Digital sampling and display technology are making digital oscilloscopes more like their analog counterparts, but there’s still enough difference to cause confusion.
Analog scopes and digital scopes have much in common. They are used to display the same waveforms, use the same probes, have similar input circuits and perform the same basic function. The main difference is that digital scopes sample the signal, while analog scopes show a continuous signal on the display.
Analog Scopes
Analog scopes paint a replica of the input signal across a cathode ray tube (CRT) while the time-base circuitry sweeps the signal across the tube. It is tempting to conclude that because the signal is written directly to the CRT, it is always a true representation of the signal, but the displayed waveform is actually a composite of multiple traces acquired on many different sweeps. Since the CRT only responds momentarily to the electron beam hitting the tube’s face, the signal must be repetitive so that multiple traces are available to update the display. A single-shot event is a brief flash on the screen of an analog scope.
Consider what happens when the waveform varies, perhaps due to modulation, glitches or other noise. If the variation is infrequent enough (such as a rare glitch), it may not even be viewable on the display. On the other hand, if the variation is frequent enough (such as the amplitude modulated signal shown in Figure 1), the signal will appear as a multivalued waveform with intensity variation corresponding to how frequently a particular segment of the waveform occurs. The analog scope handles this type of complex signal so well that it is the preferred troubleshooting tool for many engineers and technicians.
Analog scopes do not continuously show the waveform, since there is a dead time while the scope resets the CRT beam to the left side of the display. Fortunately, this dead time is usually very small, resulting in a responsive display and a scope that is rarely “blind” to the input signal.
Even though analog scopes are good for troubleshooting, they have weaknesses. On very fast time-base settings, the trace has a tendency to become dim, especially if the repetition rate is low. You may have to use a viewing hood. There is flicker on slow time-base settings, and on very slow sweeps, the trace collapses down to a single, bouncing dot.
Digital Scopes
In a digital scope, the waveform is represented only at the separate sample points and is undefined in between. However, users worried about missing an important event can take comfort from the fact that sampling the waveform often enough will capture every detail.
The Nyquist sampling theorem says the input signal must be sampled at a rate greater than twice the highest frequency component contained in the signal of interest. In practice, sampling is often performed at higher rates, namely at 4 to 10 times the input bandwidth of the digital scope.
There are two ways to get more samples on the waveform: Increase the sample rate, or sample the waveform repetitively.
The most obvious way to obtain more samples on the waveform is to increase the sample rate by using a faster analog-to-digital converter. Scopes whose sample rate exceeds the Nyquist Rate use real-time sampling and are sometimes said to oversample the waveform. For example, a 100-MHz scope might have a maximum sample rate of 500 MS/s or five times the signal bandwidth. Since this rate is 2.5 times the Nyquist Rate, it appears to be a suitable margin.
On the other hand, it gives us only five samples on a 100-MHz sine wave (Figure 2). Five samples is enough to represent the signal, but will require significant signal processing to interpolate between sample points and produce a continuous waveform. The interpolation process is not perfect and the waveform often will exhibit a wobble due to aliasing.
More importantly, the rate that appears on the data sheet is the maximum sample rate, which occurs only on the fastest time-base settings. On slower settings, the scope must reduce its sample rate to keep its memory from overflowing, so it loses the ability to oversample.
The second way to increase the number of samples on the waveform is to sample the waveform multiple times and combine samples from different acquisitions to produce a waveform with a large number of samples. Scopes that use repetitive sampling do this, producing waveforms with thousands of tightly spaced samples.
For example, a 100-MHz digital scope repetitively samples the input waveform with a 20-MS/s sampler, but uses repetitive sampling to acquire those samples on the waveform with 100-ps resolution. This gives an effective sample rate of 10 GS/s, which produces 100 samples on a 100-MHz sine wave (Figure 3). This compares favorably with the five samples obtained with the oversampling approach. With so many samples, you don’t need signal processing or interpolation to display the waveform, and no wobbling is introduced. The displayed waveform is made up of many acquisitions of the signal, similar to that of the analog scope.
A pure 10-MHz sine wave appears clean and undistorted when measured using a digital scope with repetitive sampling (Figure 4). When the same sine wave is displayed on a scope using oversampling, imperfections appear (Figure 5). These glitches are not actually present in the waveform but are caused by problems in the interpolation algorithm. Typically, these errors in the waveform change from sweep to sweep on the scope, producing a dancing or wobbling effect on the displayed waveform.
