Although they both serve similar general purposes, digital oscilloscopes (DSOs) provide capabilities superior in almost every way to those of analog oscilloscopes. DSOs offer better waveform triggering and capturing, waveform displays, wave-shape measurements, signal analysis, and data storage and archives.
These features provide benefits in three main areas:
- Troubleshooting faults faster and more thoroughly.
- Characterizing signals more accurately.
- Documenting evaluations and tests.
For faster fault troubleshooting, a DSO includes high-speed, single-shot waveform sampling; advanced triggering; pre-trigger capture; rapid trigger rates; advanced display features; the capability to compare live waveforms with stored golden waveforms; deep waveform memory, and measurement statistics.
For characterizing signals, a DSO features better system amplitude accuracy, an adequate or excessive sampling rate, flexible interpolation between sampled points, automatic pulse-parameter measurements, and measurement statistics. For easy documentation, the key features are internal storage buffers, an MS-DOS floppy drive, an ASCII data-file output, graphics file output, and output to standard printers.
DSOs with all these features carry a high price. But the cost is worth it.1
The many advantages dwarf the two disadvantages of DSOs. First, the limited DSO sampling rate can corrupt signal wave shape, even when the scope’s analog bandwidth far exceeds the signal bandwidth. In the extreme case, this under-sampling is called aliasing, because the DSO will display a waveform at a much lower frequency than the input.
Second, DSOs can completely miss transient events due to the dead time between captures caused by slow screen update rates. These DSO weaknesses can cause misinterpretation of data and devastate the utility of the DSO. However, if you know where a pothole in the road lies, you usually can avoid it. The same opportunity exists with these DSO weaknesses.
To accurately troubleshoot faults or to characterize signals, minimize the wave-shape corruption caused by the waveform capture process of the DSO. A basic DSO functional block diagram shows that the amplifier or A/D converter could modify the signal before it is stored in memory.
The amplifier can attenuate signal amplitudes differently at different frequencies, add noise, add both harmonic and nonharmonic distortion, and recover slowly from overloads or saturation. High-frequency signal attenuation from limited bandwidth usually creates the most common and the largest errors.
On signals composed of multiple summed sine waves, such as digital pulse wave shapes, high-frequency attenuation erroneously reduces glitch amplitudes, rise times, and fall times. Table 1 relates DSO bandwidth to the measured rise-time error for a square-wave input signal (fundamental frequency).
Table 1. Measured Rise-Time Error
as a Function of DSO Amplifier Bandwidth
(-3 dB Frequency)
|Measurement Error = how many times longer the measured rise time is to the actual rise time.|
Why are these errors important? Because even very high bandwidth DSOs may not accurately measure the rise times of today’s leading-edge signals. For example, measuring a Gigabit Ethernet signal with a 1-GHz DSO can display a rise time approximately five times longer than the actual rise time of the signal.
Although critical to DSO functionality, the A/D converter also creates wave-shape errors due to a limited voltage sampling rate. If the sampling rate is infinitely fast, then you would retain the complete analog input waveform.
The finite sample rate determines how much time passes between digitized voltage measurement points on the waveform. A single-shot or real-time sample rate means the DSO only needs one input waveform occurrence to capture a full memory’s worth of sample points on the waveform. For example, 1-GS/s single-shot means the DSO accumulates one billion voltage measurements per second or that the sample points have 1-ns spacing between them.
Repetitive equivalent time, random interleaved sampling, and a sampling-head DSO architecture all mean the DSO needs multiple occurrences of the waveform to accumulate the full memory’s worth of sample points to represent the wave shape. For example, the actual A/D converter clock rate may only be 1 MS/s, but the equivalent time sample rate may be much faster, perhaps 10 GS/s.
To prevent extreme errors with these DSO architectures, the signal must be perfectly repetitive, and the trigger must be stable since the DSO interleaves many waveforms to reconstruct the original shape. Variations in signal shape from trigger to trigger can create a very noisy-looking waveform display. Variations in trigger timing due to noise can generate fuzzy-looking waveform edges.
