Abstract
A framework using semidefinite programming is proposed to enable the design of sigma delta modulator loop filters at the transfer function level. Both continuous-time and discrete-time, low-pass and band-pass designs are supported. For performance, we use the recently popularized Generalized Kalman–Yakubovic–Popov (GKYP) lemma to place constraints on the $$\mathcal {H}_\infty $$ norm of the noise transfer function (NTF) in the frequency band of interest. We expand the approach to incorporate common stability criteria in the form of $$\mathcal {H}_2$$ and $$\ell _1$$ norm NTF constraints. Furthering the discussion of stability, we introduce techniques from control systems to improve the robustness of the feedback system over a range of quantizer gains. The performance-stability trade-off is examined using this framework and motivated by simulation results.
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