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arxiv: 2604.26405 · v1 · submitted 2026-04-29 · 📡 eess.SP

A 21-24 GHz Low-Phase-Noise mmWave VCO with Third-Harmonic Expansion using a Triple-Coupled Transformer based Tank

Narahari N. Moudhgalya This is my paper

Pith reviewed 2026-05-07 11:42 UTC · model grok-4.3

classification 📡 eess.SP
keywords mmWave VCOtriple-coupled transformerthird-harmonic expansionlow phase noisetransformer-based tankCMOS oscillatorclass-F designwideband tuning
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The pith

A triple-coupled transformer tank enables third-harmonic expansion over 21-24 GHz in a compact low-noise VCO.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper designs a sixth-order tank based on a triple-coupled transformer for use in millimeter-wave voltage-controlled oscillators. This tank naturally resonates at three frequencies, which supports expanding the third harmonic across a wide frequency band without adding lossy tuning capacitors. The design skips the usual head resonator and uses a noise-circulating core instead to keep phase noise low while shrinking the circuit area. Post-layout simulations in 65-nanometer CMOS confirm a 13.5 percent tuning range with phase noise down to minus 116 decibels per hertz and strong efficiency metrics at 5.4 milliwatts power.

Core claim

The proposed sixth-order triple-coupled transformer-based tank inherently supports three resonance modes, enabling wideband third-harmonic expansion without additional low-Q switched-capacitor tuning elements. In contrast to conventional class-F23 designs, the proposed VCO removes the head resonator and adopts a noise circulating core to maintain low phase noise with reduced area.

What carries the argument

Sixth-order triple-coupled transformer-based tank supporting three resonance modes for third-harmonic expansion.

If this is right

  • The VCO achieves a 13.5 percent tuning range from 21.03 to 23.99 GHz.
  • Minimum phase noise reaches -116.25 dBc/Hz at 1 MHz offset.
  • Peak FoM, FoMT, and FoMA reach 195.86, 198.24, and 212.31 dBc/Hz respectively.
  • The circuit consumes 5.4 mW while occupying 0.02268 mm2.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The three-mode resonance approach could be adapted to harmonic-expansion oscillators at higher mmWave or sub-THz bands.
  • Removing switched capacitors may preserve tank quality factor in integrated systems where layout parasitics are a concern.
  • The compact area and noise circulation might allow denser integration in full mmWave transceivers.

Load-bearing premise

Post-layout electromagnetic simulations and device models in TSMC 65-nm CMOS accurately predict the triple-coupled tank resonances and phase-noise performance at 21-24 GHz without unmodeled parasitics or process variations dominating.

What would settle it

Fabricated measurements of the VCO showing a tuning range narrower than 13.5 percent or phase noise worse than -116.25 dBc/Hz at 1 MHz offset due to unmodeled effects.

Figures

Figures reproduced from arXiv: 2604.26405 by Narahari N. Moudhgalya.

Figure 1
Figure 1. Figure 1: Comparison of recent harmonic-rich-shaping VCO Techniques view at source ↗
Figure 2
Figure 2. Figure 2: (a) Conventional fourth-order XFMR tank and (b) proposed sixth view at source ↗
Figure 3
Figure 3. Figure 3: (a) Transformer layout and Cadence EMX simulation results - (b) view at source ↗
Figure 4
Figure 4. Figure 4: Variation of frequency ratios with (a)-(b) k12 and (c)-(d) k13 branches leads to (1) and (2). For simplicity of the analysis, the tank is assumed to be lossless (ri = 0). Solving (1) and (2) for the input impedance Zin results in the expression given in (3), where the effective impedance Zeff is defined in (4). Equation (3) is the generic Zin equation for a triple-coupled XFMR tank, and it reveals that the… view at source ↗
Figure 6
Figure 6. Figure 6: Layout of the proposed triple-coupled XFMR tank based VCO view at source ↗
Figure 7
Figure 7. Figure 7: Transient waveforms of (a) Vout and (b) Vout, (c) Spectrum of Vout and (d) Phase Noise profile suppression.N1,2 and P1,2 on each side switch simultaneously within each half-cycle, enabling NC operation view at source ↗
Figure 8
Figure 8. Figure 8: Post-layout simulation results summarizing TR and PN performance of the proposed VCO: (a) frequency vs view at source ↗
read the original abstract

