Technical Article

# Important Parameters in Choosing an Digital Storage Oscilloscopes (DSO) - Part 1

July 17, 2017 by Artur Seibt

## 1. The requirements on oscilloscopes for switching circuit design and test.

By far, the oscilloscope is the most important measuring instrument of design and test engineers and their “eye”, without it they would remain blind, because the indications of other instruments depend on the waveform of signals and their measuring principles. This is especially true if a signal is not pure but corrupted by noise, hum, hf interference, or distortions. Other instruments include such disturbances and may show erroneous results, see the article “DC and AC Parameters ...” in Bodo’s Power July 2015.

SMPS and related circuitry like motor drives require high-performance oscilloscopes because they operate at clock frequencies of > 100 KHz, rise and fall times of even < 10 ns and signal amplitudes of several hundred volts to kilovolts. This requires >= 200 MHz bandwidth and a sensitivity of = 1 MB; the vast majority of DSO’s in use and still on the market offers only 1 ... 10 KB, few up to 50 KB. The author checked the homepage of a leading manufacturer and still found a wide variety of DSO’s with memories from 2.5 to 10 K, even up into the 5-digit price range, and, to boot, this manufacturer is bold enough to explicitly recommend those “for power supply design” - with memories which are 100 to 400 times too small!

While analog scopes are easy to understand and use, DSO’s are extremely complicated, this explains why even electronics engineers miss the stern warning which is implied in the advertisements “max. sampling rate 5 GS/s, bandwidth 500 MHz”; the “max.” preceding the sampling rate warns directly that it can be lower. By the way, this is the only hint manufacturers give to the many serious problems of DSO’s. The most important memory length spec is hidden in the table of specs or altogether missing! The fact that the bandwidth is tied to the sampling rate should be common knowledge, hence it should alert potential buyers why “max.” is missing preceding the bandwidth. Undersampling and insufficient bandwidth will give rise to gross distortions, ghosts, artefacts as well as worthless digital data. The bandwidth of DSO’s is not constant because the sampling rate depends on the memory length and the time scale used and shrinks to fractions of the maximum at slow time scales - without any warning to the user! This is known since the first DSO’s, the manufacturers prefer not to mention this in their advertisements, data sheets and manuals. Most potential buyers and users are hence totally unaware of this and other serious DSO problems.

The author took the trouble to download the 200 page manual of a 500 MHz, 5 GS/s model with 10 K memory and searched for a warning. There was only one short paragraph somewhere around p. 100, not prominent, headlined “Nyquist”, bluntly stating that the sampling rate depended on the time scale and could, e.g. shrink to 25 MS/s, so the Nyquist frequency was 12.5 MHz. The Nyquist frequency is of no practical value, only the bandwidth, which is - as will be shown - 1/10 of the sampling rate, so at 25 MS/s it will be down to 2.5 MHz! This is belittling the problem: at time scales like 10 ms/cm, typical in power supply work, the bandwidth will be down from 500 MHz to a ridiculous, useless 10 KHz! Would an engineer scrap his analog scope and buy such a scope if he had been fully informed? The fact is that some decades ago when DSO’s came up their functions and problems were described, but not anymore. Only if a manufacturer advertises his newest product he will describe in detail the shortcomings and problems of his former product.

“Digital is better than analog” has caused most buyers of scopes to reach for DSO’s, often intrigued more by the software features than the measuring qualities, forgetting that all those are for the birds if the digital data gathered are false to start with. Many have regretted that they replaced their reliable analog scopes.

DSO’s were massively forced into the market, not because of any better performance, but because the profits exceed those on analog scopes by orders of magnitude! The hardware of analog scopes is necessarily fairly expensive, this pertains especially to the wideband cathode-ray tubes; the manufacturing cost of such a crt surpasses that of a whole DSO! In contrast DSO’s consist of the same lowest-cost mass-produced components as any pc or similar product, in fact, a DSO is a pc with just an analog front end and an a/d converter added. The cost of a DSO display is zilch and independent of the bandwidth, because sampling converts GHz to KHz. A whole DSO fits easily on one e.c. board, production is in China anyway. The manufacturing cost of the higher-priced models is by far not proportionally higher so the profits on those are exorbitant.

