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 "title": "N-path filter",
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 "excerpt": "An N-path filter is a radio-frequency bandpass filter built from switches and capacitors driven by N clock phases, giving CMOS receivers a high-Q, widely tunable filter without off-chip components.",
 "snippet": "An N-path filter is a radio-frequency bandpass filter built from switches and capacitors driven by N clock phases, giving CMOS receivers a high-Q, widely tunable filter without off-chip components.",
 "node": "technology.engineering.engineering.electrical.electronics.circuits-and-signal-processing.filter-design-and-synthesis",
 "markdown": "# N-path filter\n\nAn N-path filter is a radio-frequency bandpass filter built from switches and capacitors that are cyclically driven by N non-overlapping clock phases, so that the center frequency is set by the clock rate rather than by inductor and capacitor values. It gives integrated RF receivers a high-Q, widely tunable filter that would otherwise require off-chip acoustic components, and it underpins SAW-less receiver front ends in CMOS.<sup>[1](https://doi.org/10.1002/j.1538-7305.1960.tb03962.x)</sup><sup> • </sup><sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup>\n\n| Key fact | Value |\n|---|---|\n| Center frequency | Set by the clock (switching) frequency; programmable digitally<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> |\n| −3 dB bandwidth | \\( f_{-3\\mathrm{dB}} = 1/(\\pi \\cdot N \\cdot R \\cdot C) \\), inversely proportional to total capacitance \\( N \\cdot C \\)<sup>[4](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)</sup><sup> • </sup><sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> |\n| Quality factor | \\( Q = N \\cdot f_{S}/f_{rc} \\), with \\( f_{rc} = 1/(\\pi \\cdot R \\cdot C) \\); can approach SAW-filter Q in nanometer CMOS<sup>[5](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)</sup><sup> • </sup><sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> |\n| Demonstrated tuning | 100 MHz–1 GHz at constant 35 MHz bandwidth (Q from 3 to 29) in 65-nm CMOS<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> |\n| Blocker tolerance (receiver level) | Out-of-band IIP3 above +40 dBm, 0 dBm-blocker noise figure below 5 dB in the low GHz range<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> |\n| Main failure modes | Harmonic folding from the \\( k \\cdot N \\pm 1 \\) harmonics, rejection ceiling set by switch on-resistance, reciprocal mixing from LO phase noise<sup>[6](https://essay.utwente.nl/fileshare/file/69636/MSc%20%20report%20LCFortgens.pdf)</sup> |\n\n## How it works\n\nThe filter operates by frequency translation: the RF signal is downconverted by the switches, low-pass filtered by baseband capacitors (and any baseband impedance), and upconverted again, so the low-pass characteristic of each RC path appears as a bandpass response centered at the commutation frequency.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> Because the center frequency is defined by a digital clock, it is accurate and widely programmable, a combination of narrow bandwidth and precise, movable center frequency that time-invariant RF filters do not offer.<sup>[4](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)</sup>\n\nThe switching frequency defines the center frequency, while the [RC time constant](https://www.edgepedia.org/rc-time-constant) and clock duty cycle define the bandwidth.<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> Smith's 1953 analysis of commutated networks predicted the 3-dB bandwidth as \\( 1/(\\pi \\cdot N \\cdot R_{S} \\cdot C) \\), where \\( R_{S} \\) is the source resistance.<sup>[4](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)</sup><sup> • </sup><sup>[7](https://doi.org/10.1109/tpgae.1953.5062331)</sup> With \\( f_{rc} = 1/(\\pi \\cdot R \\cdot C) \\) as the RC corner frequency and \\( f_{S} \\) the sampling frequency, the quality factor is \\( Q = N \\cdot f_{S}/f_{rc} \\), raised either by increasing \\( f_{S} \\), increasing \\( N \\), or reducing \\( f_{rc} \\).