A modern DSO does a lot more than just display waveforms. A particularly useful and timesaving feature is built-in waveform measurement. While you're viewing the signal of interest, parameters are displayed that you have selected from a list.
Some high-end benchtop scopes provide more than 40 different measurements, but having even a few is helpful. You can automatically measure frequency, period, peak-to-peak, rms, and average with the two-channel 20-MHz Extech Model MS400 hand-held DSO. The scope's true rms capability is especially valuable for DC + AC power signals.
On a scope that has an integral printer, you can plot the waveform and print the measured values with a push of a button. Or, this information could be transferred electronically to a design file. Of course, you could simply write down the values by hand. However they are recorded, the measurements have been made automatically and very quickly.
It's easy to see that this kind of capability has value, but it also raises questions. For example, what part of the waveform is being measured? How accurate is the measurement? How can the user affect both what is measured and the measurement accuracy? Can other parameters be included that aren't listed?
The answers to these questions vary with the model being considered although almost all automatic scope time-domain measurements are based on the definitions in IEEE 181-2003: IEEE Standard on Transitions, Pulses, and Waveforms, a substantially revised and combined version of 1977 standards. The 2003 document specifies a statistical method of identifying pulse parameters that relate to more commonly used measurements such as rise time or pulse width. Frequency-domain measurements are not included in the standard so you can expect variation in treatment by different manufacturers.
Several instrumentation companies including National Instruments contributed to the new specification. John Hottenroth, product manager for digitizers/oscilloscopes at the company, explained, “The original specification called for a histogram-based method in which the waveform samples were divided across 1,000 bins. This method works well for signals such as square waves that have sufficient sample density at the top and base to easily determine state levels. But it is less robust for arbitrary waveforms such as a triangle wave where there is a single sample at the peak.
“Following the 2003 revision, LabVIEW calculates state levels using both histogram- and peak-based methods to yield more accurate measurements for a wider variety of waveforms,” he continued. “In addition, LabVIEW offers automated selection that uses a set of criteria to determine whether the histogram- or peak-based method yields the best result.”
Figure 1a shows a square wave with over- and undershoot and the same signal with an amount of noise. Histograms of these waveforms are displayed in Figure 1b.
Without noise, the red plot shows two very high and distinct peaks corresponding to the 1.0 and 0.0 levels where the signal spends most of its time. The green plot demonstrates the effect of noise in broadening and lowering the peaks. They still are much higher than any of the other bins, but it's hard to tell from this example exactly what the two levels should be. The broad peaks are centered on the narrow red ones, but it's not obvious that the high and low levels in the presence of noise are the same as without noise.
Figure 2a shows a sine wave with and without noise. The histograms in Figure 2b are very different from those of Figure 1b. The red plot still has distinct peaks, but they are 20x smaller than for the square wave. With added noise, the green peaks are nearly the same level as values somewhat away from the peak. This example demonstrates the inappropriateness of histogram approaches for other than pulse waveforms.
Beyond Standard Measurements
Some applications require signal analysis beyond the common measurements usually supplied. Many scopes support custom MATLAB® analysis functions that you develop for your application.
Deciding how to handle outliers is an area that may be addressed with a custom routine. When can a data point be ignored, and when should it be included in a statistical analysis? Outliers are important because a single large value well outside the other data values can significantly skew statistics.
A Windows-based scope such as the Tektronix DPO7000 Series or the LeCroy WaveMaster® Series may support MATLAB routines through the internal data path between the scope's memory and the Windows interface. This arrangement provides a more tightly coupled system than transferring data to a separate PC memory and running MATLAB on the PC.
Randy White, technical marketing manager at Tektronix, said, “Typically, you would first use the scope's automated measurements to quickly qualify a signal or pulse. A deeper assessment can be made by applying histograms or advanced math to the automated measurements. For example, a histogram of a rise-time measurement provides a time trend of the measurement. The DPOJET measurement package is recommended for more flexible, advanced measurements including jitter decomposition, clock recovery, and spectral analysis of pulse edge timing.”
Alan Blankman, LeCroy senior applications engineer, noted, “Our scopes completely integrate MATLAB into the processing stream by allowing you to create and deploy a new measurement or math algorithm directly into the WaveShape Analysis Engine and display the result on the DSO in real time. With the XDEV Advanced Customization Package, you extend LeCroy scopes to include your most recent new technology algorithms the same day they're created.”
Agilent Technologies' Infiniium scopes are open Windows systems, which means you can install your own applications on the scope's integral PC. MATLAB has been verified to be compatible with the oscilloscope application. According to James Lewis, Infiniium oscilloscope product planner, with the company's N5430A User-Defined-Function Software, you can create custom math functions and measurements that appear to be integrated into the Infiniium software.
