Sunday, January 13, 2013

Interleaved Sampling in Oscilloscopes

In this post we will look at interleaved real-time sampling in oscilloscopes and how interleaved sampling errors can result in a distorted representation of a signal. After reading this post you will understand why choosing an oscilloscope based solely on sampling rate does not always give you the best representation of the signal you are measuring.

As digital signals continue to increase in speed, oscilloscope vendors are under constant pressure to increase the sampling rate and bandwidth of their products so that engineers have a means to measure the digital signals in their design. The most intuitive way to increase the sample rate of a scope is to simply use a higher sampling rate ADC in the scope, but this technique is not always cost effective or practical. To solve this design challenge a common technique adopted by all major scope vendors is to interleave multiple real-time ADCs.

The below figure shows a block diagram of a real-time interleaved ADC system consisting of two ADCs with phase delayed sampling. In this example, ADC 2 always samples ½ clock period after ADC 1 samples. After each real-time acquisition cycle is complete, the scope’s CPU or waveform processing ASIC retrieves the data stored in each ADC acquisition memory and then interleaves the samples to produce the real-time digitized waveform with twice the sample density (2X sample rate).

Real-time sampling system consisting of two interleaved ADCs
Scopes with real-time interleaved sampling must adhere to two requirements. For accurate distortion-free interleaving, each ADC’s vertical gain, offset and frequency response must be closely matched. Secondly, the phase-delayed clocks must be aligned with high precision to ensure equally spaced samples. That means ADC 2 must be delayed precisely 180 degrees after the clock that samples ADC 1. Remember equally spaced sampling is part of the Nyquist sampling theorem for accurately recreating a signal. in order to satisfy Nyquist’s rule 2 that dictates equally spaced samples. For the rest of the post we will focus on sampling spacing errors due to poor phase delayed clocking.

The timing diagram shown in the below figure illustrates incorrect timing of interleaved samples if the phase-delayed clock system of two interleaved ADCs is not exactly ½ sample period delayed relative to each other. This diagram shows where real-time digitized points (red dots) are actually converted relative to the input signal. But due to the poor alignment of phase-delayed clocking (purple waveforms), these digitized points are not evenly spaced, thus a violation of Nyquist’s sampling theorem.

Timing diagram showing non-evenly spaced samples
When the scope’s waveform processing engine retrieves the stored data from each ADC’s acquisition memory, it assumes that samples from each memory device are equally spaced. In an attempt to reconstruct the shape on the original input signal, the scope’s Sin(x)/x reconstruction filter produces a severely distorted representation of the signal, as shown in the figure below.

Timing diagram showing distorted reconstruction of waveform
Since the phase relationship between the input signal and the scope’s sample clock is random, real-time sampling distortion, which is sometimes referred to as “sampling noise,” may be interpreted mistakenly as random noise when you are viewing repetitive acquisitions. But it is not random at all. It is deterministic and directly related to harmonics of the scope’s sample clock.

Unfortunately, oscilloscope vendors do not provide their customers with a specification in their data sheets
that directly quantifies the quality of their scope’s digitizing process. This means if you just grab the scope in your lab with the highest sample rate assuming that it will deliver the best representation of your signal you may be wrong. For instance lets say you want to capture a 1 GHz digital clock signal. If you have a 6 GS/s scope and a 10 GS/s scope to choose from it makes sense to assume the latter will deliver the best representation of signal. But if the 6 GS/s scope has a single ADC and the 10 GS/s scope uses an interleaved ADC scheme, then the former may deliver a better representation of the signal, but there may not be a clear way to know this by comparing the scope's data sheets. In next week's post we will look at methods to test and evaluate a scope's sampling distortion. If you have any personal insights to add to this post please use the comments section below and if you have any questions feel free to email me.