<sup>[5](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)</sup> Because gigahertz switching is feasible in nanometer CMOS, this Q can approach that of SAW filters.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> The input impedance seen at the switching frequency is high; in a 4-path filter it is about \\( 4.3 \\cdot R_{S} \\).<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup>\n\n## How it is done\n\nThe circuit blocks are an RF input (often via a balun or matching network), N identical switched paths, each a switch and a baseband capacitor or RC impedance, and a multi-phase non-overlapping clock generator. Mixer-first receivers exploiting N-path frequency-translated filtering use a mixer with differential RF input and 25% duty-cycle switches, taking the baseband capacitor voltages as output while RF filtering still occurs at the input.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup>\n\nDesign centers on three coupled choices. First, the number of paths N: increasing N reduces attenuation at harmonics but moves folding to a higher harmonic, \\( (N-1) \\times f_{S} \\), and strongly increases clock-buffer power.<sup>[5](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)</sup> Second, switch resistance: it must be low enough to avoid degrading the transfer function, but lower-resistance switches need wider devices and more clock-generation power.<sup>[5](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)</sup> Third, clock quality: low phase-noise multi-phase clocks at acceptable power remain a key challenge.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> For analysis, switch-RC circuits are linear periodically time-varying (LPTV) systems; a unified adjoint-network treatment covers switched-RC passive mixers, samplers, and N-path filters.<sup>[8](https://doi.org/10.1109/tcsi.2017.2703579)</sup>\n\n## Origin\n\nThe term and general model of the N-path filter come from L. E. Franks and I. W. Sandberg, whose paper \"An Alternative Approach to the Realization of Network Transfer Functions: The N-Path Filter\" appeared in the Bell System Technical Journal in 1960; it described parallel transmission paths, each with input and output modulators, realizing highly selective bandpass filters without magnetic elements.<sup>[1](https://doi.org/10.1002/j.1538-7305.1960.tb03962.x)</sup> Earlier work the field built on includes a mechanical rotating-capacitor comb filter,<sup>[4](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)</sup> W. R. Lepage, C. R. Cahn, and J. S. Brown's 1953 analysis of a comb filter using synchronously commutated capacitors,<sup>[9](https://doi.org/10.1109/tce.1953.6371974)</sup> and B. D. Smith's 1953 \"Analysis of Commutated Networks\";<sup>[7](https://doi.org/10.1109/tpgae.1953.5062331)</sup> Yuh Sun and I. Frisch gave a general theory of commutated networks in 1969.<sup>[10](https://doi.org/10.1109/tct.1969.1083033)</sup> An early integrated CMOS implementation, a switched-capacitor bandpass filter based on N-path and frequency-sampling principles, was published by D.C. von Grunigen and colleagues in 1983.<sup>[11](https://doi.org/10.1109/jssc.1983.1052027)</sup> After the 1980s the topic faded from view, and time-continuous N-path filters regained research interest only in the last decade before 2017, when CMOS scaling allowed operation at TV-band RF frequencies and above 1 GHz.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup><sup> • </sup><sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> The modern RF revival is documented in a 2011 IEEE JSSC paper on tunable high-Q N-path bandpass filters,<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> though published sources do not agree on a single revival paper.\n\n## Variants\n\n**Active and gain-boosted filters.