Analysis of the Signal Transfer and Folding in N-Path Filters With a Series Inductance

Abstract

N-path filters exploiting switched-series-R-C networks can realize high-Q blocking-tolerant band-pass filters. Moreover, their center frequency is flexibly programmable by a digital clock. Unfortunately, the time variant nature of these circuits also results in unwanted signal folding. This paper proves analytically that folding can be reduced and band pass filtering can be improved by adding an inductance in series with the switched-R-C network. In contrast, a shunt capacitor degrades band-pass filter performance. The interaction between the reactive series impedance and the switched capacitors of an N-path filter complicates analysis due to memory effects associated with reactive components. Assuming identical signal paths with 1/ duty cycle, we show it is possible to solve the set of differential equations, by assuming that the signals in each path only differ in delay. Analytical equations are verified versus simulations, and the benefits in filter properties and reduction in signal folding are demonstrated.Index Terms-Cognitive radio, commutated network filters, filter, frequency translated filtering, linear periodically time variant circuit, N-path filter, reconfigurable filter, software defined radio, switched capacitor filters, tunable filter. 1549-8328

Simplified Unified Analysis of Switched-RC Passive Mixers, Samplers, and $N$ -Path Filters Using the Adjoint Network

“…Strongly simplified expressions for the harmonic transfer functions in the sampling and mixing region were derived, which also formed the basis for noise analysis. Later work, building on this analysis derived the filter transfer and noise for N -path band-pass [15] and notch filters [16] and an equivalent RLC filter model, gain-boosted N -path filters [17], and an N -path filter preceded by a series-inductor for low-pass pre-filtering [18]. Such pre-filtering is important, as mixer-first receivers and Npath filters show folding of RF-signals around multiples of f s (similar to aliasing in discrete time circuits, albeit with more attenuation).…”

N-path filters and mixer-first receivers: A review

“…3 was derived for arbitrary N to fit the fundamental response. The analysis was also used to find the transfer function for N-path notch filters [23], gain-boosted N-path filters [36], and an N-path filter preceded by a series-inductor to realize time-continuous low-pass pre-filtering [37]. Such pre-filtering is important, as N-path filters show folding of RFsignals around some harmonics of the clock-frequency.…”

“…This tunes out capacitive parasitics, reducing loss and noise, while also reducing folding (see [37]). Other work in advanced SOI technology demonstrates improved linearity and increased frequency range [51].…”

Broadband Synthetic Transmission-Line N-Path Filter Design

“…A higher order linear time-variant (LTV) state-space analysis that takes into account memory effects, similar to [17], is required for a reactive source impedance. Recently, the filter transfer function using second-order state-space analysis of a single shunt N-path filter, which includes source inductance, has been derived in [24].…”