Memory being cheap these days, it seems odd, why should DSO’s with too small memories still be on the market. This is a special, extremely fast expensive memory. Therefore even leading manufacturers use mainly so-called CCD’s (charge-coupled devices). These are cheap MOS ic’s, analog shift registers; the input signal is captured by writing it into such a shift register, each sample is converted into a charge packet. Thereafter a slow clock shifts the samples out to a serial a/d converter which may offer 12 bits. These MOS circuits contribute noise, the analog charge packets tend to dissolve and also influence each other; this is the reason why the memory length is limited to some KB. The best solution is the so-called flash or instantaneous converter, which is also the lowest-noise type, but this is much more expensive.

In the history of oscilloscopes, even the very first Tektronix scope in the 1950’s was specified for 10 MHz, the standard scope of the 50’s was the 30 MHz 545A. Even special lf scopes featured a minimum of 1 MHz.

Caveat emptor the Romans already knew, and Let the Buyer beware is the American translation, funny enough there is no equivalent in the German language. Today, it is more necessary than ever to be continuously aware of this principle and to meet all claims with a sound portion of distrust when buying electronic measuring equipment. Neither can neutral advice nor full information be expected.

Buyers were told that DSO’s were the “successors of analog scopes”, so users assumed that they would perform at least as well and provide advantages, because “digital is better and more modern than analog”.

Analog scopes can be described comprehensively by:

• Only analog scopes show the signal itself and in real-time, they are absolutely reliable. False displays are impossible, due to elementary physical laws. Their use does not require knowledge of oscilloscope technology. In contrast, more than 100 pages are necessary for a description of the functions and problems of DSO’s. The purpose of this article is limited to pointing out the worst problems of the majority of low and medium-priced models.
• DSO’s only show a more or less distorted rough and jittery reconstruction of the signal or artifacts which bear no resemblance to it. There are no “Real-Time DSO’s”, this term is misleading as it infers that a DSO were able to show a signal in real-time. All DSO’s are sampling scopes, one operating mode is called “Real-Time Sampling”. When the reconstruction becomes visible on the screen, the signal has long disappeared.
• DSO’s are not the successors of analog scopes although they pushed them out of the market. The fact that DSO’s achieve higher bandwidths than analog scopes has nothing to do with “digital”, but is due to the fact that they are sampling scopes! Sampling scopes achieved 14 GHz already in 1967. Also, further design of analog scopes stopped after the 1 GHz Tektronix 7104.

While design and manufacturing of analog scopes requires an enormous special know-how so only a few firms were ever able to make them, DSO’s can be assembled by anybody wholly from standard components, so a multitude of new manufacturers flood the market, and DSO’s are available for three-digit prices, probes for two-digit prices. Warning: Cheap probes can ruin the best scope; such a probe may contain a 1206 SMD 9 M resistor while being specified for 600 V and a capacitor with poor ceramic which distorts larger signals grossly and constitutes a safety hazard.

• In contrast to analog scopes, the use of DSO’s requires a vast knowledge of sampling, a/d converter, d/a converter and data compression technologies. Each display has to be checked whether it may be true or not.

### Because this is the First Law of DSO’s:

• He who uses a DSO must already know the signal. A leading manufacturer wrote “Know your waveform” in an earlier catalog: “Before you evaluate digitizers, evaluate your signals”. With analog scopes this is unnecessary. He who does not yet know the signal needs an analog scope to verify the DSO display. Lucky who still owns an analog scope, preferably a Tektronix 7000 series model.

## 2. Some of the main problems resp. disadvantages of DSO’s.

For the user, the advantage of DSO’s - their ability to capture and store single events for a long time - is rarely needed in practice. This advantage has to be weighed against a host of serious problems hitherto unknown and therefore not expected by the innocent user who tends to extrapolate the performance from analog scopes to DSO’s. The acceptance of DSO’s was promoted by the fact that many users were blinded by the software features of DSO’s. In this chapter only the main problems are discussed, the explanations are deferred to the later chapters.

### 2.1 Actual sampling rate, bandwidth and rise time.

The vast majority of DSO’s offered and in use are low and medium-priced models with memories of 1 to 10 KB, few to 25 ... 50 K, which creates serious problems. The overwhelming importance of the memory length is veiled by not mentioning it in the prominent specs but only in the fine print if at all! Sometimes the “maximum sampling rate window” is given instead, e.g. if it is 2 ms, this means that slower sweep speeds than 0.2 ms/cm will cause lower sampling rates and bandwidths!