The minimum acceptable sample rate depends on your desired wave-shape measurement accuracy. For simplicity, let’s use a sine-wave example. With two sample points per cycle (the Nyquist limit), amplitude errors can be up to 100%. A 1-V amplitude sine wave can appear as a grounded signal, a flat line on the screen.
With four points per cycle, the worst-case error can be up to 30% of the true amplitude. With 10 points per cycle, the amplitude error drops to roughly 2% worst-case. With sample rates not harmonically related to the input signal and with more than two points per cycle, the averaged frequency measurement is very accurate.
All oscilloscope vendors seem to have their own rules regarding minimum sample rate-and their rules have changed over time. Nyquist works well for the frequency domain, such as fast Fourier transform measurements, since it accumulates energy in frequency bins over a window of time. However, as we have seen, two points per cycle on a transient signal can create huge amplitude errors. So what should a minimum sample rate be?
For sine-wave measurement, Table 2 summarizes the errors associated with a limited sample rate. A sin(x)/x convolution is a mathematical means of stating that the signal bandwidth is limited relative to the sample rate.
Table 2. Limited Sample Rate-Induced Errors
on Sine-Wave Inputs
|Amplitude Error With
As you can see, sin(x)/x curve-fitted sample-to-sample point interpolation produces wave shapes that more accurately represent the actual signal shape of the adequately sampled source waveform data. Under these conditions, the curve fitting matches the shape of the original input signal between the sampled locations.
The DSO processor places additional points along the curve in the waveform areas between actual sampled points. As a result, the output of sin(x)/x curve fitting contains more data points than the digitized waveform record. Peak amplitude measurements especially benefit from sin(x)/x curve fitting.
With microprocessor clocks speeding along at several hundred megahertz, clock signals often contain only the first few odd harmonics and begin to look almost like sine waves. Nevertheless, most modern signals evaluated by circuit designers have a pulse wave shape.
To accurately use sin(x)/x interpolation, the highest harmonic must not exceed the Nyquist frequency. Simply put, to measure rise time accurately, at least two sample points must lie on the rising pulse edge.
The sampling clock and the input frequency usually are unrelated, so you have no guarantee where sample points will land on an edge. To ensure two points on the edge, the rise time must equal at least twice the DSO sample period. Under this condition, you always will get two points on the edge with a potential for three. This conservative approach suggests that the DSO sample rate should exceed 5.7 times the signal bandwidth (Figure 1).
For our discussions, let’s assume that five points per cycle of the highest frequency component represents our minimum acceptable sample rate. If we measure a 100-MHz sine wave, we need to sample at 500 MS/s. For a 500-MHz sine wave, we need 2.5 GS/s.
All signals are a sum of sine waves. For accurate DSO measurement of a nonsinusoidal signal, all its sinusoidal signal component frequencies must be lower than one-fifth the sample rate. For example, a 2.5 GS/s rate could accurately capture a 100-MHz square wave that contained only first, third, and fifth harmonics (100 MHz, 300 MHz, and 500 MHz). If we sampled at 500 MS/s, we would corrupt the amplitude and wave shape of the 300-MHz and 500-MHz components and the composite waveform.
For pulse waveforms, the rise and fall times of the pulse edges expose the frequency of the highest sine component (bandwidth = 0.35/rise time). With the five-sample-point/cycle rule, the minimum acceptable sample rate equals 1.75/fastest rise or fall time.
Once you have selected a DSO with an adequate sample rate for your signal, use it in a manner that does not degrade this sample rate. How? Your choice of both the display and memory configuration options can cut down the sample rate.
Using the right display options ensures an accurate picture of the true wave shape. Sin(x)/x interpolation can provide the most accurate wave shape, but first use sample points only or straight-line interpolation to ensure you have adequate sampling. Inadequate sampling with sin(x)/x creates pulse overshoot, rise-time measurement errors, and amplitude errors.
