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Part 6: Interpreting Digital Oscilloscope Displays We must learn to interpret what we see on the digital oscilloscope screen. The display is only a reconstructed image of the waveform which is sampled during a very small fraction of the total signal time. And incorrect operation can introduce alias “ghosts” – signals which don’t exist at all. By BRYAN MAHER While digital oscilloscopes are powerful instruments, they take some getting used to, particularly for peo­ ple who have used analog scopes for many years. In reality, there are significant differences between displays of the same signal seen on a digital or analog oscilloscope. And both displays are likely to be different from the real live signal. Each scope shows a different image, neither of which is a true representation of the actual electri­ cal waveform. For anyone who has used an analog scope for many years, there must first be the realisation that the screen display is not reality and that both analog and digital scopes 66  Silicon Chip give different “filtered” views of real signals. All of which is an admission that the signal seen on a digital scope can look quite different to the same signal on an analog instrument. Moreover, on a digital scope, it will probably look much noisier. Is that noise really there? Well, yes, in many cases it is and it is just not seen on the analog instrument. These noisy traces are in sharp con­ trast to the smooth traces of an analog scope. Together with the complexities of screen menus, they make some longtime analog scope users reluctant to invest in a digital storage scope. This aversion is unfortunate, for it denies those people access to the great signal processing advantages of the digital instrument. Why the trace wriggles The wriggly nature of the trace hits you in the eye, even on large amplitude signals, such as that shown in Fig.1. By contrast, the same signal displayed on an analog scope is likely to be as clean as whistle. What happens when we photo­ graphically enlarge a portion of the baseline trace seen in Fig.1? The result of an 8-times magnification is shown in Fig.2. The wriggles are a form of noise. But their large amplitude, even on signals as big as 8V, indicates some source other than random noise at the scope input. And because of the dig­ itising process the digital scope trace tends to have a characteristic “jaggy” appearance. This is very different from the nat­ ural random noise generated in high gain preamplifiers which we see on analog scopes. But some noise im­ pulses are too fast to generate enough light in the phosphor and so are not visible unless we turn up the bright­ ness. This means we are never sure of the true amount of noise when using an analog scope. The jaggies on all digital scope displays operating in simple mode Fig.1: a digital scope can find an elusive glitch but the trace is wriggly, even on 8V signals. Fig. 2: photographically enlarging the trace of Fig.1 shows an artificial jaggy waveform, characteristic of digital scopes used in simple mode. This jaggy waveform is independent of signal amplitude. stem from four sources. The first and predominant cause is inherent noise within the analog to digital (A/D) converters. Digitising rates Designers face great problems when digitising rates from 100MS/s up to 8GS/s are required. At this rate, even flash A/D converters are inadequate, because their speed is ultimately limited by the slew rate of the analog comparators used. A new technology is needed. In many Tektronix digital scopes an extra component is added. At a very fast sampling rate, one complete re­ cord (collection) of samples is passed into a proprietary line of special sem­ iconductor analog storage elements. Then the sampler pauses, while this temporarily stored analog record is shifted out at a slower rate to an A/D converter. The digital data so produced is concurrently recorded in the mem­ ory. This double shuffle achieves the complete digitisation at an apparent rate extending up to 5GS/s. Other manufacturers combine many digitising paths to achieve high speed. The Hewlett Packard HP54720/10 model contains 16 500MS/s 8-bit flash A/D converter channels. All the data outputs can be interleaved to produce an equivalent 8GS/s rate of A/D conversion, with an extremely short effective sampling period of one pico­second. Such speeds are way beyond the capabilities of any direct single stage A/D converter technology currently in existence. Digitisation in multiple