Mismatch Insensitive Double-Sampling Quadrature Bandpass $\Sigma \Delta$ Modulation

In a double-sampling quadrature bandpass sigma-delta modulator, path mismatch between the double-sampling branches and between the I/Q paths occurs. In this paper, an analytical study is presented which shows that this causes quantization noise and input signals to fold from the image band into the signal band and that this also results in a self-image component. To reduce the folding from the image band, a novel resonator is presented. This resonator has a bilinear input circuit so that noise and signals exhibits first-order shaping before folding in the band of interest. Next, three different modulator architectures based on the novel resonator are introduced. Finally, the remaining problem of self-image is tackled with a simple, yet efficient offline calibration strategy. Various design examples are shown and simulated to illustrate and prove the effectiveness of the proposed architectures and methods.