This work presents the design and analysis of a sixth-order triple-coupled transformer-based tank, enabling third-harmonic expansion for mmWave VCOs. Unlike conventional fourth-order tanks, the proposed tank inherently supports three resonance modes, enabling wideband third-harmonic expansion without additional low-Q switched-capacitor tuning elements. In contrast to conventional class-F23 designs, the proposed VCO removes the head resonator and adopts a noise circulating core to maintain low phase noise with reduced area. Implemented in TSMC 65-nm CMOS, post-layout simulation results demonstrate a 21.03-23.99 GHz (13.5%) tuning range, minimum phase noise of -116.25 dBc/Hz at 1 MHz offset, and peak FoM/FoMT/FoMA of 195.86/198.24/212.31 dBc/Hz while consuming 5.4 mW and occupying 0.02268 mm2.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper claims to introduce a sixth-order triple-coupled transformer-based tank for a mmWave VCO that inherently supports three resonance modes, enabling wideband third-harmonic expansion without low-Q switched-capacitor tuning elements. By removing the head resonator and using a noise circulating core, it aims to maintain low phase noise with reduced area. Post-layout simulations in TSMC 65-nm CMOS report a 13.5% tuning range from 21.03 to 23.99 GHz, phase noise as low as -116.25 dBc/Hz at 1 MHz offset, peak FoM of 195.86 dBc/Hz, FoMT 198.24, FoMA 212.31, with 5.4 mW power and 0.02268 mm2 area.

Significance. If the simulation results hold in silicon, this would represent a meaningful advance in mmWave VCO design by demonstrating a tank topology that provides inherent multi-mode resonance for third-harmonic expansion, offering a path to wider tuning ranges and competitive phase noise without additional lossy tuning components or head resonators, while achieving small area and good FoM.

major comments (1)
  1. Post-layout simulation results: The central claims of three distinct resonance modes enabling wideband third-harmonic expansion and the reported phase noise of -116.25 dBc/Hz rest entirely on post-layout EM simulations in TSMC 65 nm. No fabricated silicon measurements are provided to confirm that the sixth-order tank resonances remain well-separated and high-Q across 21-24 GHz under real parasitics, interconnect inductance, or process variation, which directly impacts the asserted advantage over conventional class-F23 designs.
minor comments (1)
  1. Abstract and title: The title states a 21-24 GHz range while the abstract gives the more precise 21.03-23.99 GHz; align these for consistency.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential significance of the triple-coupled transformer tank. We address the major comment point by point below.

read point-by-point responses

  1. Referee: Post-layout simulation results: The central claims of three distinct resonance modes enabling wideband third-harmonic expansion and the reported phase noise of -116.25 dBc/Hz rest entirely on post-layout EM simulations in TSMC 65 nm. No fabricated silicon measurements are provided to confirm that the sixth-order tank resonances remain well-separated and high-Q across 21-24 GHz under real parasitics, interconnect inductance, or process variation, which directly impacts the asserted advantage over conventional class-F23 designs.

    Authors: We agree that the results are based entirely on post-layout simulations, as stated in the abstract and throughout the manuscript. The simulations incorporate full electromagnetic extraction of the sixth-order tank using industry-standard tools, along with parasitic extraction of the active core and interconnects in the TSMC 65 nm process. The theoretical analysis of the three resonance modes is validated against these simulations, showing clear separation and high Q across the 21-24 GHz range. While silicon measurements would provide definitive confirmation under real process variation, this work focuses on the novel tank topology and its analysis; fabrication is beyond the current scope. In the revised manuscript we will add Monte Carlo simulations and corner-case analysis of the resonance frequencies and Q factors to further address robustness concerns. revision: partial

Circularity Check

0 steps flagged

No significant circularity; claims rest on circuit equations and EM simulations.

full rationale

The paper derives the triple-coupled tank's three resonance modes from sixth-order network analysis and validates tuning range, phase noise, and FoM via post-layout EM simulations in TSMC 65 nm. No load-bearing step reduces to a self-definition, fitted parameter renamed as prediction, or self-citation chain. Performance numbers are direct simulation outputs, not forced by construction from the input assumptions. The design choices (noise-circulating core, removal of head resonator) are justified by standard circuit theory rather than circular re-labeling of known results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of CMOS process modeling and EM simulation accuracy for mmWave frequencies; no new physical entities or ad-hoc constants are introduced beyond conventional circuit design parameters.

