New multirate bandpass sigma-delta modulators

A new architecture for fourth- and sixth-order bandpass sigma-delta (BP-SD) modulators is proposed here. The basic BP-SD modulator is obtained from its low-pass (LP) counterpart by means of the standard transformation z^-1 → -z^-2, which transforms the integrators in the LP modulator into resonators in the BP modulator, and places the input signal band at the frequency f_s/4, where f_s is the sampling rate. In the proposed architecture, the second resonator (and the third one for the sixth-order case) is implemented using a two-path strategy, by means of two high-pass filters (whose poles are located at f_s/2) operating in a time-interleaved mode. However, unlike other BP-SD modulators using the two-path strategy, in our approach, the effective sampling frequency in the second resonator (and in the third one for the sixth-order case) is increased to 2·f_s by maintaining the clock rate of the high-pass filters to f_s which, in turn, places their poles at f_s/2. The signal band in the input of the second resonator is moved from the center frequency f_s/4 to f_s/2 by a modulation process that separates the signal into their in-phase and quadrature components. Another demodulation process in the digital domain reverses this frequency translation of the signal band before the output signal is converted to the analog domain and fed back to the modulator input. A detailed theoretical analysis of the architecture is done in the paper. Owing to the multirate nature of the proposed modulators, simulation results show an improvement of approximately 12 dB in the input dynamic range (fourth-order case) when compared to conventional modulators of the same order clocked at the same frequency rate (in the first resonator).