On the other hand, MATLAB on a separate PC together with a low-cost scope can be an effective combination. Instek's Model GDS-2000 includes 27 measurements and automatically determines if averaging across several cycles will be more accurate than measuring a single cycle. In addition, the scope will output a complete 25,000-sample acquisition for further MATLAB analysis.
“This method is popular with engineers in research labs because of its flexibility and affordability,” according to Jack Lin, marketing manager of Instek America. “A complete set of data input together with a good PC provides the lab engineers better flexibility in research and analysis.”
Gleb Geguine, software manager at GaGe Applied Technologies, commented that one of the benefits of a high-speed digitizer is its fast data-transfer capability. “The user can download data to a PC at rates orders of magnitude faster than a DSO. GaGe CompuScopes are available with a CompuScope MATLAB SDK that provides multiple oscilloscope-like examples of data analysis and presentation.”
What Does a Scope Measure?
If you don't indicate an alternative, a measurement will be applied to an automatically selected part of the captured data. For example, the pulse-width measurement algorithm will find the first rising edge after the trigger and then the next trailing edge and finally will calculate the time between the 50% point on each edge—the crossing point default value.
What if you captured five pulses in a single acquisition and wanted to measure the third one? Many scopes allow you to use cursors to bracket the area to be measured. Rather than measuring time from the actual cursors, an automatic measurement bracketed in this way only uses the cursors to identify the appropriate pulse. Then the pulse width is measured in the usual way.
Of course, you may select manual mode, which indeed would measure time from the left to the right cursor so the pulse width then would depend on the accuracy of the cursor placement. GaGe's Mr. Geguine observed that because “the user making the manual measurement may have implicit knowledge of the overall nature of the signal, for non-pulse-like signals, the accuracy of the manual measurement will most likely be superior to an automated measurement over one cycle.”
Joseph Ting, product manager for high-frequency instruments at Yokogawa, explained, “Any parameter measurement can apply to all the acquired memory, either zoom window or between cursors. Additionally, we support continuous statistics calculated over multiple acquisitions, cycle-by-cycle statistics, and statistics measured on history traces. We also can present any parameter in a real-time list, trend, or histogram view.”
This kind of flexibility is very useful in practice. It's convenient to capture one or more video lines relative to a trigger and then zoom the data to examine the synch area and the color burst. Using the cursors to bracket the color burst will allow the frequency to be measured unambiguously.
Some scopes go beyond captured data to create computed traces. In other words, after channels 1 through 4 have been acquired, they can be combined according to formulas that you specify to create computed channels A through D.
The data measured and the display presented to the user may not have a simple relationship if a scope's measurement system is very flexible. You need to understand what you want to measure, how the results should be displayed, and if the scope has that capability. If it does, and some scopes have several layers of sophistication in this area, you need to carefully set the relevant parameters so that what you get is what you intended. Testing with simple waveforms should confirm correct operation. See the sidebar for a discussion of future scope measurement developments.Analysis to Synthesis
Today, there is a drive for oscilloscope technology to enable analysis of increasingly complex high-frequency signals generated by the transmission of next-generation serial data standards. For example, the emerging PCIe 3.0 signals need greater than 20-GHz bandwidth to accurately see the harmonics of the 8-Gbit/s signals. Even lower bandwidth signals produced by standards such as USB 2.0 and USB 3.0 require oscilloscopes to calculate and extract information from the eye and estimate jitter down to single-digit picoseconds.
Compliance test routines defined and approved by the various standards committees have led to automated compliance test packages for oscilloscopes that ensure device compliance. However, before getting to the compliance test, an engineer must characterize and verify the design.
A rich set of debugging tools is important for measuring and interpreting the signal during the characterization/validation process but is equally or more important when the design fails pre-compliance. While the existence of tools is the first requirement, the integration and ease of applying the tools require an oscilloscope architecture design that does not compromise the engineer's thinking process or sacrifice time when more unit intervals are included in the measurement.
Along with the requisite for more unit intervals and longer memory, the need for more measurements has resulted in the near doubling of the number of measurements and measurement types within an oscilloscope over the past five years. All these measurements are used to break the signal down into its components and extract information for analysis. To analyze is to understand an aspect of the physical nature of the signal being explored.
However, as complexity increases, there is a need to combine the separate elements of analysis to form a coherent and complete understanding of the serial data signal. You see this when an engineer is trying to measure the jitter, the jitter breakdown, the eye pattern, and jitter histogram all at the same time. It is the combination of these separate analysis functions that provides the synthesis of information. Synthesis leads to deeper and more rapid insight into the behavior of the design.
