What is sampling rate and why is it important in the selection of test and measuring equipment?

What is sampling rate? Furthermore, why is it important? The answers to these questions should be understood so that accurate troubleshooting information can be obtained from available test and measurement instruments in commercial and industrial field service.

Before we answer these questions, let's discuss the basics of digital and analog technologies.

Analog versus digital sampling technology

Digital technology is rapidly replacing older analog technologies, both in equipment control systems and in the test instruments we use for troubleshooting, servicing, and calibrating these systems. Digital storage oscilloscopes are replacing their analog counterparts in many applications because they offer many advantages, such as automatic measurements, single-shot capture of intermittent electrical signals, memory storage, and hard-copy output. Also, the continual advance of digital circuit integration has produced extremely lightweight hand-held oscilloscopes and other related waveform-display tools that are well suited to portable use in commercial and industrial field service and maintenance.

Digital signal capture and display technology, however, does have certain limitations compared to analog technology. The most important limitation is related to sample rate.

Analog technology. Analog instruments work with continuously variable voltages. For example, an analog oscilloscope works by directly applying an input voltage to an electron beam that is moving across the oscilloscope screen. The voltage deflects the beam up and down proportionally, tracing an image of the input waveform, as shown in Fig. 1, on the screen. This gives an immediate and continuous picture of the waveform.

Digital technology. Digital instruments work with a series of voltage samples that are represented by discrete binary numbers. As such, a digital storage oscilloscope (DSO) samples the waveform, or measures it, at discrete points in time and uses an analog-to-digital converter (ADC) to convert these measured voltages into digital information (or "samples"). The DSO then uses this digital information to reconstruct the waveform on the screen, as shown in Fig. 2. In general, the faster the sampling rate, the more accurate the representation (waveform display) of the measured input signal.

This relationship can be compared to your PC display screen: newer VGA displays provide a much better representation of graphic images than older CGA screens of several years ago because they use many more pixels (or "samples") to construct the image.

Sample rate and bandwidth

The most familiar specification frequently used to gauge the performance of oscilloscopes is bandwidth. How does bandwidth relate to sample rate? Well, these two features are indeed related, but not always in a clear or direct dependency. This can lead to confusion when trying to interpret specifications from different oscilloscope manufacturers. The reason for this potential confusion is that several different sampling methods are used by different manufacturers. This variance is also from model-to-model.

To create a waveform accurately, a DSO must gather a sufficient number of samples relative to a trigger. In theory, a digital scope needs more than two samples per sine wave period (one full cycle of a regular waveform) to reproduce a sine wave. Otherwise, the acquired waveform will be a distorted representation of the input signal. This requirement usually limits the maximum signal frequency that a digital scope can acquire in real-time. Because of the limitation in real-time acquisition, many DSOs specify two bandwidths: repetitive-signal (or analog) bandwidth and real-time bandwidth.

The repetitive-signal bandwidth represents the highest-frequency sinewave signal that the scope's input circuits can accept with three decibel maximum attenuation (the point where distortion becomes unacceptable). It's important to note that this frequency limit applies to repetitive waveforms (signals that repeat in a regular and reliable fashion).

The real-time bandwidth, in contrast, defines the highest frequency sinewave that a DSO can capture by sampling in a single pass, using a single trigger. This is also sometimes called the single-shot bandwidth.

Is there more than one kind of bandwidth? The answer to this question lies in the two methods of sampling that are used in different scope designs: equivalent-time sampling and real-time sampling.

Equivalent-time sampling. The equivalent-time sampling method allows a DSO to have a bandwidth that is higher than its sample rate, which in fact many DSOs do. For instance, one popular DSO has a sample rate of 25 MS/s (mega-samples per second), but an analog bandwidth of 50 MHz. Because the sample rate must be more than twice the maximum signal bandwidth to build an accurate waveform, equivalent-time sampling must be used in this scope's design. The scope uses a series of successive trigger events to gradually build up a picture of the waveform. With each trigger, another set of samples are added to the picture, until enough samples have been collected to "fill in the blanks" so to speak and meet the Nyquist requirement (see sidebar on page 72) for minimum number of samples required.

In equivalent-time, a slower, lower-cost digitizer can be used to sample high-frequency signals. This is because the samples are collected over time and by capturing multiple acquisitions. This is depicted in Fig. 3.

