Tunable High-Q N-Path Band-Pass Filters: Modeling and Verification

Abstract

In this paper a differential single-port switched-RC N-path filter with bandpass characteristic is proposed. The switching frequency defines the center frequency, while the RC-time defines the bandwidth. This allows for high-Q highly tunable filters which can for instance be useful for cognitive radio. Using a linear periodically timevariant (LPTV) model, exact expressions for the filter transfer function are derived. The behavior of the circuit including non-idealities such as maximum rejection, spectral aliasing, noise and effects due to mismatch in the paths is modeled and verified via measurements. A simple RLC equivalent circuit is provided modeling bandwidth, quality factor and insertion loss of the filter. A 4-path architecture is realized in 65nm CMOS. An off-chip transformer acts as a balun, improves filter-Q and realizes impedance matching. The differential architecture reduces clock-leakage and suppresses selectivity around even harmonics of the clock. The filter has a constant -3dB bandwidth of 35MHz and can be tuned from 100MHz up to 1GHz. Over the whole band IIP3 is better than 14dBm, P 1dB =2dBm and NF<5.5dB,while the power dissipation increases from 2mW to 16mW (only clocking power).

A 4-Element Phased-Array System With Simultaneous Spatial- and Frequency-Domain Filtering at the Antenna Inputs

“…8 for θ=0° is shown in Fig. 9 which is consistent with the N-path frequency domain filtering property [16].…”

“…The network of conducting. From the LPTV network analysis, extensively discussed in [16,22], the output spectrum on the baseband capacitors in state "k" can be shown have a general form:…”

“…This spatial filtering is up-converted to the RF node via passive mixers, so that it occurs directly at the antenna inputs. Moreover RC low-pass filtering also occurs on the capacitors, which is also up-converted, rendering high-Q N-path frequency-domain filtering at RF [12][13][14][15][16][17][18][19][20].…”

“…3, N-path RC frequency-domain filtering also occurs on the baseband capacitors, which is up-converted to the switching frequency and its harmonics [14,16,18,21]. The periodically time-variant nature of N-path filters introduces frequency shifts by multiples of the clock frequency.…”

“…4a can be simplified to the one in Fig. 4c and it can be analyzed with the LPTV approach presented in [16,22], with two changes: 1) R S is 4 times lower (more bandwidth); 2) the source signal contains a weighted sum of 4 antenna signals components with time shifts…”