Monday, January 21, 2013

Testing for Interleave Distortion in Oscilloscopes

The level of interleave distortion or just sampling distortion in general to expect from an oscilloscope measurement is often not clear from examining an oscilloscope's data sheet. In this post we will look at how to measure and evaluate an oscilloscope's sampling distortion. This post builds on the information from last week's post entitled Interleaved Sampling in Oscilloscopes. Without knowing a scope's level of sampling distortion there is no way to know how accurate a representation of a measured signal the scope is providing. A scope with a high sampling rate may not deliver the best representation of a measured signal compared to a scope with a lower sampling rate. This depends on such factors as the measured signal's bandwidth and if the scope uses an interleaved sampling scheme and how well it was implemented in the design.

The following is a list of tests or methods that we will look at to evaluate interleave distortion:
  1. Effective number of bits analysis using sine waves
  2. Visual sine wave test
  3. Spectrum analysis
Effective number of bits analysis
The closest specification that some scope vendors provide to quantify sampling fidelity is effective number of bits (ENOB). But ENOB is a composite specification consisting of several error components including input amplifier harmonic distortion and random noise. Although an effective number of bits test can provide a good benchmark comparison of overall accuracy between scopes, effective bits is not a very well understood concept, and it requires exporting digitized data to a PC for number crunching. Basically, an effective number of bits test first extracts a theoretical best-fit sinusoidal signal from the digitized sine wave. This sine wave curve-fit algorithm will eliminate any errors induced by oscilloscope amplifier gain and offset inaccuracies. The test then computes the RMS error of the digitized sine wave relative to the ideal/extracted sine wave over one period. This RMS error is then compared to the theoretical RMS error that an ideal ADC of “N” bits would produce. For example, if a scope’s acquisition system has 5.3 effective bits of accuracy, then it generates the same amount of RMS error that a perfect 5.3-bit ADC system would generate. For more detail on ENOB click here.

Visual sine wave test
A more intuitive and easier test to conduct to see if a scope produces ADC interleave distortion is to simply input a sine wave from a high-quality signal generator with a frequency that approaches the bandwidth of the scope. Then just make a visual judgment about the purity of the shape of the digitized and filtered waveform.
Let's look at an example comparison using the visual sine wave test. The below figures show two screen captures from two different scopes of a high quality 200 MHz sine wave. The top screen capture is from 1-GHz bandwidth scope sampling at 4 GSa/s. This scope has a sample-rate-to-bandwidth ratio of 4:1 using non-interleaved ADC technology. The bottom screen capture is from the 1-GHz bandwidth scope sampling at 10 GSa/s. This scope has a maximum sample-rate-to-bandwidth ratio of 10:1 using interleaved technology.

200-MHz sine wave captured on a 1-GHz bandwidth oscilloscope sampling at 4 GSa/s
200-MHz sine wave captured on a  1-GHz bandwidth oscilloscope sampling at 10 GSa/s

Although we would intuitively believe that a higher-sample-rate scope of the same bandwidth should produce more accurate measurement results, we can see in this measurement comparison that the lower sample rate scope actually produces a much more accurate representation of the 200 MHz input sine wave. This is not because lower sample rates are better, but because poorly aligned interleaved real-time ADCs negate the benefit of higher sample rates.

Spectrum analysis comparison tests

The visual sine wave test doesn't really prove where the distortion is coming from. It merely shows the effect of various error/components of distortion. However, a spectrum/FFT analysis will positively identify components of distortion including harmonic distortion, random noise, and interleaved sampling distortion. Using a sine wave generated from a high-quality signal generator, there should be only one frequency component in the input signal. Any frequency components other than the fundamental frequency detected in an FFT analysis on the digitized waveform are oscilloscope induced distortion components. The figure below shows an FFT analysis of a single-shot capture of a 2.5 GHz sine wave using an oscilloscope sampling at 40 GSa/s. The worst-case distortion spur measures approximately 90 dB below the fundamental. This component of distortion is actually second harmonic distortion, most likely produced by the signal generator. And its level is extremely insignificant and is even lower than the scope’s in-band noise floor.

FFT analysis of 2.5-GHz sine wave captured on a sampling at 40 GSa/s scope
The figure below shows an FFT analysis of a single-shot capture of the same 2.5-GHz sine wave using a different scope with the same sample rate (40 GSa/s). The worst-case distortion spur in this FFT analysis measures approximately 32 dB below the fundamental. This is a significant level of distortion that would most likely be visually apparent in the time domain. The frequency of this distortion occurs at 7.5 GHz. This is exactly 10 GHz below the input signal frequency (2.5 GHz), but folded back into the positive domain. The next highest component of distortion occurs at 12.5 GHz. This is exactly 10 GHz above the input signal frequency (2.5 GHz). Both of these components of distortion are directly related to the 40-GSa/s sampling clock and its interleaved clock rates (10 GHz). These components of distortion are not caused by random or harmonic distortion. They are caused by real-time interleaved ADC distortion.


In this post we looked at three methods for measuring or evaluating interleaved sampling distortion and general sampling distortion. The three methods included ENOB, visual test, and spectrum analysis. This type of test is necessary when you need to evaluate a low noise signal, such as a digital clock, and you want to ensure that you are actually seeing the measured signal noise and not the noise of the measuring device. 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.




15 comments:

  1. Neil,
    A question, and a comment.
    1. In the very first image, is that capture from a single shot? The waveform looks relatively thicker, almost like multiple waveforms are being overlaid, whereas in the second image, it looks very much like a single-shot. Would be interesting to have you redo the capture as a single shot on the first scope, just to compare apples to apples.
    2. In the set of images, I notice the Tek scope is displaying 1 ps/pt. That doesn't make sense to me, can they really capture 1TS/s on a single shot? Maybe if you back off the RL to 2K (like on the Agilent scope), the results might square a bit more? Just curious.

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