Synthesis of ∑-Δ Modulators with Elliptic Noise-Shaping Functions

摘要

This paper presents a method for synthesizing sigma-delta (∑-Δ) modulators. The synthesis method is derived from a new noise-shaping equation which interprets the modulator as a device performing frequency-weighted minimization of the modulation error. In the equation, a noise-shaping function which spectrally shapes the modulation error is chosen to be an elliptic filter. The resulting elliptic noise-shaping function, featuring a high attenuation of in-band noise, satisfies the modulator's stability requirement. A four-bit 6MHz wideband modulator and a single-bit 10.7MHz bandpass modulator are designed to demonstrate the superiority of this simple synthesis method.