A 0.032-mm2 43.3-fJ/Step 100–200-MHz IF 2-MHz Bandwidth Bandpass DSM Based on Passive N-Path Filters

Abstract

In this article, we demonstrate a bandpass (BP) delta–sigma modulator (DSM) using passive $N$ -path filters to implement resonators for high power efficiency, wide intermediate-frequency (IF) tuning range, and small area. The fourth-order modulator loop requires only one active element: an open-loop amplifier. The input magnitude of the amplifier is small due to the modulator’s global negative feedback and the passive $N$ -path filter preceding it. This lowers the power consumption of the amplifier and relaxes the design constraints of the switches in the $N$ -path filter. A system model of the linear periodically time-variant structure of the proposed modulator is developed, and its nonidealities are analyzed. A BP DSM prototype realized in a 65-nm CMOS with an active area of 0.032 mm2 features an IF tunable from 100 to 200 MHz with a sampling frequency ranging from 400 to 800 MHz. Over a fixed 2-MHz bandwidth, the modulator achieves a signal to noise and distortion ratio (SNDR) greater than 55.5 dB over the entire IF range. A maximal SNDR of 60.5 dB is achieved at 175-MHz IF while consuming 150 $\mu \text{W}$ , which corresponds to a Walden’s and Schreier’s figure of merits of 43.3 fJ/conv-step and 164.4 dB, respectively.