The following comments apply specifically to the amazing Tektronix MDO3104 oscilloscope. The relations between analog bandwidth, sampling rate and record length pertain equally to other makes and models, but specific metrics are different.
The Tektronix MDO3104, with a 1 GHz bandwidth and 5 GS/sec sampling rate, has a maximum 10M-point record length. We shall see how and why bandwidth and record length can be reduced to optimize the oscilloscope’s performance in specific applications. First, some definitions:
Bandwidth in an oscilloscope may be roughly defined as the highest frequency that can be measured or accurately depicted in a particular instrument. In actuality, a more definitive statement is that it is the frequency at which a sinusoidal signal is attenuated by 3 dB. This amounts to 70.7% of the signal’s analog aptitude.
Record length of a given acquisition as displayed in a digital oscilloscope is expressed not in time, such as a certain fraction of a second, but rather in total points or samples. The maximum record length of a particular instrument is spelled out in the specifications. This number may be adjusted downward by the user, but can’t go above the maximum. If the record length were zero, there would be no display. At a low record length, the display would be less informative, consisting of just a few dots on the screen.
Sampling rate is a fixed amount (set by the record length divided by the time captured). It is given in the specifications for a particular oscilloscope and cannot be changed by the user. However, it may drop because of memory constraints, depending on the frequency of the signal of interest. The maximum sampling rate is usually printed on the front panel along with the bandwidth. The sampling rate is expressed in samples-per-second and is typically a high number, rising dramatically for higher bandwidth machines.
The Tektronix MDO3104 has a sampling rate of 5GS/sec. Each second, the scope takes five billion samples of an analog electrical signal to create the digital version. A higher sampling rate enables a more accurate representation in memory and in the display.
The Nyquist Sampling Theorem, named after Harry Nyquist who laid the groundwork in 1928, states that in rendering an analog signal as digital data, the sampling rate must be greater than at least twice the frequency of the analog signal. This is called the Nyquist Frequency. If this criterion is not met, aliasing may arise. Aliasing is generally harmful and to be avoided. That is because at a sampling rate that is less than twice the frequency of the signal under investigation, ambiguous results may appear in the form of errors in the display. In its published specifications, the Tektronix MDO3104 oscilloscope sampling rate, 5 GS/sec, is indeed higher than twice the 1 GHz bandwidth, so aliasing does not become an issue.
It’s worth taking a look at precisely what aliasing is and how it can arise. Phenomena in nature are analog as opposed to digital unless we are working at a very small-scale, where quantum effects become operative. A forerunner to digitization was cinematography, which emerged in the 1800s. It was found that successive still images could be merged to create the illusion of motion. This technique of sampling was effective, but it did not always work as intended.
In old westerns, fast-moving wagon wheels would sometimes incongruously appear to be turning too slowly or even rotating backwards. This effect arose because the discrete samples and the moving spokes had a relationship that gave rise to ambiguous visual interpretation. It would be possible to eliminate the erroneous representation by speeding up both recording and playback rate, multiplying both by the same factor so as to avoid slow or fast motion.
A similar error can take place today if a digital storage oscilloscope under-samples a high-frequency analog waveform. An insufficient sampling rate can give rise to temporal aliasing, where erroneous waveforms may be improperly synthesized. These aliases can be eliminated by choosing a sampling rate that is appropriate to the frequency of the signal being viewed.
Real signals other than pure sine waves have a frequency content outside the fundamental, in accord with the Fourier Transform, that extends indefinitely in an upward direction. There will always be aliasing in this situation. However, that harmful tendency is controlled by the fact that the instrument itself has limited bandwidth. So we see there is actually a palpable up-side to the otherwise toxic effects of capacitive and inductive reactance.
An effective method for preventing aliasing errors is to filter the original signal so as to attenuate high-frequency components prior to sampling. To the extent that the high-frequency portion of the analog signal is not diminished, there may be some low-level aliases, but their amplitudes will be much less than if the original signal had been left alone.
Memory Depth places an upper limit on the number of samples that can be stored in a digitizing oscilloscope. The sampling rate published in an oscilloscope’s specifications may not always be placed in memory if the memory lacks sufficient depth for a given application.
Two relationships are relevant in this discussion:
Sample Rate = Record Length/Time Duration
Time Duration = Record Length/Sample Rate
To optimize specific measurements in the context of differing circuit parameters, it is useful to change some of the oscilloscope settings. It’s customary to lower the bandwidth of the instrument when displaying a signal that is low in frequency relative to the bandwidth of the instrument and when there’s a lot of noise superimposed on the signal of interest. This has the effect of filtering out the unwanted high-frequency noise and preventing it from displaying.
To perform this filtering, first connect the signal to one of the analog channel inputs. Press Autoset to get a good display. Then, in the Tektronix MDO3104, press the relevant channel button, twice if necessary. At the center bottom is a menu item marked Bandwidth which should be labeled Full. Press the Softkey associated with Bandwidth and you will see to the right of the display that the bandwidth can be reduced from Full (1 GHz) to either 250 MHz or 20 MHz.
Determine if one of these bandwidth levels eliminates the noise. If not, it may be possible to insert an external capacitor in parallel with the signal and/or an external inductor in series with the signal to eliminate the noise without wiping out the signal. It may be necessary to press Autoset for each setup. Don’t neglect to revert to full bandwidth before going on to other measurements. This may be done by pressing Default Setup.
Another scope specification that users can adjust is Record Length. To do this, after pressing Default Setup and Menu Off just to clear the table, press Acquire. The menu choices appear across the bottom, under the display. The second from the left is Record Length. Pressing the associated Softkey, we see there are six alternate values. They are all expressed in number-of-points rather than units-of-time. The maximum record length as noted in the oscilloscope specifications for the Tektronix MDO3104 is 10M. The other values, which may be selected by turning Multipurpose Knob a, are 5M, 1M, 100K, 10K and 1,000.
So why would the user want to select any but the maximum record length setting? The answer lies in the fact that there is no direct way to adjust the sample rate in the MDO3104 oscilloscope. The sample rate is determined solely by the ratio of the record length and the length of the horizontal scale. For this reason, the various record length options let the user adjust the sample rate indirectly.
A higher record length gives a better representation of the signal. Between representation and resolution, there is a choice to be made. Maximum record length does not always equate to the highest sample rate. It takes a faster sample rate to capture some signals. However, when there are not enough samples, the accuracy of the measurement could degrade. Always, to avoid aliasing, the Nyquist ratio must be observed.