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The subject of DSO "bandwidth vs sample rate" is one that seems to cause much confusion.

To those familiar with the sampling theorem, it seems strange that an ADC that has a maximum sample rate of 40 MHz is able to measure signals up to 75 MHz, let alone being able to even see anything at 100 MHz or more.

However, under the right circumstances it is quite possible to do all this and more...

Periodic waveforms

The key to understanding how this "magic" works is to realize that most signals of interest to an oscilloscope user are invariant periodic. That is, they a have fixed frequency and wave shape. Indeed it is not easy to see any other type of signal with an analogue CRO.

A DSO like Bitscope can of course capture and display a non-periodic waveform, but if we're interested in seeing signals with frequency content higher than half the sample rate, as the specification of this new ADC suggests we can, then it will be limited to periodic waveforms.

ADCs used in DSOs like Bitscope are designed to exploit this contraint by sampling the analogue input for a much shorter time span than a sample period. That is, they have a short "aperture" (ie, time to capture the input signal) but a require longer time to convert the analogue sample to its binary output value (ie, one sample period).

The short aperture allows the ADC to "see" a maximum frequency much higher than the sample rate alone might suggest, but there is some work to do first to make sense of the data.

Sub-sample waveform capture

If you display a buffer of raw data captured from a signal with higher frequency than half the sample rate, you will still see a waveform; just not the right one !

Instead you will see an "alias", or frequency shifted version of the waveform. However, if certain conditions are met, the alias is unique, meaning you can "unwrap" the raw data to reveal the true waveform.

This process is known as sub-sampling and is a technique used by most modern DSOs to capture very high frequency signals. It is similar to a radio circuit where two frequencies are "mixed" to produce the "sum and difference" to shift from high frequency to a lower one. Indeed, ADCs like this one are often used to perform this very function in systems like cellular telephones.

So, when you read a specification that says "DSO X has a 100 MHz bandwidth but a 20 MHz sample rate" you'll know it means that using sub-sampling, the DSO can display a periodic waveform with frequency components up to 100 MHz.

Using this ADC, you can say "Bitscope has a bandwidth of 75 MHz and a sample rate of 40 MHz.

What's the catch ?

Sub-sample capture does not free you from the contraints of the sampling theorem: the bandwidth of the signal you are viewing must still be less than half the sample rate.

However, with sub-sampling the signal may appear anywhere in the capture bandwidth of the A/D convertor so long as its bandwidth remains less than half the sample rate.

If you have a 100 MHz capture bandwidth and a 40 MS/s sample rate you can (for example) measure a signal with a fundamental frequency of 65 MHz and bandwidth of 20 MHz (ie you can see frequencies up to 85 MHz). If the signal is not sufficiently bandlimited, it must be filtered to prevent aliased components in the result.

There is one exception: if the signal is harmonic (ie, you know there are no frequency components that are not related to the fundamental) and the sample rate is different to and not related to the fundamental, it is possible to unwrap all signal harmonics up to the physical capture bandwidth.

An extreme sub-sampling example

It must also be remembered that the analogue circuitry should have an input bandwidth sufficient to pass the signal to the ADC without distortion. Bitscope's analogue inputs have a 3dB bandwidth of 100 MHz. It is even possible to "see" signals at higher frequencies if you are not concerned that the signal will be somewhat attenuated. For example, the following screen-shot shows a 125 MHz signal captured using the new ADC module.

ADC 5540 converter captures a 125MHz sine wave.

This signal was captured running the ADC at 25 MHz using sub-sampling to unwrap the display.