I/Q Imbalance Effects in Quadrature ΣΔ Modulators – Analysis and Signal Processing

This article focuses on the in-phase/quadrature (I/Q) imbalance problem in quadrature ΣΔ modulators (QΣΔM). In the literature, such quadrature modulators have been seen as a promising possibility for software defined radio (SDR) receivers, but matching the quadrature circuits is an inevitable problem for this kind of systems. In this article, an analytic closed-form model will be derived for a mismatched first order QΣΔM by means of the modulator transfer functions and the underlying implementation components. In addition, notching the signal transfer function (STF) on the desired signal mirror frequency inside the modulator is proposed for cancelling the mirror frequency interference originating from the blocking signal on that band. This is shown to be effective in case of the modulator feedback branch mismatches and can be implemented with simple additional feedforward coefficient(s) compared to ordinary modulator. Index Terms — Analog-digital conversion, bandpass filters, complex filters, digital radio, I/Q imbalance, mirror frequency interference, radio receivers, sigma-delta modulation