Design and analysis of multi-stage quadrature sigma-delta A/D converter for cognitive radio receivers

In this article, the design and analysis of sophisticated multi-band quadrature ΣΔ modulators (QΣΔM) are addressed, offering a high-performance and easily-reconfigurable solution for the analog-to-digital (A/D) interface of cognitive radio receivers. Based on spectrum sensing information, the multi-band principle stemming from multi-stage converter implementation enables multiple reconfigurable noise transfer function (NTF) notches for efficient quantization noise shaping. Also mirror-frequency-rejecting signal transfer function (STF) design is proposed for multi-stage QΣΔM, which implements part of the receiver selectivity and offers also robustness against certain circuit implementation nonidealities. More specifically, we concentrate here on the so-called in-phase/quadrature (I/Q) imbalance problem, being an unavoidable problem in quadrature circuits and thus also in QΣΔMs. An analytical closed-form model is derived for a two-stage QΣΔM under implementation nonidealities, realizing multi-band noise shaping with first-order building blocks. Stemming from this analysis, it is shown that clever design of the NTF and the STF of the multi-stage QΣΔM offers both straightforward reconfigurability and robustness against converter implementation mismatches.