Summary
In this paper, based on mathematical approaches and behavioral modeling of internal blocks, an algorithm of designing a continuous‐time delta‐sigma modulator (CT ΔΣM) with aggressive noise shaping is discussed. Using proposed methods, the coefficients of modulator can be calculated directly while the finite gain‐band‐width of amplifiers and rise/fall time of digital‐to‐analog convertors (DACs) in feedback path are included in the transfer function of CT loop filter. To decrease the number of amplifiers, a unique resonator is proposed. Also, an extra feedback DAC is introduced to further reduction of gain‐band‐width requirement of last amplifier. To verify the effectiveness of proposed methods, a fourth‐order, single loop, CT ΔΣM that benefits proportional‐integrator element for compensation of excess‐loop‐delay is realized in system and behavioral circuit levels. It has a 4‐bit quantizer, over‐sampling‐ratio of 10, and out‐of‐band‐gain of 12 dB. The peaking in signal‐transfer‐function is alleviated using a feed‐forward capacitor along with proper choosing of rest coefficients. The designed modulator has 78‐dB signal‐to‐noise‐ratio; even the non‐ideal behaviors of amplifiers and DACs are involved in simulations. Independent to sampling frequency, the proposed methods can be applied to other topologies of CT ΔΣMs. Copyright © 2017 John Wiley & Sons, Ltd.