Short memories will overflow quickly at high sampling rates. It depends on the time scale selected how long one acquisition takes, e.g. at 0.1 us/cm this is 1 us. At a sampling rate of 1 GS/s, this will fill 1 KB of memory in just that time. Already at 0.2 us/cm, the sampling rate must thus be reduced by half and so on. At 0.1 ms/cm it will be only 1/1,000 of the maximum, i.e. 1 MS/s, at 1 ms/cm 100 KS/s. The Shannon - Nyquist theorem is common knowledge although it is misunderstood more often than not. It will be shown later that the bandwidth is 1/10 of the sampling rate. Therefore not only does the actual sampling rate decrease to fractions of the maximum one, but also the bandwidth! The bandwidth of analog scopes is constant.

• The sampling rate and the bandwidth of DSO’s are NOT constant, they depend on the memory depth and the time scale used. They can shrink to fractions of the maximum values! Hundreds of MHz can decrease to KHz! This is independent of the maximum values.
• It is common practice to advertise: “max. sampling rate 2 GS/s, bandwidth 200 MHz”. This is factually wrong, the bandwidth is never constant, the correct specification is: “max. bandwidth 200 MHz”,
• The bandwidth depends on the sampling rate and is always limited to 1/10 of the actual sampling rate. So it decreases with the sampling rate the slower the time scale becomes. For each time/cm position the sampling rate and the bandwidth are different.
• Formula: Actual sampling rate = Memory depth/Time/cm x 10 cm

Note that neither the maximum sampling rate nor the maximum bandwidth appear in this formula, they are irrelevant! Hence an assumption that a 500 MHz DSO would easily handle any low-frequency work is only valid if that DSO is a very expensive one with a large memory.

• DSO’s with smaller memories than 1 MB, better 10 MB, are entirely unfit for any work on switching circuitry and should be scrapped.

Consequently, some DSO’s, especially handhelds, are not even capable of showing 50 Hz decently. Increasing the memory of existing models is hardly possible, a CCD can not simply be replaced by a better sampler/converter, this would be a new instrument.

The overwhelming importance of a large memory in switching circuitry work will be immediately apparent by these examples from daily practice:

Example 1: The current flowing in the choke of a pfc shall be measured which operates at 125 kHz. In order to see the 100 Hz half-sine, the time scale is switched to 10 ms/cm. The 125 kHz sawtooth rides on top of the 100 Hz half-sine and is typically 20 %.

What happens? Assumed there is a 1 KB memory; the DSO must reduce the sampling rate below 0.1 us/cm - without any warning to the user - and also the bandwidth:

• At 10 ms/cm the sampling rate will be reduced from 2 GS/s to 10 KS/s and the bandwidth from e.g. 200 MHz to 1 kHz! For a 10 KB memory to 100 KS/s and 10 kHz.

Of course, the 125 kHz sawtooth ontop the 100 Hz half-sine will not be visible at 1 or 10 kHz bandwidth, maybe some artefacts of it.

With a 1 MB memory, 1 MHz bandwidth will be left, so the 125 kHz sawtooth will be visible. But even with 10 MB, only 10 MHz bandwidth will be left of the 200 MHz. The oldest museum analog scope of the 1950’s, a Tektronix 545A with its 30 MHz constant bandwidth will still outperform such a DSO 60 years later by far! The DSO would require at least 30 MB of memory in order to come to a par with the oldtimer. So much memory is only available in extremely expensive top DSO’s. But the needle-sharp infinite resolution analog display with its Z-axis information in the trace would still remain far superior.

A DSO knows very well when it decreases sampling rate and bandwidth; it would be easy to display a warning on the screen: “Warning! Low sampling rate, low bandwidth!” But few DSO’s show even the actual sampling rate, never prominently, none shows the actual bandwidth! If manufacturers had been forced to display prominent warnings on the screen, DSO’s would never have displaced analog scopes. Considering the fact that many users of scopes, e.g. in medicine, have no knowledge of electronics, the absence of a clear warning cannot be condoned.

Example 2: A well-known German semiconductor manufacturer brought a so-called combo ic to market which contains the control circuitry for an SMPS with a PFC and a Flyback. The data sheet proudly said that the firm had invented a “new method of power MOSFET gate drive which eliminates the high current step at the start of a flyback completely”. For proof, a DSO printout was shown in which indeed no such step was visible. But the actual sampling rate was on the screenshot: 25 MS/s. This is equivalent to a bandwidth of only 2.5MHz resp. a rise time of 140 ns. Of course, a scope with 140 ns rise time can not display a current spike of 10 to 20 ns! On an analog scope, the current spike stood high as a tower. So the engineers of this firm fell prey to a false DSO display, because nobody ever told them that this was highly probable! For sure, the firm also applied for a patent, all based on a false DSO display!