stages, though necessary to achieve the required speed, unfortunately does generate noise. This is the dominant cause of the wriggly baseline and trace observed when any digital storage scope is used in simple mode. Digital oscilloscope manufacturers admit that the displayed baseline and trace always contains wriggles of two to three pixels in amplitude. One pixel is the smallest possible increment in vertical amplitude of the display and is equal to 1/256 or 0.4% of the screen height. Because the digitising section comes after the preamplifier and attenuator stages, this noise introduced by A/D conversion is the same at all signal levels. In stark contrast, analog scopes only show baseline noise on tiny signals, of much less than a millivolt. Averaging mode One way to reduce the apparent noise on a digital scope waveform is to operate in averaging or High Resolution mode. Averaging means the digital data from a number of suc­ cessive recurrent sweeps is averaged before being displayed. HighRes is an ingenious method wherein averaging can be done even on a oneshot. Be­ cause random noise averages out to Fig.3: to demonstrate quantisation noise, the lower trace sinewave signal was sampled, digitised and immediately reconverted back to analog, then displayed in the upper trace. Any imperfections not noticed in the lower trace are enlarged in the upper trace by the digitisation. February 1997  67 zero, the trace then seen on the screen is much smoother. We will investigate averaging and high resolution modes in the next chapter. Quantisation noise A second cause of the wriggly trace in digital scopes is the quantisation noise described in the previous chapter. Readers will recall that the A/D converter breaks down the continuous analog signal into 256 or more discrete decision levels. The A/D converter output data is a digital code representing the nearest decision level below the voltage of the analog sample. Quantisation noise arises from the difference between the actual voltage of each sample and the smaller voltage values represented by the corresponding digital words. A steadily rising analog voltage into an A/D converter produces a digital output rising in a staircase of discrete steps. The same applies for falling slopes. So the trace displayed on any digital scope is fundamentally a series of small increments, rather than a smooth continuous line. Quantisation also results in a secondary source of noise. If an analog signal is just below some particular decision level, any tiny fluctuation or noise spike can push the signal momentarily above that decision level. Thus the next higher digital data is generated by the A/D converter, lifting the display up one whole pixel each time this occurs. It is possible to demonstrate quantisation noise. In the analog scope photo of Fig.3, the lower trace shows a sinewave which was also fed into a sampler and A/D converter. The resulting digital data was immediately converted back to analog form by a digital/analog (D/A) converter and the result shown as the upper trace. Small irregularities are present in the lower sinewave but are too fast or too small to be noticed. And some noise exists in the reference voltage of the A/D convert­ er. Each fast noise impulse momentarily lifts the analog amplitude up into the next decision level, so producing a higher digital word. Thus lots of small step errors are produced. Pulse stretching This sequence of scope waveforms shows a sinewave signal at 10kHz displayed on a digital and an analog scope. The top waveform is from a Tektronix TDS 360 digital scope in sample mode at 2 megasamples/second while the middle waveform is at the same sample rate but in average mode (128 waveforms averaged). Finally, the bottom waveform is from an analog scope. Note the very smooth trace. 68  Silicon Chip A third effect which makes quantisation noise worse could be called “interference pulse stretching”. Many noise pulses are too fast to be seen on an analog scope but when captured by a digital scope’s sampler, it holds the signal voltage steady until the next sample is taken. Hence the sampler stretches fast noise pulses out to equal the sampling period, so they can be more clearly seen. A fourth very important contribution to the wobbly trace displayed on any digital scope is directly related to the waveform capture rate and screen update rate. This points up the vital difference between the dis­ play on any scope and the real live signal we wish to investigate. Using an analog scope, in many circumstances