Response analysis of second-order multi-band quadrature ΣΔ modulators with applications in cognitive radio devices

In this article, a novel analytical closed-form model is derived for second-order quadrature ΣΔ modulators (QΣΔM) taking implementation inaccuracies of QΣΔM coefficients into account. The model enables analytical examination of the modulator I/Q imbalance effects on input-output relation as well as signal and noise transfer functions (STF and NTF) independently. Thus, the image rejection of the QΣΔM can be evaluated both from the input signal and quantization error point-of-view. With the help of the model, it is shown analytically that a mirror-frequency rejecting STF design is an efficient way to mitigate mirror-frequency interference originating from blocking signals at the input of the modulator because of the QΣΔM feedback branch I/Q mismatches. The straightforward parametrization allows reconfigurability of the transfer functions which can be exploited, e.g., together with multi-band noise shaping capabilities. These concepts are valuable in A/D converters aimed to cognitive radio (CR) solutions. In CR receivers, A/D interface has been considered as a major bottleneck and QΣΔM offers frequency agile performance well fit for the purpose.