Loop delay compensation in bandpass continuous-time ΣΔ modulators without additional feedback coefficients

Loop-delay is one of the major sources of instability and signal-to-noise ratio degradation in continuous-time band-pass ΣΔ modulators. In this paper, we use the modified-z-transform technique to calculate the value of the additional feedback coefficient required to compensate for the loop-delay. It is shown that, in certain conditions, this additional feedback coefficient can be removed and the loop-delay is compensated only by modifying the modulator coefficients. This is illustrated by several examples of loop-delay compensation in 2^nd, 4^th and 6^th order bandpass modulators.