axioms (1)
  • domain assumption TSMC 65-nm CMOS device models and electromagnetic simulation tools accurately capture mmWave behavior of coupled transformers
    Invoked implicitly to support all post-layout results and resonance mode claims.

pith-pipeline@v0.9.0 · 5478 in / 1276 out tokens · 75099 ms · 2026-05-07T11:42:00.815028+00:00 · methodology

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Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    A 0.083-mm2 25.2-to- 29.5 GHz Multi-LC-Tank Class-F234 VCO With a 189.6-dBc/Hz FOM,

    H. Guo, Y . Chen, P.-I. Mak, and R. P. Martins, “A 0.083-mm2 25.2-to- 29.5 GHz Multi-LC-Tank Class-F234 VCO With a 189.6-dBc/Hz FOM,” IEEE Solid-State Circuits Letters, vol. 1, no. 4, pp. 86–89, 2018

    work page 2018

  2. [2]

    26.2 A 0.08mm2 25.5-to-29.9GHz Multi-Resonant-RLCM-Tank VCO Using a Single-Turn Multi-Tap Inductor and CM-Only Capacitors Achieving 191.6dBc/Hz FoM and 130kHz 1/f3 PN Corner,

    ——, “26.2 A 0.08mm2 25.5-to-29.9GHz Multi-Resonant-RLCM-Tank VCO Using a Single-Turn Multi-Tap Inductor and CM-Only Capacitors Achieving 191.6dBc/Hz FoM and 130kHz 1/f3 PN Corner,” in2019 IEEE International Solid-State Circuits Conference - (ISSCC), 2019, pp. 410–412

    work page 2019

  3. [3]

    A 3.3-mW 25.2-to-29.4-GHz Current-Reuse VCO Using a Single-Turn Multi-Tap Inductor and Differential-Only Switched-Capacitor Arrays With a 187.6- dBc/Hz FOM,

    Y . Huang, Y . Chen, H. Guo, P.-I. Mak, and R. P. Martins, “A 3.3-mW 25.2-to-29.4-GHz Current-Reuse VCO Using a Single-Turn Multi-Tap Inductor and Differential-Only Switched-Capacitor Arrays With a 187.6- dBc/Hz FOM,”IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 67, no. 11, pp. 3704–3717, 2020

    work page 2020

  4. [4]

    A low phase-noise CMOS VCO with harmonic tuned LC tank,

    H. Kim, S. Ryu, Y . Chung, J. Choi, and B. Kim, “A low phase-noise CMOS VCO with harmonic tuned LC tank,”IEEE Transactions on Microwave Theory and Techniques, vol. 54, no. 7, pp. 2917–2924, 2006

    work page 2006

  5. [5]

    H. Guo, Y . Chen, P.-I. Mak, and R. P. Martins, “A 0.082mm2 24.5- to-28.3GHz Multi-LC-Tank Fully-Differential VCO Using Two Sep- arate Single-Turn Inductors and a 1D-Tuning Capacitor Achieving 189.4dBc/Hz FOM and 200±50kHz 1/f3 PN Corner,” in2020 IEEE Radio Frequency Integrated Circuits Symposium (RFIC), 2020, pp. 235– 238

    work page 2020

  6. [6]

    A Millimeter-Wave CMOS VCO Featuring a Mode-Ambiguity-Aware Multi-Resonant-RLCM Tank,

    H. Guo, Y . Chen, C. Yang, P.-I. Mak, and R. P. Martins, “A Millimeter-Wave CMOS VCO Featuring a Mode-Ambiguity-Aware Multi-Resonant-RLCM Tank,”IEEE Transactions on Circuits and Sys- tems I: Regular Papers, vol. 69, no. 1, pp. 172–185, 2022

    work page 2022

  7. [7]

    A general theory of phase noise in electrical oscillators,

    A. Hajimiri and T. Lee, “A general theory of phase noise in electrical oscillators,”IEEE Journal of Solid-State Circuits, vol. 33, no. 2, pp. 179–194, 1998

    work page 1998

  8. [8]

    A filtering technique to lower LC oscillator phase noise,

    E. Hegazi, H. Sjoland, and A. Abidi, “A filtering technique to lower LC oscillator phase noise,”IEEE Journal of Solid-State Circuits, vol. 36, no. 12, pp. 1921–1930, 2001

    work page 1921

  9. [9]

    A Class-F CMOS Oscillator,

    M. Babaie and R. B. Staszewski, “A Class-F CMOS Oscillator,”IEEE Journal of Solid-State Circuits, vol. 48, no. 12, pp. 3120–3133, 2013

    work page 2013

  10. [10]

