanding single-shot waveforms is simple. Single-shot waveforms occur only once, so you get only one chance to measure them. Alternatively, they occur so infrequently that it seems as though you get only one chance to measure them. Either way, the scope must have sufficient sample rate to capture the event and store it in memory. Again, you could argue about how high the sample rate needs to be to capture the signal faithfully, but a sample rate above the Nyquist frequency is a minimum requirement.
If you have only one chance to capture a signal, the scope needs to know when the signal occurs, which leads to the issue of triggering. Triggering is a key feature in all scope measurements, but it deserves special mention here, because if you can't trigger on a single-shot event, you will never see the event. If the event is something simple, such as a single pulse, edge triggering should be sufficient to capture the event.
If the event is more complex, you need a more sophisticated triggering capability. Suppose the single-shot event is a single narrow pulse in a stream of wider pulses. This is a single-shot event, but it's in a signal that hides it from an edge trigger. A trigger feature such as glitch trigger or time-qualified pattern trigger could identify the one narrow pulse in the signal and trigger on it. Most high-sample-rate scopes for single-shot capture include an advanced triggering system. Although triggering is an important issue for single-shot signals, dead time is not. Because the event occurs only once, there is no need to quickly acquire a second event.
Repetitive waveforms are also easy to understand. The classic function-generator waveforms—sine, square, and triangular waves—all fall into the repetitive category. Most scopes display these waveforms well because the waveforms don't vary and triggering on them is usually easy. Sample rate is not a big issue for these measurements; another cycle of the waveform will come along soon enough, so the scope can use repetitive sampling. Repetitive signals are not necessarily simple, though; complex signals, such as composite video, can be repetitive.
To effectively view repetitive signals, you need to trigger on them; otherwise, they are unstable and wander across the display. Simple signals require only edge triggering, but others, such as composite video, can require other trigger modes.
Dead time is not a big issue for truly repetitive signals. The scope need not be in any great hurry to acquire the next cycle; a cycle just like it will be along when the scope is ready. Don't neglect dead time, however, because the scope's responsiveness depends on a quick acquisition system. Scope users expect a signal to appear instantly when they move a probe from point to point in a circuit. Also, the scope should respond instantly to changes in its front-panel settings. Scopes with long dead time (sluggish acquisition systems) tend to respond sluggishly to changes in control settings.
Varying-repetitive waveforms are more difficult to understand than the previous two categories but represent an important and common class of waveforms that are often difficult to measure. Think of these waveforms as basically repetitive with some variation in the waveshape. For example, a sine wave that varies in amplitude as a function of time is basically repetitive but varies from cycle to cycle. This variation might be very slow, producing a scope display that shows a sine wave gradually changing in size. Alternatively, the variation could be very fast, occurring instantly on only one cycle of a waveform. The slowly varying case is easy to view with almost any scope, but the quickly varying signal presents a greater challenge. A scope with a short dead time and a high display rate is more likely to show the single short cycle, assuming that the scope triggers on the normal cycles of the sine wave. If the scope can trigger on the reduced-amplitude cycle, the measurement problem degenerates to the single-shot case.
Fig 2 shows some representative examples of varying repetitive waveforms. Often, these signals are the unexpected ones that make an engineer's or technician's job difficult. These are the hardware bugs that are unavoidable even though you never intentionally design them into a circuit.
Sample rate is a confusing issue for varying-repetitive waveforms. The repetitive nature of the waveform means that you can use repetitive sampling to acquire the waveform. But what about waveform variations? How well will repetitive sampling follow these variations? Using the sine-wave example, if the amplitude variation is slow, repetitive sampling with sufficiently small dead time easily keeps up with the waveform variations. The case of one reduced-amplitude cycle is less clear; you can't be sure how many times you will sample a particular cycle unless you look carefully at the sample rate, the period of the sine wave, and how often the reduced-amplitude cycle occurs. Fig 3 summarizes the three waveform categories and their characteristics.
A look at some practical measurement examples will help you to apply these principles.