** Milad Darvishi, Ronan van der Zee, Eric A. M. Klumperink, and [Bram Nauta](https://www.edgepedia.org/bram-nauta) reported a widely tunable 4th-order switched Gm-C bandpass filter based on N-path filters in 2012,<sup>[12](https://doi.org/10.1109/jssc.2012.2225542)</sup><sup> • </sup><sup>[13](https://doi.org/10.1109/jssc.2013.2285852)</sup> Placing an N-path filter in an LNA feedback path (Miller boosting) needs \\( (A_{v}+1) \\) times less capacitance and tolerates \\( (A_{v}+1) \\) larger switch on-resistance; Joung Won Park and [Behzad Razavi](https://www.edgepedia.org/behzad-razavi) applied this idea to channel selection at RF in 2014,<sup>[14](https://doi.org/10.1109/jssc.2014.2362843)</sup> and Zhicheng Lin, Pui-In Mak, and Rui P. Martins analyzed a gain-boosted N-path switched-capacitor bandpass filter the same year.<sup>[15](https://doi.org/10.1109/tcsi.2014.2312476)</sup>\n\n**Two-port and high-order filters.** Negar Reiskarimian, Jin Zhou, Tsung-Hao Chuang, and Harish Krishnaswamy introduced a two-port N-path filter with embedded phase shifting in 2016, offsetting the input and output clock sets relative to each other; a 65-nm CMOS 0.8–1.4 GHz implementation achieved 13-dB gain control and full 360° phase-shift range.<sup>[16](https://doi.org/10.1109/tcsii.2016.2530338)</sup> High-order responses can be built by gyrator-coupling stages.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> A 2020 design methodology by Poorya Karami, Amirali Banaeikashani, Baktash Behmanesh, and Seyed Mojtaba Atarodi used weighted extra paths for harmonic rejection, power reduction, foldback elimination, and spectrum shaping.<sup>[17](https://doi.org/10.1109/tcsi.2020.3009191)</sup>\n\n## Applications\n\nMeasured prototype results show the achievable envelope. The 2011 Twente 4-path filter in 65-nm CMOS tuned from 100 MHz to 1 GHz with constant 35 MHz bandwidth (Q from 3 to 29), IIP3 better than +14 dBm, P1dB of 2 dBm, NF below 5.5 dB, and clocking power from 2 mW to 16 mW.<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup> At receiver level, a 28-nm CMOS SAW-less receiver achieved in-band IIP3 of +10 dBm, out-of-band IIP3 of +44 dBm, blocker 1-dB compression of +13 dBm at 80 MHz offset, and 38–96 mW consumption over 0.1–2 GHz in 0.49 mm²;<sup>[18](https://doi.org/10.3990/1.9789036546201)</sup> a 45-nm PDSOI mixer-first receiver reached sub-3 dB NF with out-of-band IIP3 of +39 dBm.<sup>[18](https://doi.org/10.3990/1.9789036546201)</sup> Across the field, the last decade demonstrated blocker compression points above +10 dBm, out-of-band IIP3 above +40 dBm, and 0 dBm-blocker noise figure below 5 dB in the low GHz range.<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup>\n\nApplications include SAW-less GSM/EDGE receivers meeting the 15 dB blocker-noise-figure requirement for a 0 dBm blocker at 80 MHz offset,<sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> ultra-low-power ISM-band receivers,<sup>[19](https://www.mdpi.com/2079-9292/11/24/4111)</sup> and wideband RF self-interference cancellation and phased-array front ends using two-port filters with embedded variable attenuation and phase shift.<sup>[16](https://doi.org/10.1109/tcsii.2016.2530338)</sup>\n\n## Limitations and alternatives\n\n**Harmonic folding.** Because the circuit is LPTV, blockers at harmonics of the clock fold into the passband; an N-path filter folds harmonics \\( k \\cdot N - 1 \\) and \\( k \\cdot N + 1 \\) into the desired signal, and which harmonic folds is a property of the number of clock phases, not the duty cycle.<sup>[6](https://essay.utwente.nl/fileshare/file/69636/MSc%20%20report%20LCFortgens.pdf)</sup> For a 4-path filter, folding occurs from \\( 3 \\cdot f_{S} \\) and \\( 5 \\cdot f_{S} \\), while an 8-path architecture's first folding comes from \\( 7 \\cdot f_{S} \\), relaxing pre-filter requirements.