    Implicit Common-Mode Resonance in LC Oscillators,

    D. Murphy, H. Darabi, and H. Wu, “Implicit Common-Mode Resonance in LC Oscillators,”IEEE Journal of Solid-State Circuits, vol. 52, no. 3, pp. 812–821, 2017

    work page 2017

  11. [11]

    An Inverse- Class-F CMOS Oscillator With Intrinsic-High-Q First Harmonic and Second Harmonic Resonances,

    C. C. Lim, H. Ramiah, J. Yin, P.-I. Mak, and R. P. Martins, “An Inverse- Class-F CMOS Oscillator With Intrinsic-High-Q First Harmonic and Second Harmonic Resonances,”IEEE Journal of Solid-State Circuits, vol. 53, no. 12, pp. 3528–3539, 2018

    work page 2018

  12. [12]

    A 1/f Noise Upconversion Reduction Technique for V oltage-Biased RF CMOS Oscil- lators,

    M. Shahmohammadi, M. Babaie, and R. B. Staszewski, “A 1/f Noise Upconversion Reduction Technique for V oltage-Biased RF CMOS Oscil- lators,”IEEE Journal of Solid-State Circuits, vol. 51, no. 11, pp. 2610– 2624, 2016

    work page 2016

  13. [13]

    A Low-Flicker-Noise 30- GHz Class-F23 Oscillator in 28-nm CMOS Using Implicit Resonance and Explicit Common-Mode Return Path,

    Y . Hu, T. Siriburanon, and R. B. Staszewski, “A Low-Flicker-Noise 30- GHz Class-F23 Oscillator in 28-nm CMOS Using Implicit Resonance and Explicit Common-Mode Return Path,”IEEE Journal of Solid-State Circuits, vol. 53, no. 7, pp. 1977–1987, 2018

    work page 1977

  14. [14]

    A 196.5 dBc/Hz FOMT 16.8–21.6- GHz Class-F23 CMOS VCO With Transformer-Based Optimal Q-Factor Tank,

    F. Hong, T. Ding, and D. Zhao, “A 196.5 dBc/Hz FOMT 16.8–21.6- GHz Class-F23 CMOS VCO With Transformer-Based Optimal Q-Factor Tank,”IEEE Solid-State Circuits Letters, vol. 5, pp. 62–65, 2022

    work page 2022

  15. [15]

    A Compact 0.2–0.3-V Inverse-Class-F23 Oscillator for Low 1/f3 Noise Over Wide Tuning Range,

    J. Du, Y . Hu, T. Siriburanon, E. Kobal, P. Quinlan, A. Zhu, and R. B. Staszewski, “A Compact 0.2–0.3-V Inverse-Class-F23 Oscillator for Low 1/f3 Noise Over Wide Tuning Range,”IEEE Journal of Solid-State Circuits, vol. 57, no. 2, pp. 452–464, 2022

    work page 2022

  16. [16]

    High-Performance Harmonic- Rich Single-Core VCO With Multi-LC Tank: A Tutorial,

    Y . Chen, P.-I. Mak, and R. P. Martins, “High-Performance Harmonic- Rich Single-Core VCO With Multi-LC Tank: A Tutorial,”IEEE Trans- actions on Circuits and Systems II: Express Briefs, vol. 69, no. 7, pp. 3115–3121, 2022

    work page 2022

  17. [17]

    A 5.2GHz Trifilar Transformer-Based Class-F23 Noise Circulating VCO with FoM of 192.6 dBc/Hz,

    H. Cao, T. Huang, X. Liu, H. Wang, J. Jin, and W. Wu, “A 5.2GHz Trifilar Transformer-Based Class-F23 Noise Circulating VCO with FoM of 192.6 dBc/Hz,” in2023 IEEE Asian Solid-State Circuits Conference (A-SSCC), 2023, pp. 1–3

    work page 2023

  18. [18]

    Analysis and Design of a 15.2-to-18.2-GHz Inverse-Class-F VCO With a Balanced Dual-Core Topology Suppressing the Flicker Noise Upconversion,

    X. Meng, H. Li, P. Chen, J. Yin, P.-I. Mak, and R. P. Martins, “Analysis and Design of a 15.2-to-18.2-GHz Inverse-Class-F VCO With a Balanced Dual-Core Topology Suppressing the Flicker Noise Upconversion,”IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 70, no. 12, pp. 5110–5123, 2023

    work page 2023

  19. [23]