you will never see noise impulses, for two reasons, as illus­ trated in Fig.4. Firstly, they are usually not in synchronism with the scope’s horizontal sweep and so occur on a different part Fig.4: an analog scope may update its display every five microseconds, with about 500 sweeps superimposed. Individual asynchronous noise pulses do not overlay, so they are usually not seen. of the trace each sweep. Secondly, and this is of the utmost importance, very often the display on an analog scope is an overlay of hun­ dreds or thousands of superimposed sweeps. Suppose for example that you are looking at the 3MHz signal shown in Fig.4(a), with the sweep speed set to 0.1µs/div. The forward trace takes 1µs and the retrace and holdoff might occupy 2µs each, as illustrated in Fig.4(b). That is 5µs for each complete display cycle. Therefore, your scope trace will sweep across the screen 200,000 times each second. This is your update rate, the num­ ber of times your display is renewed each second. All these traces are being drawn on your screen, each one on top of the last. You are capturing and displaying only one out of every five microsec­ onds of the live signal. You could say your waveform capture rate is 200,000 waveforms/second, which in this case is 20% of the live signal. If you have turned up the brightness (intensity) such that the effective per­ sistence time of the screen phosphor is 2.5 milliseconds, then the display you see is the overlay of about 500 traces superimposed, each showing the same signal pattern. The display is really the average of 500 views of the input signal, with the noise averaging towards zero. Therefore you will never notice the noise that is present and the trace and baseline will be the smooth clean lines which analog scope users have come to expect. But this means that analog scope us­ ers are blissfully ignorant of noise and interference which could be playing Fig.5: a conventional digital scope may sample the real live signal for only one microsecond, then display that segment for perhaps 33,000us. You see only 0.003% of the live signal. February 1997  69 Fig.6: a 2kHz sinewave was sampled at 2200S/sec. This too-slow rate generated a 200Hz alias frequency which modulated the input sinewave, producing the false waveform displayed. havoc with the circuit or equipment they are measuring. When those same signals and inter­ ferences are fed to a digital scope as illustrated in Fig.5, the display will be quite different. Because of the effects listed above, noise pulses are recorded along with the wanted signal. Even though these interference pulses may be only nanoseconds in duration, they are liable to be dis­ played. That might be regarded as a disadvantage of the digital scope. But many digital scopes also have a big advantage – they can be programmed to find glitches. The scope waveform of Fig.1 is such a case. The scope was programmed to search for and trigger the scope display on any pulse which had a duration between 0.5 and 4.5µs. The instrument found one interfer­ ence pulse having a duration of 2.01µs within a collection of thousands upon thousands of clean signals. With the scope triggered on this glitch you can see and analyse it. Some digital scopes can be set up to be triggered on runt pulses or on specified glitches as short as 2 nano­ seconds. This is just not possible with analog scopes. sinewave you will see about two cycles of that signal, indicating a frequency of only 50Hz! But if you raise the sweep speed to 20ns, the scope will sample at 2GS/s. Then a little more than two cycles of the same input signal will be displayed, indicating the true fre­ quency, 13MHz. We should always use the scope to achieve the fastest sample rate possible, otherwise the display may show the wrong frequency reading. Or in other cases we may observe distortion on fast edges in a complex waveform, with the low harmonics re­ produced larger and out of proportion to the high harmonics. In other cases a signal may seem to drift across the screen untriggered, like some weird apparition. Alternatively the screen may display a signal component at a fre­ quency which does not exist at the scope’s input terminals, as illustrated in Fig.6. Here the input signal is a 2kHz sinewave and the digital scope is in­ correctly operated with an effective sampling rate of 2200 samples/second. The display of the 2kHz signal ap­ pears to be modulated with a slower component, which has a period of 5ms, representing a frequency of 200Hz. Yet no 200Hz signal was ap­ plied