Henk ten Pierick wrote: > On Jul 24, 2007, at 1:32, Dr Bruce Griffiths wrote: > > >> Perhaps a software implementation of a 1 bit oversampled DAC the 1 bit >> output of which is low pass filtered to control the EFC input is the >> closest approach to this ideal. >> With an appropriate algorithm the idle tone and inherent instability >> problems (of high order modulators - 3rd or higher order) of the sigma >> delta modulator will not occur. >> > > It is easy to design stable sigma delta converters of orders higher > than two. I have calculated a 7th order ADC which is implemented on > silicon and stable of coarse. A 11th order sigma delta with > oversampling ratio 128 is stable in simulation and has 228dB snr. > {This is no typo two hundred and twenty eight dB) > Higher order sigma delta converter require higher order > reconstruction filters but it is easy to design for more bandwidth > than needed and so to relax the filter spec. > > Henk > Henk There is no theory to show that sigma delta modulators of order higher than 2 are actually unconditionally stable. Merely simulating the device is not conclusive proof that the modulator will never saturate, albeit infrequently. Most implementations include saturation detection circuitry that resets the modulator should this occur. If saturation isn't too frequent then for most purposes this is only a minor annoyance. However cascaded first order modulators as employed in the MASH technique are stable in theory and practice. However if one adopts a non linear control theory approach, one can actually design high order modulators that both stable in theory and in practice. The resulting circuit isn't a sigma delta modulator, however it has similar noise shaping characteristics. Bruce

On Aug 1, 2007, at 0:51, Dr Bruce Griffiths wrote: >> > Henk > > There is no theory to show that sigma delta modulators of order higher > than 2 are actually unconditionally stable. Yes, but with the Gerzon-Craven theory is is possible to predict stability of noise shapers. My experience with Gerzon-Craven in a number of noise shapers is very good, and upto 11th order (never tried more). > Merely simulating the device is not conclusive proof that the > modulator > will never saturate, albeit infrequently. > Most implementations include saturation detection circuitry that > resets > the modulator should this occur. We use feed-forward and graceful degradation. In this way saturated noise shapers recover correct. In our application overdriven noise shapers can not be avoided at input signal transients. > If saturation isn't too frequent then for most purposes this is only a > minor annoyance. > However cascaded first order modulators as employed in the MASH > technique are stable in theory and practice. How to match analog circuits with digital circuits for the mash, that is the question. How do you avoid leakage? > However if one adopts a non linear control theory approach, one can > actually design high order modulators that both stable in theory > and in > practice. Unconditionally? Do you have a link for me? Henk

Henk ten Pierick wrote: >> However if one adopts a non linear control theory approach, one can >> actually design high order modulators that both stable in theory >> and in >> practice. >> > > Unconditionally? Do you have a link for me? > > Henk > Henk Try: http://ieeexplore.ieee.org/Xplore/login.jsp?url=/iel5/9861/31519/01470725.pdf?arnumber=1470725 http://txspace.tamu.edu/bitstream/1969.1/3768/1/etd-tamu-2005A-ELEN-He.pdf Bruce