Optimal design of the noise transfer function of ΔΣ modulators: IIR strategies, FIR strategies, FIR strategies with preassigned poles

Recently, strategies based on semidefinite programming (SDP) have been proposed for the design of the noise transfer function (NTF) of ΔΣΔΣ modulators. Contrarily to conventional approaches, these strategies can formally deal with diverse NTF optimality criteria. However, in most cases they only deliver finite impulse response (FIR) type NTFs that may require a high order to achieve the desired features and thus are not well suited for analog modulators. With a tutorial take, this paper reviews fundamental constraints and possible merit factors to be considered in the NTF selection, as well as conventional and recent design strategies, profiling the former for critical cases. Then, it shows how preassigned pole arrangements can be plugged into SDP based design methods. With this, a hybrid between conventional strategies (limited in flexibility) and recent ones (limited in requiring high orders) can be obtained, getting the best of both realms. Furthermore, this approach provides new insight on the quality of some choices made in conventional design methods.