This article discusses the technology behind the new PicoScope 9404 SXRTO (sampler-extended real-time oscilloscope). The 9404 features four 5-GHz 12-bit channels, each supported by real-time sampling to 500 MS/s per channel and up to 1-TS/s (1-ps timing resolution) equivalent-time sampling.
The 9404 offers vertical and timing resolutions typical of the highest-performance broadband oscilloscopes but at an affordable price. To understand how this is achieved, we need to go back to digital storage oscilloscope (DSO) fundamentals. In a DSO, all waveforms are sampled (digitized) as analog signals. Sampling is achieved by capturing a portion of the input waveform, which is converted to a digital representation of that signal, which is then stored in memory.
The number of ADC bits determines the voltage or vertical resolution, and the number of samples taken of the input waveform determines the timing or horizontal resolution, both contributing to overall accuracy. If too few samples are acquired, the digital reconstruction of the waveform will not be an accurate representation of the original analog signal. When the waveform is displayed as an image, it will be incorrect. Therefore, the waveform is stored in digital memory, where it can be analyzed by high-speed signal-processing software. The PicoScope 9404 SXRTO provides advanced analysis of waveforms with 45 math functions that can be used in both real-time and equivalent-time modes.
DSO REAL-TIME SAMPLING
With real-time sampling, the oscilloscope samples the whole waveform in a single acquisition. This sampling mode is therefore ideal for capturing single-shot transient events and non-repetitive waveforms. If the sampling rate is not high enough, the high-frequency components of the signal will be incorrectly represented as indistinguishable artifacts known as aliasing. Nyquist’s sampling theorem states that the sampling rate should be at least twice that of the highest-frequency component of the signal. This means that for an oscilloscope with a real-time sampling rate of 500 MS/s, the highest-frequency component that can be captured accurately is 250 MHz. Or to put it another way, a 5-GHz-bandwidth oscilloscope would need a minimum real-time sampling rate of 10 GS/s to represent the highest-frequency component without aliasing.
As we have already seen, the larger the number of samples of the input waveform, the better the timing or horizontal resolution of the acquired signal, allowing accurate representation of the high-frequency components of the analog signal. As a result, at this bandwidth, oscilloscope manufacturers commonly offer sampling rates of 1× to 2× the minimum usable real-time sampling rate. In the case of a 5-GHz-bandwidth scope, this would be 10 GS/s to 20 GS/s. Likewise, the more bits of sampling resolution, the more accurate the voltage or vertical resolution can be.
It is worth noting that lower-frequency components (such as amplitude modulation) of a signal can be represented accurately even if the oscilloscope’s sampling rate is inadequate to accurately represent the high-frequency carrier without aliasing. It is this high sampling rate and the number of bits in each sample that push the required digital bandwidth far higher than the analog front-end bandwidth, placing tremendous cost constraints on the oscilloscope designer. For these reasons, making a real-time digital oscilloscope with high bandwidth, a high sampling rate, and high resolution is an extremely difficult challenge if you want to combine that performance with affordability. This is why the equivalent-time sampling method was developed.
DSO EQUIVALENT-TIME SAMPLING
Equivalent-time sampling takes advantage of the fact that most high-bandwidth waveforms are repetitive. This means that samples can be made over multiple acquisitions of the waveform with one or more samples being taken during each acquisition. The oscilloscope can thus acquire waveforms that contain frequency components many times higher than that of the real-time sampling rate of the oscilloscope. In addition, the lower sampling rate means that equivalent-time sampling typically offers higher vertical resolution than the extremely fast real-time sampling used at such frequencies. In the case of the PicoScope 9404 SXRTO, the vertical resolution is 12 bits rather than the more common 8 bits.
The most common form of equivalent-time sampling is random equivalent-time sampling, wherein the digitizer uses an internal clock that runs asynchronously with respect to the trigger and the input waveform. Successive samples are made irrespective of the trigger position. They are then displayed relative to the trigger position using a separate and high-accuracy measurement of the time between the trigger and one of the samples. Although these samples are successive, they are made randomly with respect to the trigger position; hence, the name of the technique.
As the samples are acquired randomly with respect to the trigger position, it is possible to display the sampled waveform prior to and including the trigger position, which allows design engineers to view the waveform leading up to the trigger condition. The ability to capture and view pre-trigger information is a valuable aid in fault analysis, allowing the design engineer to view the cause of a fault condition.
Data acquired with equivalent-time sampling may be reconstructed and displayed either as the original waveform in a similar way to a real-time DSO display or as an eye diagram. The name “eye diagram” is derived from the characteristic display, which resembles the shape of an eye. This display is used to reveal information about the input signal such as noise, jitter, distortion, signal level, and, in communications signals, intersymbol interference. An open-eye pattern corresponds to minimal signal distortion, and a closed-eye pattern corresponds to distortion of the signal due to jitter, noise, and other effects that might lead to unreliable or failed recovery of the data or communication.
To generate an eye diagram, we use a clock that is synchronous to the data clock as our trigger. This might be the clock that was used to generate the data or one that has been recovered from the data by a clock recovery circuit. With equivalent-time sampling, as the acquisition window is increased, the oscilloscope makes more samples per trigger until the digitizer becomes a real-time digitizer and acquires the whole waveform from a single trigger. Conversely, as the acquisition window is decreased, the oscilloscope takes fewer samples per trigger and it takes longer to display the complete waveform.
Some readers, and particularly existing customers of Pico’s 9300 family of instruments, will be familiar with the so-called “sampling oscilloscope.” This has been and will continue to be an important and highly cost-effective instrument for the capture of very high-bandwidth signals. However, this oscilloscope architecture uses a sequential equivalent-time sampling mechanism and typically needs a separate trigger signal to be provided. Sampling of a signal begins only after the trigger event and capture of the trigger or waveform that preceded it becomes difficult, impractical, or an additional source of jitter.
High-performance real-time sampling DSOs may also offer equivalent-time sampling, but the high-sampling-rate provision still leads to an extremely costly architecture to implement, especially when using high-resolution 12-bit digitizers. The diagrams below show the differences in architecture between a typical DSO and a PicoScope SXRTO of the same bandwidth.
Many high-bandwidth signals are repetitive in nature, and it is with these signals that the high-performance 12-bit vertical/voltage resolution, 1-ps horizontal/timing resolution, and 5-GHz internal trigger (with less than 2-ps RMS trigger jitter) of the PicoScope 9404 allow extremely high-precision measurements of up to 5-GHz bandwidth, all with a fast display time and at an affordable price.
The SXRTO is indeed a new type of oscilloscope that offers the capability to capture and view extremely high-bandwidth signals in high vertical and horizontal resolution without the cost of a typical high-performance DSO or the measurement compromises of a sampling oscilloscope. ■