With oscilloscope acquisition memory >250 Mpoints/channel, what was once a single pulse calculation now has the potential to include millions of pulses. IEEE 181-2003 defines how the measurement is to be performed. However, it does not address the understanding gained by examining the statistics of multiple pulse measurements—all calculated in a single trigger acquisition. Including more measurements extends the measurement confidence and speeds the time of interpreting the behavior of the design.
Until very recently, oscilloscopes frequently had one screen and one setup operation for each measurement. Depending on the complexity of the calculation and the methodology used to acquire and measure, some oscilloscopes could only complete one measurement at a time. It is as if the oscilloscope architecture treated the measurements as separate appendages to the acquisition of the signal.
While calculation power has increased in the past five years, scope architectures have lagged in delivering instruments that fulfill an engineer's desire to integrate the various types of analysis necessary to synthesize an under-standing of the high-speed and complex signals and maximize the insight gathered on the bench. Good analysis tools intelligently applied together through integrated hardware and software are next in the oscilloscope evolution.
Can You Believe Scope Measurements?
As an example of how frequency-dependent Johnson noise affects accuracy, the Agilent Technologies Model 90254A 2.5-GHz Infiniium DSO has an rms noise floor of 12.5 mV on the 1-V/div range. A common rule of thumb is that peak-to-peak noise is about 6x rms or 75 mV in this case. If an instantaneous measurement happened to occur at a noise peak, a 1-V signal could read anything between 0.9625 V and 1.0375 V.
Measurement algorithms don't simply measure peaks but instead determine the high and low levels of a pulse-shape waveform from a histogram of the sampled values. This approach tends to average noise because truly random noise will be smeared across many histogram bins. It broadens and lowers the peaks as shown in Figure 1b.
DC inaccuracy often is expressed as two parts: a gain error and an offset error. High-speed DSOs use 8-b ADCs, which means that signal resolution is one part in 256 or about 0.4%. Even if a DSO's ADC were perfectly linear and the input preamplifier and attenuator preceding it contributed no gain or offset errors, the ADC itself would contribute a ±0.4% error relative to a full-scale signal. For a 1.024-V signal, if the ADC changes states exactly at 4-mV increments, it still is outputting its old value when the input has changed by ±3.99 mV.
Some scopes feature enhanced resolution modes that are forms of averaging. They really do provide much higher resolution, and if the ADC is the major source of DC errors, those may be improved as well. However, the ADC's integral linearity comes into play when determining the accuracy of a high-resolution mode.
An ADC's differential nonlinearity must be less than ±1/2 lsb for the device to be monotonic. If the differential nonlinearity were greater than ±1/2 lsb, the output could decrease for an increasing input signal. Nevertheless, this doesn't tell the entire story. The distribution of the differential nonlinearity isn't necessarily uniform, so an ADC's integral nonlinearity can have a large effect on absolute accuracy.
Relative accuracy describes the relationship of one measurement to another but without involving their true values. It eliminates the effects of DC offsets when comparing a set of measurements. If two signals measured 2.0 V and 3.0 V, their difference would be 1.0 V. It still would be 1.0 V even if the signal values actually were 1.9 V and 2.9 V but the measuring instrument had a 0.1-V offset.
Precision is a measure of stability and repeatability, not absolute accuracy. Agilent's Mr. Lewis commented, “Precision is the reported resolution of a measurement result. As we increase the number of events averaged into a result, the number of digits displayed for that measurement grows.”
If you averaged a sufficiently large number of clock cycles from a very stable low-noise source, you could compute a pulse width similar to the number in the title of this article. The true value might be 150 ps, so 154.263 ps would be very precise but not accurate. Nevertheless, if the clock source and measuring instrumentation were sufficiently stable and the noise low enough, you really could report a result with six significant digits because the value would be repeatable.
Just as ADC quantization affects vertical resolution, the time-base clock rate limits timing resolution, and various kinds of jitter degrade precision and accuracy. High-speed scopes go to great lengths to provide stable, low-jitter, accurate time bases.
Compared to vertical accuracy in the 1% to 2% range, horizontal timing accuracy is orders of magnitude better. Agilent's 90000A Series Infiniium Scopes specify time-scale error of <±(0.4+0.5 x YrsFromCal) ppm pk. Tektronix lists <±1.5 ppm initial error, aging <1 ppm/year for the DPO/DSA70000 Series Scopes. LeCroy claims <±1 ppm with <1 ppm/year aging for the WaveMaster 8000A Series but also specifies a 1-ps rms typical jitter noise floor.