to the scope. Where is it coming from? We say the 2kHz real signal is also masquerading under an “alias” (a false name) at a lower frequency, 200Hz. You can see an apparent modulation pattern which has a 5ms period. It is important to understand what causes these strange phenomena and how to prevent them. Picturing voltage signals Normally, when we draw a signal waveform, we get something like Fig.7(a) which depicts a 1kHz sine­ wave signal. We say that this is drawn in the frequency domain because the horizontal axis of the diagram is time which can be seconds, milliseconds, microseconds or whatever. But there is another way of depict­ ing the same 1kHz sinewave signal and that is the frequency domain, as shown in Fig.7(b). In this case, the horizontal axis of the diagram is frequency and since we only have one frequency it is depicted as a vertical line at the 1kHz spot on the axis. The height of the vertical line is measure of the amplitude, just as it is in the time domain. When you connect a 1kHz signal to a digital scope it will be sampled at some rate, which we will call the effective sampling frequency, fs. Any sampling process generates harmonics and so the sampler output will contain the 1kHz input frequen­ Aliasing A completely different type of error is sometimes seen on a digital scope when incorrectly used. The effective sample rate achieved is approximately proportional to the sweep speed you select. For example, a scope which is ad­ vertised to sample at 2GS/s will only achieve that rate when you select the fastest sweep speed. But the same scope, when switched to a sweep speed of 5ms/div has an effective sampling rate of only 10kS/s! That difference is crucial. At that setting, if you apply a 13MHz 70  Silicon Chip Fig.7: a 1kHz sinewave (a) can be represented in the frequency domain (b) as a vertical line on the horizontal frequency axis. Its height shows its amplitude. Sampling (c) at rate fs produces extra frequencies at fs ±1kHz. Fig.8: complex waveforms (a) can be depicted in the frequency domain (b) by a sequence of vertical lines representing the fundamental and all significant harmonics. The sampler (c) generates extra copies of all harmonics at the sum and difference of the sample rate fs and each harmonic frequency. cy, the sampler frequency fs, plus the sum frequency (fs + 1kHz) and the difference frequency (fs - 1kHz). These frequencies are shown graphically in Fig.7(c). If the sampling frequency is 1MHz, then the diagram of Fig.7(c) will show the input at 1kHz, sampling frequency at 1MHz, and the sum and difference frequencies: (1MHz + 1kHz) = 1,001kHz; and (1MHz - 1kHz) = 999kHz This description is a simplification, for the sampling process also generates an almost infinite number of other multiples at still higher frequencies, which we choose to ignore. But most real life waveforms, espe­ cially digital signals, are more com­ plex and might be like the example depicted in Fig.8(a). Squarish wave­ forms like this can be represented as the sum of a fundamental frequency sinewave plus many harmonics. And each harmonic is a sinewave with an appropriate amplitude and a frequen­cy which a multiple of the fundamental. So the waveform shown in the time domain diagram of Fig.8(a) might be described in the frequency domain of Fig.8(b) as a fundamental frequency of 1kHz plus many harmonic multiples at frequencies 2kHz, 3kHz, 5kHz, 7kHz . . . 21kHz, etc. We have stopped at the 21st harmon­ ic on the assumption that harmonics beyond 21kHz will be insignificant. We say that the input signal occu­ pies a frequency spectrum extending from zero to the highest significant harmonic. In this case the bandwidth B ex­ tends up to 21kHz. We refer to 21kHz as fB, the highest frequency in the input signal. We imagine an envelope shown as a dotted line in Fig.8(b) as the boundary of this spectrum B. When the complex waveform shown in Figs.8(a & b) is sampled, the sampler output looks something like Fig.8(c). Here we arbitrarily chose the sampling rate fs = 1MHz, so that fs is much larger than fB. The sum components generated by the sampler include the frequency fs added to the fundamental and to each harmonic of the input. These extend from fs up to the frequency (fs + fB). The difference components extended from fs down to the frequency (fs - fB). That is, the spectrum of the sampling products extends from (fs - fB) up to (fs + fB). Low pass filter The A/D converter must only see the spectrum of the input signal up to fB but none of the products of sampling; ie, above 