The real-time oscilloscope
Real-time oscilloscopes (RTOs) are designed with a high enough sampling rate to capture a transient, non-repetitive signal with the instrument’s specified analog bandwidth. According to Nyquist’s sampling theorem, for accurate capture and display of the signal the scope’s sampling rate must be at least twice the signal bandwidth. Typical high-bandwidth RTOs exceed this sampling rate by perhaps a factor of two, achieving up to four samples per cycle, or three samples in a minimum-width impulse.
For signals close to or above the RTO’s Nyquist limit, many RTOs can switch to a mode called equivalent-time sampling (ETS). In this mode the scope collects as many samples as it can after a trigger event, and then continues to collect samples on subsequent trigger events. Because the scope’s sampling clock is independent of the trigger event, each trigger has a random time offset relative to the scope’s clock. The scope measures this offset and displays the samples at their correct times. After a large number of trigger events the scope has enough samples to display the waveform with the desired time resolution, called the effective sampling resolution (the inverse of the effective sampling rate), which is many times higher than is possible in real-time (non-ETS) mode. As this technique relies on a random relationship between trigger events and the sampling clock, it is more correctly called random equivalent-time sampling (or sometimes random interleaved sampling, RIS). It can only be used for repetitive signals – those that vary little from one trigger event to the next.
Uniquely, the PicoScope 9404 SXRTO has a maximum effective sampling rate in ETS of 1 TS/s. This corresponds to a timing resolution of only 1 ps, 20,000x higher than its actual maximum sampling rate.
The sampler-extended real-time oscilloscope (SXRTO)
Now that we have a technique (ETS) for extending the sampling rate of a real-time oscilloscope, we find that we can achieve an effective sampling rate far higher than is needed to match the instrument’s analog bandwidth. In order to make better use of these high effective sampling rates, we can increase the analog bandwidth of the scope. Pico has developed a way to achieve this at a moderate cost, compared to the very high cost of increasing the real-time sampling rate. The result is the sampler-extended real-time oscilloscope (SXRTO).
The PicoScope 9404-05 SXRTO has an analog bandwidth of 5 GHz. This means that it requires a sampling rate of at least 10 GS/s, but for an accurate reconstruction of wave shape without interpolation, we need far higher than this. The 9404 gives us 200 sample points in a single cycle at 5 GHz and 140 points in a minimum-width impulse.
So is the SXRTO a sampling scope?
All this talk of sampling rates and sampling modes may suggest that the SXRTO is a type of sampling scope, but this is not the case. The name sampling scope, by convention, refers to a different kind of instrument. A sampling scope uses a programmable delay generator to take samples at regular intervals after each trigger event. The technique is called sequential equivalent-time sampling and is the principle behind the PicoScope 9300 Series sampling scopes. These scopes can achieve very high effective sampling rates but have two main drawbacks: they cannot capture data before the trigger event, and they require a separate clock signal – either from an external source or from a built-in clock-recovery module.
We've compiled a table to show the differences between the types of scopes mentioned on this page. The example products are all compact, 4-channel, USB PicoScopes.
||PicoScope 9300 Series
|Sequential equivalent-time sampling?
|Random equivalent-time sampling?
|Trigger on input channel?
||No** – requires external clock or internal clock recovery option
*Higher-bandwidth real-time oscilloscopes are available from other manufacturers. For example, a 5 GHz analog bandwidth, 25 GS/s sampling model is available for about $57,000.
**These functions are possible at low sampling rates, up to 1 MS/s.