Equivalent-time sampling should only be used when measuring repetitive signals. If there are intermittent glitches or single-shot events, they cannot be accurately captured and displayed using an equivalent-time reconstruction scheme because the events will probably not be captured at all. Even repetitive signals can be represented inaccurately if they vary over time, and the result can be image distortion that misrepresents the actual signal.

Real-time sampling. Scopes using the real-time sampling method must gather all the samples for a waveform from a single trigger event. This requires a higher sample rate to achieve the same bandwidth, as compared to an equivalent-time scope. This high sample rate is sometimes referred to as oversampling: a term meaning more than the minimum two samples are used per waveform period, as shown in Fig. 4 (see page 70).

The benefit gained from real-time sampling is quickly realized when trying to view a signal that changes over time, as when making an adjustment in a piece of equipment or when trying to capture a single-shot or intermittent signal. Intermittent or transient events, which are common in equipment troubleshooting applications, must be viewable. Equivalent-time DSOs can capture single-shot events, but at speeds that are much slower. For example, a 50-MHz equivalent-time scope with a sample rate of 25 MS/s has an actual maximum single-shot bandwidth of only 10 MHz.

Other performance issues

Other performance characteristics tied to sample rate are waveform capture rate and a phenomenon known as aliasing. Aliasing occurs when the scope is not able to sample fast enough to accurately reproduce the input waveform. Here, the waveform displayed on-screen will appear to be a lower frequency than the actual signal, which can easily lead to misinterpretation. [ILLUSTRATION FOR FIGURE 5 OMITTED] Special display modes such as peak detect (available on some scopes) can overcome this problem.

Waveform capture rate is the number of times per second the display can be updated with a new view of the input waveform. (Analog scopes have superior waveform capture rate since the electron beam drawing the trace is able to retrace and accept a new trigger with less hold off delay than a typical DSO.) Real-time DSOs can sometimes approach analog waveform capture rates, but equivalent-time sampling slows down the process because the waveform image must be built up over many acquisitions, which takes time.

Selecting an instrument

What does all this mean when selecting a test instrument? It means that your choice should be guided by the requirements of the application. If your measurements are on repetitive signals only, then an equivalent-time DSO may offer a cost-effective solution; here sample rate may be a non-issue.

If, however, you need to capture intermittent noise, glitches, or other single-shot phenomena, then a DSO with real-time capture and a high sample rate is the only choice to meet your performance requirement.

RELATED ARTICLE: TERMS TO KNOW

Analog and digital data: Analog data implies continuity as contrasted to digital data, which is concerned with multiple discrete states.

Analog-to-digital converter: A device thai converts a signal that is a function of a continuous variable into a representative number sequence.

Bandwidth (for osilloscopes): The frequency range over which an oscilloscope can accurately display the amplitude of sinewave input signals. The accuracy criterion, by convention, is defined as the 3 decibel attenuation point.

CGA, VGA: These are acronyms which identify display monitor technologies used for personal computers. CGA stands for Color Graphics Adaptor; VGA stands for Video Graphics Adaptor.

Holdoff delay: Trigger holdoff is a technique used to control which part of a complex signal is captured, by inhibiting triggering for a specified time interval after an initial trigger has occurred.

Peak detect: An acquisition made for some digital oscilloscopes which ensures that you see the extremes of a signal's amplitude.

Trigger event: An electrical event that is used as the horizontal time reference for acquired waveform samples.

RELATED ARTICLE: WHAT IS THE NYQUIST SAMPLING THEOREM?

The mathematical rule governing proper sampling methodology is referred to as the Nyquist Sampling Theorem. The theorem states that "...the sampling rate must be at least twice the frequency of the highest frequency component in the waveform being sampled." In other words, for a complete determination of a specific waveform, the maximum separation in time given to regularly spaced instantaneous samples of a wave having a bandwidth W is equal to 1/2 Wsec.

Reference: The FFT: Fundamentals and Concepts, Robert W. Ramirez, Prentice-Hall, 1985 and the IEEE Standard Dictionary of Electrical and Electronic Terms.

Ken Price is Product Manager and Chuck Saxe is Engineering Manager of Tools Business Unit, Tektronix, Inc.