Clearly, timing is much more tightly controlled than vertical accuracy in a modern scope. Nevertheless, there always is a limit to accuracy, and this may be expressed as a delta time measurement accuracy specification.
All scopes have this kind of limitation, but manufacturers state it in different ways. Agilent provides formulas that include various limits depending on whether you're interested in determining absolute accuracy with or without averaging or standard deviation with or without averaging. For example, if you make any delta-time measurement with the 90000A Series Infiniium Scopes, the absolute accuracy without averaging is
This formula clearly shows that there is a minimum 4.5-ps absolute error for small time interval measurements. It also highlights the difficulty of determining the timing of a slowly rising signal edge. Slow slew rates significantly contribute to the absolute timing uncertainty.
If you take greater than 256 averages of a measurement, however, the factor of 20 in this formula reduces to 0.1, and the factor of 5.0 decreases to 0.35. This means that a very large amount of the absolute accuracy uncertainty is caused by random noise. With >256 averages, the 4.5-ps limit reduces to 316 fs or 3.16 ppm pk for a 100-ns interval.
Unless your job involves quantum mechanics, the signals you measure have only one value at a particular instant in time. To be certain that an absolute measurement is accurate, it must be traceable through a series of calibrated standards, eventually getting back to a standard measured by the NIST in the United States or similar agencies in other countries.
Each intermediate voltage reference encountered in tracing back to NIST adds some amount of measurement uncertainty. The result is that scope measurement accuracy is limited by the sum of the calibration uncertainties in addition to scope manufacturing tolerances, ADC quantization, component aging characteristics, circuit temperature coefficients, and noise.
Typically, the DC accuracy of a very wide bandwidth scope is approximately ±2%, much worse than a cheap multimeter. ZTEC makes the ZT-410 Series of 14-b and 16-b DSOs as well as many other 8-b DSOs, and the higher-resolution models are specified with <±0.25% full-scale measurement error. These modular scopes also are unusual in making on-board automatic measurements rather than relying on the host PC.
Few manufacturers quantify high-frequency accuracy. DSP-enhanced-bandwidth scopes generally have very good pulse fidelity, but the only guaranteed amplitude spec is a 30% error at the 3-dB frequency.
Although scopes inherently limit the accuracy with which measurements can be made, user incompetence often has an even greater effect. Here are 11 things you can do to minimize errors and enhance automatic measurement accuracy:
• Use probes matched to your scope and calibrate them according to your scope manual. High-impedance passive probes can't be used beyond 500 MHz, so if your signals are faster, use low-impedance passive or high-impedance FET active probes. All probes degrade accuracy to some degree by loading the circuit under test, because of insufficient bandwidth, or by inaccurate gain.
• If you are using a probe, keep the ground return as short as possible. Ideally, use a probe socket that has been directly soldered into the circuit under test.
• Deskew all channels using the probes that will be used to make the measurements. For accurate timing comparisons among channels, deskewing must be done to ensure alignment. Agilent's 90000A Infiniium Scopes have a generous ±25-µs range with 100-fs resolution.
• If you are using cables, deskew all channels taking the cables into account. You may need to use different length cables even though the signals are nominally simultaneous. The scope's deskew capability can give the appearance of exactly equal delays.
• In a 50-Ω system, if your signals are large enough, insert a good-quality 6-dB pad between the cable and scope input. This will minimize mismatch reflections and improve signal fidelity.
• Display signals as near to full scale as possible. The scope's 8-b resolution causes up to 0.4% accuracy error for full-scale signals. The error is larger for signals that span fewer ADC codes.
• Avoid time measurements that start from the trigger. Allow built-in measurement algorithms to work between captured signal edges. This eliminates errors related to trigger jitter.
• Acquire signals at the fastest time-base setting commensurate with the signal detail and length that must be captured and the available memory. This provides the highest timing resolution, which is necessary to capture high-frequency signal components. You can examine the detail with the zoom facility and make automatic measurements.
• Use cursors to bracket the area of interest to ensure only that part is measured. This works two ways. You can pick out a particular event to measure, or you can identify a series of events. For example, measuring the frequency of many cycles between cursors is more accurate than trying to measure only one.
• Use the lowest possible bandwidth. By all means, use the full scope bandwidth to examine the signal, but don't use any more. Noise increases with the square root of bandwidth, so for the same signal source impedance, a 1-GHz bandwidth scope will have 31x the noise voltage of a 1-MHz scope. Most DSOs provide a few lower bandwidth choices, but many Yokogawa scopes offer 16 different values.
• Read the instruction manual. Along with other instrument companies, Agilent participated in the IEEE 181-2003 revision committee and publishes many of the algorithms used for automatic measurements in its scopes. The Infiniium help system provides good examples.
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