Sunday, 27 April 2014

The Noise Effects Of Aperture Jitter And Timing Variation

In any sampling system there is a requirement for the period between samples to remain constant within certain boundaries, the timing variation. Random noise on the timing is called the aperture jitter and the effect of it is to add noise on the digital samples; timing variation due to changes in the crystal oscillator frequency add a modulation artefact to the digital samples. These effects are shown in the following diagram.

The diagram shows that ts is the time of sampling the signal and it can be seen that if the time varies outside the limits shown by the arrows then the output will give the wrong digital value.

The range of analog converter performance requirements for different applications is very wide, ranging from 8 bits for instrumentation through 14 bits for telecommunications and control, 24 bits for pro-audio or seismic and sonar applications. So it is important that timing jitter and sinusiodal variations are managed to meet these requirements.

Any random component in the jitter can be removed by averaging however the sinusoidal component causes a modulation artefact that is often impossible to remove once present.

The timing variation artefact was was illustrated to me many years ago by a very experienced analog design engineer who hooked up the outputs of a dual frequency crystal oscillator to an oscilloscope set in X-Y mode. The display was setup in such a way that the Lissajou figure rotated slowly clockwise. He then proceeded to spray the oscillator with freezer spray and the scope display went crazy, finally slowing down to rotate in an anti-clockwise direction.

Why is this important ?

The main reason is that this sinusoidal component causes a modulation effect on the output of the ADC (or DAC) and this has serious implications in all DSP processing algorithms but especially those that perform any kind of modulation/demodulation or sample rate conversion.

Twice in my engineering career, once in a V.32 voiceband modem and secondly in a 3G mobile basestation, I have seen modems completely screwed up by using crystal oscillators that do not meet the required specification. The result was that the modems would work for a period of time and then fail with no apparent cause. In the case of the V.32 modem the failure only appeared to happen over night when the systems had been left running for many hours. Arriving at work in the morning was always a worrying time and caused a lot of stress for the team until the root-cause was found and fixed. We thought it might be temperature related (the modems at the bottom of the test rack ran for longer but all were within the temperature spec.), power surges, electrically noisy vacuum cleaners, the timing error detector algorithm, the Viterbi decoder etc in the end it turned out to be the crystal oscillator - some 100 ppm parts had been fitted instead of the specified 32 ppm version.

Accuracy And Precision

In my DSP classes I often cover the difference between precision and accuracy when measuring and processing input values from a transducer.
I recently came across an excellent little illustration of this on page 7 of the Keller-Druck Brochure :

From a signal processing point of view the key points from this diagram are :
  1/ When the measurements are very precise (as shown in diagram A) then accuracy can be improved by removing the offset via subtraction of the average of the samples.
  2/ When measurements are more accurate but there is a larger deviation (as shown in diagram B) then the deviation can be reduced by oversampling and averaging the results.