N-path gmC filter modeling and analysis for direct delta-sigma receiver

This paper presents the analysis and a model for obtaining the delta-sigma loop filter coefficients of a direct delta-sigma receiver (DDSR). The analysis is done by modeling a key element of the DDSR, the N-path filter, with an s-plane transfer function in the baseband. The s-plane model includes the most important non-idealities, such as switch resistances and the limited output resistances of the RF-stages. The model allows the designer to approximate the key parameters for DDSR and enables the optimization of the DDSR performance. As an example, the coefficients of a third-order DDSR are obtained by examining the s-plane and the corresponding z-plane signal and quantization noise transfer functions. The results are evaluated with circuit level simulations.