Terugblik Project 147

door Erik Larsen (©2002):

The return of Sigma-Delta converters


How evils can help you if they are random

On Labour Day 2002 chairman Peter Swarte explained to the evening's audience of about 40 people the return of Prof. John Vanderkooy to his native Holland; John on his part gave a captivating account on the return of the Sigma-Delta (S-D) converter. A return which is manifest in the SACD format, which has sparked -or rather ignited- a series of studies and publications on this converter's behaviour. Most recently, during the 112th AES Convention in Munich, another series of papers on the topic were presented by researchers from a variety of institutes. The talk John gave to our local section was just prior to this Munich series.

After a few remarks on the historical reasons for preferring 1-bit converters over multi-bit converters, John started by introducing the basic properties of a S-D converter, an essential element of which is the two-level quantizer which generates the digital 1-bit signal. The input to the quantizer is the analog input signal, from which is subtracted a filtered version of the quantized output signal. The purpose of this filtered error feedback is to 'shape' the noise spectrum which is caused by the quantization process and 'push down' the noise level in the audio band. If the sample rate of the AD converter is sufficiently high (about 2.8 MHz for SACD), the noise level in the audio band can be reduced to levels of -120 dB, while at the same time pushing up the noise level at higher (inaudible) frequencies, such that the total wide-bandwidth error remains constant. An analogous situation occurs when pusing down on one side of a balloon - the other side will bulge, such that the total volume of the entire balloon remains constant (as demonstrated by James Angus at the 110th AES Convention). The advantage of the SACD standard over CD is thus a higher S/N ratio and a larger bandwidth.

The main problem with the S-D converter is the occurence of idle tones, or limit cycles. These are an inherent non-linear instability of the S-D converter, and are manifested as multiple high-amplitude single-frequency components in the output of the converter. A simple DC input will cause a series of idle tones (fundamental and aliased harmonics), which might also occur in the base (audio) band, leading to audible distortion, possibly at full scale level... Fortunately, the noise shaping characteristic of the converter will push down the amplitude of the idle tones in the base band to very low levels, which makes their audibility questionable.

For analysis purposes, John showed us how coherent averaging (a method by which one computes the frequency spectrum of thousands of repeating segments of a signal) will reduce the 'random' noise components of the converter and bring out the idle tones more clearly. Because a sine wave with a frequency in the audio band will appear as 'almost' DC compared to the SACD sample rate (2.8 MHz), such a sine wave input will be biasing the S-D converter with a varying quasi DC. Since the idle tone frequencies depend on the DC value at the input, the output will now contain a ballet of idle tones sweeping up and down the frequency spectrum.

Since John and his colleague Stanley Lipshitz have been very critical of the SACD standard, John was asked how he viewed SACD now that he was at Philips for this sabbatical term. His diplomatic reply was that SACD seems to be the only standard with force - on the technical side he still has a few worries. On the bright side, John quoted new work from Derk Reefman at Philips and Malcolm Hawksford at the University of Essex which are aimed at improving 1-bit converters.

In the latter part of the talk the emphasis was on another crucial aspect of 1-bit converters, namely dither. This is the application of a quasi-random signal resembling noise, added to the input signal prior to the AD conversion. Addition of noise would seem to degrade the quality of the reproduced signal, but dither actually has a beneficial effect. It can be used in any AD converter to remove the signal dependent properties of the quantization noise, thus linearizing the converter. It is also beneficial for a S-D converter in that dither reduces significantly the strength of idle tones and their harmonics. By showing spectra of dithered and undithered signals John made the effect of the process clear to the audience. He then went on to detail on a few properties of dither and how it can best be applied.

The evening was closed at 22:00h, but many people took the opportunity to continue discussions with John.