21kHz in this case. To achieve this rejection, digital scopes include a programmable dig­ ital low pass filter (LPF) between the sampler and the A/D converter. The lower part of Fig.8(c) shows this filter and its passband, drawn here just a smidgen wider than fB. This filter passes the input signal spectrum on to the A/D converter but blocks all other frequencies above fB. That desirable result depends on the sampling rate fs being much higher than the highest significant harmonic (fB) in the input signal. That point is vital! Just how much higher is enough? And what happens if fs is not high February 1997  71 Fig.9: if the sampling rate is too low (a) the spectrum (fs - fB) overlaps the filter passband, so alias frequencies are displayed. But (b) if fs > 2fB, all terms generated by the sampler are rejected by the filter LPF, so preventing aliasing. enough? Fig.9(a) illustrates a case where the input signals extend 21kHz but the sampling rate is only 22.5kHz; much too low. This could occur if you operate the digital scope at too slow a sweep rate. This figure shows just the outline of Fig.10: this diagram explains the alias frequency component seen mixed with the 2kHz signal in Fig.5. The alias frequency is: (fs - f(in)) = (2.2kHz 2kHz) = 200Hz. 72  Silicon Chip each spectrum instead of depicting each and every harmonic. The vital point Now here is the vital point. Because fs is so low, the sampler products in­ trude into the spectrum of the input signal. More importantly, many of those sample frequencies will pass through the low pass filter (LPF). So they pass to the A/D converter and are displayed on the screen! Frequencies generated by the sam­ pler which overlap the LPF passband include (fs - fB) = (22.5kHz - 21kHz) = 1.5kHz; then (22.5kHz - 19kHz) = 3.5kHz; then 5.5kHz, etc in steps up to 20.5kHz. These “false” signals will appear on the screen, mixed in with the real signal. With all those false frequency com­ ponents mixed into the input signal, the waveform displayed on the screen will be nothing like the true shape. Aliasing can make a signal look like something it is not! Nyquist criterion So what is the minimum sampling frequency needed to avoid aliasing? Fig.9(b) shows the situation where aliasing is just avoided. Here the lowest frequency produced by the sampler, (fs - fB), is just a smid­ gen higher than fB. The frequency clearance between fB and (fs - fB) pre­ vents any overlap of the two spectra. So under this condition aliasing is avoided. To put that into figures, we need: (fs - fB) > fB; meaning that fs > (fB + fB) or ultimately, fs > 2fB. In plain English, that means that the sampling frequency must be more than twice the highest frequency com­ ponent in the input signal. This requirement is called the Nyquist Criterion, which is invoked to prevent aliasing errors in any system which uses sampling. The foregoing discussion supposes that the response of the filter drops like a rock to zero at the end of its nominal passband; ie, a “brick-wall” filter. But the response of real low pass filters is never as steep as that and some harmonic components beyond the nominal passband will always pass through. Hence, to prevent aliasing distor­ tions, we prefer the sampling frequen­ cy to be at least five or even 10 times the input signal bandwidth. Weird modulation explained We can now explain the weird mod­ ulation of the waveform seen in Fig.6. As Fig.10 shows, the input in Fig.6 was a single frequency sinewave at 2kHz but the sampling rate was too low at 2.2kHz. Sampling generates the extra frequencies: (fs - fB) = (2.2kHz - 2kHz) = 200Hz and also: (fS + fB) = (2.2kHz + 2kHz) = 4.2kHz. 200Hz is the alias frequency which intrudes into the passband of the low pass filter and mixes with the 2kHz input signal. This produces the amplitude modulated waveform seen in Fig.6 even though no 200Hz component was present in the input signal. At very slow sweep speeds, you might only see the 200Hz signal, noth­ ing else; a real trap for young players! To avoid alias problems when using a digital scope, keep the sampling rate high by using either the auto setup facility or the highest possible sweep speed. To determine if a signal seen is an alias, raise the sweep speed or use the Peak Detect mode. Lastly, we observe that analog scopes, because of their linear vertical deflection systems, cannot produce SC aliasing errors. Acknowledgements Thanks to Tektronix Australia, Philips Scientific & Industrial and Hewlett Packard for data and illustrations. February 1997  73