When the waveform memory exceeds the number of display pixels, display binning can become the largest DSO error source. For example, if the DSO waveform memory stores 50,000 data points but the display can only show 500 pixels across, then somehow the DSO must bin 50,000 into 500, or 100:1.
Decimation binning means the DSO displays every 100th point. Waveform glitches residing between the first and 101st points disappear from sight. Zooming in exposes the glitch-if you know where to zoom.
Envelope binning accumulates and displays both the maximum and minimum values among each 100 point set. Enveloping displays the full signal bandwidth. As you zoom in, the DSO exposes more waveform details. However, enveloping requires much processing and typically slows the screen update rate.
The most common display method to overcome both of these problems is 1:1 mapping, one pixel maps to one data point (no binning). The 1:1 mapping does not require signal processing and offers the fastest screen updates. In our example, 500 points reside on screen, and the remaining 49,500 sit off screen awaiting de-zooming or scrolling for your inspection.
Slow on the Trigger
Analog oscilloscopes offer screen update rates from 10,000 to 100,000 sweeps per second. Often, a transient glitch would appear and remain on the phosphor display tube long enough for the operator to notice it. In contrast, a typical DSO has a screen update rate at roughly a movie rate of about 30 frames per second, just fast enough for the human eye to integrate it into continuous motion.
Why the radical difference? DSOs equal analog scopes in recording speed (Figure 2). The input signal passes through an amplifier, then is converted to digital and stored in a block of memory. So far, it is just as fast as the analog scope.
But in the DSO, a processor translates this serial data array into a video bit map for display. This translation typically takes 5 ms to 30 ms, depending on the processor type and speed.
Since the overall system operates like a serial pipeline, the DSO holds off new triggers during this translation time. This trigger hold-off creates a 5-ms to 30-ms dead time between triggers when the scope cannot look at or capture signals. In simple terms, it is the black hole for glitches, an opportunity for you to miss the glitch of the day. If you try to troubleshoot a rare and intermittent fault, you have less than a 1% chance of ever capturing and seeing the fault.
The best way to troubleshoot a fault is to see it first, then catch it. Consequently, the first key to quick troubleshooting requires a DSO with a fast trigger repetition rate. Fast processors, direct memory-mapped displays, and 1:1 binning all contribute to a faster trigger repetition rate.
Once you see the nasty fault, isolate it, catch it, and compare it with potential fault generators. For example, if the fault is a glitch, trigger on it and view preceding gates for race conditions or synchronous EMI sources. You may need to capture the glitch on one channel and look at potential glitch generators on the other channels. Usually, it takes probing around the circuit at many locations to isolate fault causes. Even though the fault occurs rarely, you need it to repeat many times.
How do you trigger on the fault? The DSO must contain advanced triggering functions for your particular fault signal shape. Some of the new advanced triggering modes include nth event, glitch, width, runt, missing event, slew rate (great for metastability), state qualified, multiple line parallel pattern, and skew triggering.
Select the trigger mode that filters out the normal signal behavior and isolates the fault. The DSO will not trigger until the next fault occurs. It may hold off capture for seconds, minutes, or even days. But when the fault occurs again, you will have a snapshot of it with a single-shot DSO of adequate sample rate.
This approach still requires intelligence from you to set up the advanced triggering mode properly. The more complex the triggering mode, the less likely you will set it up properly the first time.
A basic knowledge of DSO triggering modes, display techniques, and memory management will help you to maintain your sample rate and consistently capture waveforms, even faulty ones. You will obtain more DSO benefits and avoid pitfalls.
1. “Digital Oscilloscopes: How to Pick the Right Tool for Your Job,” Test & Measurement Institute, 1998.
|About the Author|
|Steve Montgomery, P.E., has more than 10 years DSO industry experience and has presented over 350 half-day seminars for senior engineers and scientists. For several years, Mr. Montgomery taught DSO courses for AT&T Bell Labs. He also has written numerous articles and application notes for primary DSO vendors. Test & Measurement Institute, 11613 124th Ave. NE, Building G100, Kirkland, WA 98034, (425) 867-0500.|
Published by EE-Evaluation Engineering
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