<sup>[3](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)</sup><sup> • </sup><sup>[2](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)</sup> Suppression still requires LTI pre-filtering with passive LC filters.<sup>[20](https://ieeexplore.ieee.org/document/8066456/footnotes#footnotes)</sup>\n\n**Rejection and clock limits.** Rejection at large offsets is capped by switch on-resistance at roughly \\( R_{sw}/(R_{S}+R_{sw}) \\).<sup>[4](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)</sup> LO phase noise is translated to the mixer input, causing reciprocal mixing in both N-path and charge-sharing architectures.<sup>[5](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)</sup> Parasitic shunt capacitance limits the RF range by introducing signal loss and degrading NF, shifting the peak-gain frequency left of \\( f_{S} \\), while source inductance shifts it right; a chosen series inductor can restore the peak to \\( f_{S} \\).<sup>[20](https://ieeexplore.ieee.org/document/8066456/footnotes#footnotes)</sup>\n\n**Alternatives.** SAW and BAW acoustic filters offer steep skirts and low loss; BAW's intrinsically higher Q and lower series resistance make it the choice where skirt steepness matters most, but AlN-based BAW is limited to a relative bandwidth below about 4.3% and is unattractive below 1 GHz, where resonator area grows as \\( 1/f^{2} \\).<sup>[21](https://engineering.purdue.edu/oxidemems/conferences/ultrasonics2008/files/IUS2008-000405.pdf)</sup> An N-path filter of only switches and capacitors can approximate LC tanks with potentially higher Q and a clock-tunable center frequency, making it CMOS-integrable and suited to software-defined radio.<sup>[6](https://essay.utwente.nl/fileshare/file/69636/MSc%20%20report%20LCFortgens.pdf)</sup>\n\n**Recent work.** A 2026 review classifies N-path mixer harmonic rejection into active gain, passive gain, and pulse-width-modulation families, with active gain achieving the highest rejection at increased power cost, passive gain offering moderate rejection with lower power and higher linearity, and PWM balancing the two.<sup>[22](https://doi.org/10.1109/lascas67804.2026.11457130)</sup> Recent hardware includes a wideband tunable N-path mixer with calibrated harmonic rejection including the 7th LO harmonic, by Sana Ibrahim and colleagues (2024),<sup>[23](https://doi.org/10.1109/tcsi.2024.3414183)</sup> and harmonic reset switching in passive mixers by Soroush Araei and Negar Reiskarimian (2024).<sup>[24](https://doi.org/10.1109/jssc.2024.3462296)</sup>\n\n## References\n\n1. [L. E. Franks, I. W. Sandberg (1960). An Alternative Approach to the Realization of Network Transfer Functions: The N -Path Filter. Bell System Technical Journal.](https://doi.org/10.1002/j.1538-7305.1960.tb03962.x)\n2. [N-path filters and Mixer-First receivers: A review (Klumperink et al., IEEE CICC 2017)](https://ris.utwente.nl/ws/files/17136075/Klumperink_CICC_2017.pdf)\n3. [Tunable High-Q N-Path Band-Pass Filters: Modeling and Verification (Ghaffari, Klumperink, Soer, Nauta, IEEE JSSC 2011)](https://www.csun.edu/~jou/classes/ece644/2022s/lectures/nauta.pdf)\n4. [Translational Circuits (B. Razavi, IEEE Solid-State Circuits Magazine, Winter 2016)](https://www.seas.ucla.edu/brweb/papers/Journals/BRWinter16Translation.pdf)\n5. [Discrete-time Receivers, from N-Path to Charge Sharing Band-pass Filters: a Comparison (Journal of Integrated Circuits and Systems)](https://jics.org.br/ojs/index.php/JICS/article/download/797/464/3579)\n6. [Approximation of an ideal bandpass filter using an N-path filter (MSc thesis, University of Twente)](https://essay.utwente.nl/fileshare/file/69636/MSc%20%20report%20LCFortgens.pdf)\n7. [B. D. Smith (1953). Analysis of Commutated Networks. Transactions of the IRE Professional Group on Aeronautical and Navigational Electronics.](https://doi.org/10.1109/tpgae.1953.5062331)\n8. [Shanthi Pavan, Eric Klumperink (2017). Simplified Unified Analysis of Switched-RC Passive Mixers, Samplers, and $N$ -Path Filters Using