Such display problems can mislead an engineer or technician into thinking that there is a problem in a circuit when there is not. We don’t really need to stretch the performance of the scope to see this problem, since the 10-MHz sine wave is 10 times less than the bandwidth of the scope.
Single-Shot Sampling
So far, we’ve assumed that the signal is repetitive. What about single-shot events? When you have only one chance to capture an event (a true single-shot transient), there is no substitute for a high sample rate; repetitive sampling techniques will not suffice. Keep in mind, however, that the large majority of signals are repetitive in nature; otherwise they could not be viewed with the industry-standard analog scope.
A higher sample rate gives us better single-shot capability, but repetitive sampling produces more samples on a repetitive waveform independent of sample rate. Therefore, many high-sample-rate scopes offer a repetitive mode to avoid aliasing and wobbling effects when measuring repetitive signals.
While dead time is a minor issue with analog scopes, it assumes more importance with digital scopes, especially ones that use interpolation to fill-in between samples. Interpolation can take significant time, depending on the computing horsepower of the scope, and during this interpolation time, the scope is blind to any changes or variations in the waveform. A small glitch or noise burst is much less likely to be captured.
Even though a scope may have a high sample rate, the dead-time problem may make it less likely to capture a rare event on a repetitive waveform. Some scopes overcome this by providing advanced triggering capability so you can trigger directly on the event of interest.
Evaluating Performance
The best way to decide if a digital scope meets your needs is to evaluate the true sampling performance. Get answers to these questions:
· Sample Rate–If single-shot transients need to be measured, does the scope have a sufficient sample rate? Does the scope have enough triggering capability or memory depth to make use of this sample rate?
· Repetitive Sampling–Does the scope offer a repetitive sampling mode so that repetitive signals can be measured with the best possible fidelity? If you are not sure how the scope samples, view a sine wave whose frequency is about one-tenth to one-half of the scope bandwidth (e.g., a 10- to 50-MHz sine wave for a 100-MHz scope). Look for any wobbles or amplitude variation not really present in the signal. Slow down the time base and see if any strange sampling anomalies occur.
· Dead Time–Does the scope respond quickly to changes in the waveform? Put in an amplitude modulated signal and see if the scope gives the expected display. Do rare events, such as an intermittent pulse, show up quickly on the display? If an analog scope is available, do a side-by-side comparison.
· Responsiveness–Does the display respond quickly to front-panel adjustments or is there a noticeable lag when a knob is turned? Turn on a few automatic measurements such as Vpp or frequency to see if the overall scope response slows. Some scopes that rely on signal processing and interpolation don’t have enough computing power to keep the scope responsive.
Summary
Look beyond the simple specifications on the data sheet and evaluate how well a scope gets the job done. Besides considering the sample rate (for single-shot applications), consider whether a repetitive sampling mode is offered, the responsiveness of the scope and the dead time between acquisitions.
References
1. Stanley, W.D., Dougherty, G.R. and Dougherty, R., Digital Signal Processing, 2nd ed., Reston Publishing Co., Inc., 1984.
2. Witte, R.A., “A Simple Analysis Helps to Clarify a DSO’s Performance Specs,” Electronic Design News, Feb. 16, 1989.
3. Witte, R.A., “Sample Rate and Display Rate in Digitizing Oscilloscopes,” Hewlett-Packard Journal, February 1992.
4. Witte, R.A., Electronic Test Instruments: Theory and Applications, Prentice-Hall, Inc., 1993.
About the Author
Robert Witte is an R&D Project Manager responsible for the design and development of digitizing oscilloscopes at Hewlett-Packard’s Personal Measurements Operation in Colorado Springs. He received a B.S.E.E. degree from Purdue University and an M.S.E.E. degree from Colorado State University. Mr. Witte has taught electrical engineering at the undergraduate level and is a Senior Member of the IEEE. He is the author of two books and numerous magazine articles on test and measurement instrumentation. Hewlett-Packard Co., Personal Measurements Operation, 1900 Garden of the Gods Rd., Colorado Springs, CO 80907-3483, (800) 452-4844.
DSO
digital storage oscilloscope
instrumentation
Copyright 1995 Nelson Publishing Inc.
August 1995