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bzo 21st February 2004 09:00 PM

DSO Bandwidth vs sample rate
Can someone help me understand the relationship between the bandwidth vs the sample rate in digital storage oscilloscopes? A typical DSO might be speced at 100mhz bandwidth with 30MS/s sample rate. It seems to me that due to Nyquist, the maximum theoretical signal resolvable is half the sample rate, which would be 15mhz. So where does the 100mhz bandwidth come in? Am I missing something here?

claudio 22nd February 2004 12:36 PM


The first feature to consider is bandwidth. This can be defined as the maximum frequency of signal that can pass through the front-end amplifiers. It therefore follows that the analogue bandwidth of your scope must be higher than the maximum frequency that you wish to measure (real time).

Bandwidth alone is not enough to ensure that a DSO can accurately capture a high frequency signal. The goal of scope manufacturers is to achieve a specific type of frequency response with their designs. This response is known as the Maximally Flat Envelope Delay (MFED). A frequency response of this type delivers excellent pulse fidelity with minimum overshoot, undershoot and ringing. However, since a DSO is composed of amplifiers, attenuators, ADCs, interconnects, and relays, MFED response is a goal that can only be approached, and never met completely.

It is worth noting that most scope manufacturers define the bandwidth as the frequency at which a sine wave input signal will be attenuated to 71% of its true amplitude (-3dB point). Or, to put it another way, they allow the displayed trace to be 29% in error of the input before calling it a day.

Remember also that, if your input signal is not a pure sine wave, it will contain higher frequency harmonics. For example, a 20MHz pure square wave viewed on a 20MHz bandwidth scope will be displayed as an attenuated and distorted waveform. As a rule of thumb, try to purchase a scope with a bandwidth five times higher than the maximum frequency signal you wish to measure. Unfortunately, high bandwidth scopes are expensive, so you may have to compromise here.

On some scopes, the quoted bandwidth is not available on all voltage ranges, so check the data sheet carefully.

Sample rate
With analog scopes life was simple: you just selected the bandwidth that you required. For digital scopes, sampling rate and memory depth are equally important. For DSO's, the sampling rate is usually specified in mega samples per second (MS/s) or giga samples per second (GS/s). The Nyquist criterion states that the sampling rate must be at least twice the maximum frequency that you want to measure: for a spectrum analyser this may be true, but for a scope you require at least 5 samples to accurately reconstruct a waveform.

Most scopes have two different sampling rates (modes) depending on the signal being measured: real time and equivalent time sampling (ETS) - often called repetitive sampling. However, ETS only works if the signal you are measuring is stable and repetitive, since this mode works by building up the waveform from successive acquisitions.


bzo 23rd February 2004 06:06 AM

thanks for the information, that link was useful.

Sounds like the resolution of a DSO is limited by the lesser of the bandwidth or sample rate. So in my hypothetical example of a 100mhz DSO with 30MS/s rate, this is effectively equivalent to a analog scope with 15Mhz bandwidth? (ignoring A/D resolution)

claudio 23rd February 2004 03:53 PM

Some DSO manufacturer, just show the SR, while the analog Bandwidth is given by SR/2 (Nyquist). So when choosing a DSO, check the SR first, since the bandwidth can be calculated from it. However keep in mind this: if you have a 15MHz signal, measuring it with your sample DSO (30 MS/s) will came up from 2 point (30/15), that is not very readable!
So my suggestion is: divide the DSO SR by 10, so that you will have 10 points to draw the signal, and it will be your bandwidth: a 30 MS/s DSO will have a 3MHz bandwidth.
Also check if the SR doesn't divide itself in case you are using both the DSO channels.


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