Analysis and Modeling of a Gain-Boosted N-Path Switched-Capacitor Bandpass Filter

摘要

It has been studied that, an N-path switched-capacitor (SC) branch driven by an N-phase non-overlapped local oscillator (LO), is equivalent to a tunable parallel-RLC tank suitable for radio-frequency (RF) filtering. This paper proposes a gain-boosted N-path SC bandpass filter (GB-BPF) with a number of sought features. It is based on a transconductance amplifier $({rm G}_{rm m})$ with an N-path SC branch as its feedback network, offering: 1) double RF filtering at the input and output of the ${rm G}_{rm m}$ in one step; 2) customized passband gain and bandwidth with input-impedance match; and 3) reduced physical capacitance thanks to the loop gain offered by ${rm G}_{rm m}$. All have been examined using a RLC model of the SC branch before applying the linear periodically time-variant (LPTV) analysis to derive the R, L, and C expressions and analytically study the harmonic selectivity, harmonic folding, and noise. The latter reveals that: 1) the noise due to the switches is notched at the output, allowing smaller switches to save the LO power and 2) the noises due to the source resistance and ${rm G}_{rm m}$ are narrowband at the output, reducing the folded noise during harmonic mixing. To study the influence of circuit non-idealities, an intuitive equivalent circuit model is also proposed and verified. The design example is a four-path 0.5–2-GHz GB-BPF simulated with the 65-nm CMOS. It exhibits $>$11 dB gain, $<$2.3 dB NF, and $+$21-dBm out-of-band IIP3 at 150-MHz offset, while consuming just- 7 mW of power.