the Adjoint Network. IEEE Transactions on Circuits and Systems I Regular Papers.](https://doi.org/10.1109/tcsi.2017.2703579)\n9. [W. R. Lepage, C. R. Cahn, J. S. Brown (1953). Analysis of a comb filter using synchronously commutated capacitors. Transactions of the American Institute of Electrical Engineers Part I Communication and Electronics.](https://doi.org/10.1109/tce.1953.6371974)\n10. [Yuh Sun, I. Frisch (1969). A General Theory of Commutated Networks. IEEE Transactions on Circuit Theory.](https://doi.org/10.1109/tct.1969.1083033)\n11. [D.C. von Grunigen and colleagues (1983). An integrated CMOS switched-capacitor bandpass filter based on N-path and frequency-sampling principles. IEEE Journal of Solid-State Circuits.](https://doi.org/10.1109/jssc.1983.1052027)\n12. [Milad Darvishi and colleagues (2012). Widely Tunable 4th Order Switched G$_m$-C Band-Pass Filter Based on N-Path Filters. IEEE Journal of Solid-State Circuits.](https://doi.org/10.1109/jssc.2012.2225542)\n13. [Milad Darvishi, Ronan van der Zee, Bram Nauta (2013). Design of Active N-Path Filters. IEEE Journal of Solid-State Circuits.](https://doi.org/10.1109/jssc.2013.2285852)\n14. [Joung Won Park, Behzad Razavi (2014). Channel Selection at RF Using Miller Bandpass Filters. IEEE Journal of Solid-State Circuits.](https://doi.org/10.1109/jssc.2014.2362843)\n15. [Zhicheng Lin, Pui-In Mak, Rui P. Martins (2014). Analysis and Modeling of a Gain-Boosted N-Path Switched-Capacitor Bandpass Filter. IEEE Transactions on Circuits and Systems I Regular Papers.](https://doi.org/10.1109/tcsi.2014.2312476)\n16. [Negar Reiskarimian and colleagues (2016). Analysis and Design of Two-Port $N$ - Path Bandpass Filters With Embedded Phase Shifting. IEEE Transactions on Circuits & Systems II Express Briefs.](https://doi.org/10.1109/tcsii.2016.2530338)\n17. [Poorya Karami and colleagues (2020). An N-Path Filter Design Methodology With Harmonic Rejection, Power Reduction, Foldback Elimination, and Spectrum Shaping. IEEE Transactions on Circuits and Systems I Regular Papers.](https://doi.org/10.1109/tcsi.2020.3009191)\n18. [SAW-less radio receivers in CMOS (PhD thesis, Klumperink group / University of Twente)](https://doi.org/10.3990/1.9789036546201)\n19. [A 320 μW Multi-Band Receiver with N-Path Switched-Capacitor Networks (MDPI Electronics)](https://www.mdpi.com/2079-9292/11/24/4111)\n20. [Analysis of the Effect of Source Capacitance and Inductance on N-Path Mixers and Filters (Pavan & Klumperink, IEEE TCAS-I 65(5), May 2018)](https://ieeexplore.ieee.org/document/8066456/footnotes#footnotes)\n21. [SAW and BAW Technologies for RF Filter Applications (Ruby, IUS 2008)](https://engineering.purdue.edu/oxidemems/conferences/ultrasonics2008/files/IUS2008-000405.pdf)\n22. [A Comprehensive Review of State-of-the-Art Harmonic Rejection Techniques in N-Path Mixers (2026)](https://doi.org/10.1109/lascas67804.2026.11457130)\n23. [Sana Ibrahim and colleagues (2024). Wideband Tunable N-Path Mixer With Calibrated Harmonic Rejection Including the 7th LO Harmonic. IEEE Transactions on Circuits and Systems I Regular Papers.](https://doi.org/10.1109/tcsi.2024.3414183)\n24. [Soroush Araei, Negar Reiskarimian (2024). Implementation and Application of Harmonic Reset Switching in Passive Mixers. IEEE Journal of Solid-State Circuits.](https://doi.org/10.1109/jssc.2024.3462296)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Engineering and manufacturing › Electrical and electronics engineering › Circuits and signal processing › Filter design and synthesis*\n\n*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Sep 30, 2026 · Last review: Sep 30, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n",
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 "speakable": "An N-path filter is a radio-frequency bandpass filter built from switches and capacitors driven by N clock phases, giving CMOS receivers a high-Q, widely tunable filter without off-chip components."
}