Methods for the transfer function design of multiple narrow-band bandpass sigma-delta modulators

This paper presents the design analysis of novel tunable narrow-band bandpass sigma-delta modulators, which can achieve concurrent multiple noise-shaping for multi-tone input signals. Four different design methodologies based on the noise transfer functions of comb filters, slink filters, multi-notch filters and fractional delay comb filters are applied for the design of these multiple-band sigma-delta modulators. The latter approach utilises conventional comb filters in conjunction with FIR, or allpass IIR fractional delay filters, to deliver the desired nulls for the quantisation noise transfer function. Detailed simulation results show that FIR fractional delay comb filter-based sigma-delta modulators tune accurately to most centre frequencies, but suffer from degraded resolution at frequencies close to Nyquist. However, superior accuracies are obtained from their allpass IIR fractional delay counterpart at the expense of a slight shift in noise-shaping bands at very high frequencies. The merits and drawbacks of each technique for the various sigma-delta topologies are assessed in terms of in-band signal-to-noise ratios, accuracy of tunability and coefficient complexity for ease of implementation.

Effective-fourth-order resonator based MASH bandpass sigma-delta modulators

Two novel effective-fourth-order (eighth-order) resonator based MASH (MultistAge noise SHaping) bandpass Σ-Δ modulators are introduced at the behavioural level and subsequently examined by simulations utilising the ALTA SPW environment. The considered bandpass configurations have in their loop filter a cascade of standard second-order resonator structures in order to achieve appropriate noise shaping. The quantisation noise in each stage is suppressed by feeding the error of each section into the input of the following stage. It is demonstrated in this paper that the quadruple effective-first-order cascade configuration has significantly better performance as well as conforming more closely with theory in comparison with the effective-second-order effective-second-order cascade. The superior performance of the former can be attributed to the cumulative effect of the multi-bit outputs as well as the presence of more notch filters.

MASH structures for bandpass sigma-delta modulators

The paper presents simulation results from investigating the behaviour of multistage (MASH) oversampled bandpass sigma-delta (Σ-Δ) modulators for use in analogue to digital converters for high frequency narrowband applications such as the signals out of the intermediate frequency (IF) section of a superheterodyne radio receiver. The bandpass configurations under consideration have in their loop filter a cascade of second-order resonator structures in order to achieve acceptable noise shaping. The quantisation noise in each stage is suppressed by feeding the error of each section into the input of the following stages. It is demonstrated that the triple effective-first-order bandpass MASH structure has significantly better performance compared with the effective-second-order effective-first-order bandpass MASH structure.