All these low and medium-priced scopes with the short memories can only be used at the fast sweep speeds. There is only one solution: scrapping, or, to return them to their manufacturers, but the answer would probably be that it was the buyer’s own fault if he did not know enough about DSO’s...

The time of an engineer is much too precious and expensive to waste it questioning the validity of a DSO display and searching for the reason of false displays, not to speak of today’s time pressure. And the consequences of false measurements can be serious - like in the example above.

Why DSO manufacturers do now mention this? Oh yes, they do, but neither in their advertising, nor in data sheets or manuals, only in their other and older publications:

### Quotations Tektronix:

"Sample rate varies with time base settings, the slower the time base setting, the slower the sample rate. Some DSOs provide peak detect mode to capture fast transients at slow sweep speeds.“ Note that it was “forgotten” to state that the bandwidth is also reduced!

“The usable rise time and the usable memory bandwidth elucidate a remarkable difference between analog and digital scopes: While bandwidth and rise time of analog scopes do not not change with the time scale this is, in fact, the case with DSO’s because of the changing sampling resp. digitizing rate.”

### Quotations LeCroy:

"As the time base is reduced (more time per division), the digitizer must reduce its sample rate to record enough signal to fill the display. By reducing the sample rate, it also degrades the usable bandwidth. Long memory digitizers maintain their usable bandwidth at more timebase settings than shorter memory digitizers.“

“In contrast to analog scopes DSO’s show significant variations of parameters like bandwidth, sampling rate, resolution.”

“Oscilloscopes with nominally equivalent specifications may differ substantially in their actual performance so they may be totally unfit for certain applications!”

### Quotation HP:

“The sampling rate specification of DSO’s refers to the fastest time scale setting. If you select a slower time scale, the sampling rate will be automatically so far reduced that the signal portion captured fits into the memory. Assumed your DSO has a 1,000 point memory, it must capture 1,000 samples to fill it. If you select a time scale of 1 ms/ cm, it can store 10 ms/10 cm. In this case, the signal must be sampled every 10 ms/1,000 = 10 us; the sampling rate is thus 100 KS/s... The memory length influences the single-shot bandwidth.”

The quotation “forgets” to say that the bandwidth at 100 KS/s is a mere 10 kHz, but it shows a diagram in which 100 MHz bandwidth = 8 mm, so that 10 kHz = 0.0008 mm! In earlier publications, the company called users of analog scopes “analog hold-outs”.

The Shannon-Nyquist theorem is mostly misinterpreted: the highest frequency in the signal is mixed up with bandwidth!

• In discussions about digitizing it is usually assumed that a sampling frequency of twice the desired bandwidth is sufficient. This is absolutely false! Each system which should transmit a signal without distortions must obey a Gaussian frequency response which rolls off very gradually. At half the sampling frequency all frequency components must be sufficiently small in order to prevent aliasing. In practice, this requires that the sampling frequency must be at least ten times the bandwidth.

Quotations of leading firms advocate 10:1, and almost all DSO’s today follow this rule, e.g. a sampling rate of 2 GS/s allows for not more than 200 MHz bandwidth. Consequently, the 44.1 kHz of the DC as well as the 48 kHz used by radio stations are ridiculously inferior; audio requires at least 100 to 200 kHz.

##### Figure 2.1: The Gaussian response starts to decay very early, any steeper fall-off would cause overshoots. Therefore oscilloscopes are not suited for measuring the amplitude of sine wave signals, at least not for frequencies beyond 1/10 the bandwidth.

Oscilloscopes must be designed for a Gaussian frequency response because this is the only one which provides an undistorted pulse response with the shortest rise time. The amplifier’s group delay must be constant. The pulse response of a square wave will be symmetrical to half the amplitude.

Bandwidth and rise time are related by Rise time x bandwidth = 0.35

This relationship still holds even if the pulse response differs substantially from the Gaussian one, e.g. in case of an RC amplifier. The rise times of amplifiers or other units in a signal path add up geometrically if each has a Gaussian response:

$\LARGE&space;t_{rtotal}=&space;\sqrt{t_{r1}\;^2&space;+t_{r2}\;^2}$

From this, the rule of thumb follows that a scope should be at least three times faster than the signal to be measured.

#### About the Author

Dr.-Ing. Artur Seibt is a professional electronics design lab consultant with specialization in SMPS with 40 yrs. experience incl. SiC, GaN, D amplifiers. Inventor of current-mode control (US Patent) and He is also an expert in EMI design.

This. article originally appearedin the Bodo’s Power Systems magazine.

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