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

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 (Gm) with an N-path SC branch as its feedback network, offering: 1) double RF filtering at the input and output of the Gm 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 Gm. 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 Gm 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.