Varying-width pulse: This waveform is a repeating pulse whose width normally varies from 30 to 50 nsec and occasionally jumps to 80 nsec. This situation is common in digital systems in which the mostly nominal clock cycles are accompanied by an occasional worst-case cycle that is longer than the rest.
If you use a scope with a long dead time to the measure the signal, the chances of capturing the variation in the pulse are very small. You can simulate this case by setting a large trigger hold-off on an HP 54600B scope to increase the normally small dead time (Fig 4a). In Fig 4a, the pulse appears to have little or no variation. Fig 4b shows the measured waveform with the scope operating normally, showing the pulse width varying from 30 to 50 nsec. You can't easily see the longer 80-nsec cycle, but occasional samples may fall on such a pulse. The scope operates on a timebase range that uses repetitive sampling. Even though the pulse variation is infrequent, enough of the repetitive samples fall on the wide pulse to create a useful display.
DSOs normally discard older sample points as new ones become available. This technique makes perfect sense in most situations, but when dealing with infrequent events, you might do better to keep all the sample points you can. Most digital scopes provide an infinite-persistence mode that accumulates all samples on the display. (The HP 54600-series scopes' Autostore mode has the added benefit of showing the old samples in half-bright intensity and the most recent samples in full-bright intensity.) Regardless of the dead time, using the infinite-persistence mode helps uncover infrequent variations in the waveform. Fig 4c shows the varying pulse measured with the Autostore display mode. The extremes of the pulse width are now visible, including the 80-nsec-wide cycle.
Another way to capture the wider pulse is to use a scope that can trigger on the event. For example, the HP 54542A provides a glitch-trigger feature that can trigger directly on the wider pulse. With the glitch trigger set to trigger on pulses greater than or equal 60 nsec wide, you can easily capture and display the wide pulse (Fig 4d). Using this triggering capability along with a sample rate high enough to capture the event in one acquisition generally provides the best measurement of the waveform. To use this capability, you must know what to trigger on, however.
Sine wave with dropout: This signal is a basic sine wave that occasionally drops out, leaving a 0V baseline in place of a sine-wave cycle.
A scope with a long dead time tends to miss the flat baseline (Fig 5a). You might conclude that the sine wave is continuous and that the signal source is operating correctly when, in reality, the signal drops out occasionally. Shorter dead time causes the waveform imperfection to easily appear (Fig 5b). Again, the scope is operating at a timebase setting that uses repetitive sampling, showing that repetitive sampling is useful for identifying waveform irregularities.
Again, if you know what to trigger on, you may be able to use the information to trigger directly on the event. Many scopes with advanced logic triggering can directly trigger on the waveform. On the other hand, even the most advanced triggering system can't capture some signals. For example, a small dip in the amplitude of a sine wave would be difficult to trigger on. Although scope manufacturers keep creating more powerful triggering systems, there will always be cases in which the scope cannot trigger on the waveform variation.
Triggering plays a role in viewing infrequent events. If you can trigger on an event of interest, you essentially reduce the problem to the single-shot case and eliminate the dead-time issue. How does this stratagem fit into everyday scope use? Triggering is often the ultimate solution to viewing a tough problem, provided that you can describe and trigger on the problem. In troubleshooting, you often don't know what the problem is; otherwise, you'd have fixed it by now. In such cases, a high-update-rate scope that doesn't miss much between acquisitions may be the best choice.
In summary,
How do you determine the dead time of a digitizing oscilloscope? Well, it depends. Some scopes specify their displays update rate or dead time, but most don't. In general, a scope manufacturer that designed a scope for a fast display update rate will specify the rate. If there is no spec, you must determine the rate through experimentation.
Robert Witte has worked at Hewlett-Packard for 16 years. Witte is an R&D project manager who heads a team of engineers designing digital oscilloscopes and related instruments at HP's Colorado Springs, CO, facility. A senior member of the IEEE, he holds a BSEE from Purdue University, West Lafayette, IN, and an MSEE from Colorado State University, Fort Collins, CO. He lists his hobbies as amateur radio and backpacking.