An automatic-design methodology for designing high-tolerance modulator coefficients for high-order sigma-delta modulators (SDM's) from system specifications is presented. The methodology covers many design concerns including SDM coefficient tolerances for circuit component mismatch, stability, reduction of in-band tones, design tradeoffs among in-band noise suppression, oversampling ratio, and modulator order. Moreover, a high-order SDM synthesis tool (HOST) based on the methodology has been implemented in a C language program. Even for inexperienced designers, reliable and high-tolerance SDM coefficients for various applications can be automatically and efficiently generated using HOST. For synthesized SDM's with orders from three to eight and oversampling ratios from 32 to 256, coefficient variations within 2% (1% for the eighth order) are allowed and the resulting peak signal-to-noise ratio degradation is less than 3 dB. Several design examples synthesized by HOST are included.

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