Design of delta–sigma modulators via generalized Kalman–Yakubovich–Popov lemma

This paper is concerned with the design of delta–sigma modulators via the generalized Kalman–Yakubovich–Popov lemma. The shaped noise transfer function (NTF) is assumed to have infinite impulse response, and the optimization objective is minimizing the maximum magnitude of the NTF over the signal frequency band. By virtue of the GKYP lemma, the optimization of an NTF is converted into a minimization problem subject to quadratic matrix inequalities, and then an iterative algorithm is proposed to solve this alternative minimization problem. Each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages. Moreover, specifications on the NTF zeros are also integrated in the design method. A design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal-to-noise ratio.