    A Class-F23 CMOS Oscillator With Second and Third Harmonic Resonances Expansion,

    S. Tian and X. Liu, “A Class-F23 CMOS Oscillator With Second and Third Harmonic Resonances Expansion,”IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 73, no. 1, pp. 87–99, 2026

    work page 2026

  20. [24]

    A Noise Circulating Oscillator,

    F. Wang and H. Wang, “A Noise Circulating Oscillator,”IEEE Journal of Solid-State Circuits, vol. 54, no. 3, pp. 696–708, 2019

    work page 2019

  21. [25]

    20.1 A 5.0-to-6.36GHz Wideband-Harmonic-Shaping VCO Achieving 196.9dBc/Hz Peak FoM and 90-to-180kHz 1/f3 PN Corner Without Harmonic Tuning,

    H. Guo, Y . Chen, P.-I. Mak, and R. P. Martins, “20.1 A 5.0-to-6.36GHz Wideband-Harmonic-Shaping VCO Achieving 196.9dBc/Hz Peak FoM and 90-to-180kHz 1/f3 PN Corner Without Harmonic Tuning,” in2021 IEEE International Solid-State Circuits Conference (ISSCC), vol. 64, 2021, pp. 294–296

    work page 2021

  22. [26]

    An X-Band CMOS VCO Using Ultra-Wideband Dual Common-Mode Resonance Technique,

    F. Hong, H. Zhang, and D. Zhao, “An X-Band CMOS VCO Using Ultra-Wideband Dual Common-Mode Resonance Technique,”IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 69, no. 9, pp. 3579–3590, 2022

    work page 2022

  23. [27]

    A Low- Phase-Noise VCO With Common-Mode Resonance Expansion and Intrinsic Differential 2nd-Harmonic Output Based on a Single Three- Coil Transformer,

    Z. Lin, H. Jia, R. Ma, W. Deng, Z. Wang, and B. Chi, “A Low- Phase-Noise VCO With Common-Mode Resonance Expansion and Intrinsic Differential 2nd-Harmonic Output Based on a Single Three- Coil Transformer,”IEEE Journal of Solid-State Circuits, vol. 59, no. 1, pp. 253–267, 2024

    work page 2024

  24. [28]

    An X-Band Low-Phase- Noise Class-F23 VCO Without Manual Harmonic Tuning Based on Switched-Transformer and Wideband Common-Mode Resonance,

    Y . Li, Z. Huang, L. Song, T. Yang, and X. Li, “An X-Band Low-Phase- Noise Class-F23 VCO Without Manual Harmonic Tuning Based on Switched-Transformer and Wideband Common-Mode Resonance,”IEEE Transactions on Microwave Theory and Techniques, vol. 72, no. 5, pp. 3076–3090, 2024

    work page 2024

  25. [29]

    A Reconfigurable Injection-Locked LO Generator With a Wideband-Harmonic-Shaping Class-F23 VCO for Multibands 5G mm-Wave,

    Z. Wang, K. Ma, Z. Ma, H. Shi, H. Fu, and J. Xu, “A Reconfigurable Injection-Locked LO Generator With a Wideband-Harmonic-Shaping Class-F23 VCO for Multibands 5G mm-Wave,”IEEE Transactions on Microwave Theory and Techniques, vol. 71, no. 9, pp. 4144–4157, 2023

    work page 2023

  26. [30]

    A 19.5-GHz 28-nm Class-C CMOS VCO, With a Reasonably Rigorous Result on 1/f Noise Upconversion Caused by Short-Channel Effects,

    A. Franceschin, P. Andreani, F. Padovan, M. Bassi, and A. Bevilacqua, “A 19.5-GHz 28-nm Class-C CMOS VCO, With a Reasonably Rigorous Result on 1/f Noise Upconversion Caused by Short-Channel Effects,” IEEE Journal of Solid-State Circuits, vol. 55, no. 7, pp. 1842–1853, 2020

    work page 2020

  27. [31]

    A Transformer-Based Technique to Improve Tuning Range and Phase Noise of a 20–28GHz LCVCO and a 51–62GHz Self-Mixing LCVCO,

    O. Esmaeeli, S. Lightbody, A. H. M. Shirazi, H. Djahanshahi, R. Zavari, S. Mirabbasi, and S. Shekhar, “A Transformer-Based Technique to Improve Tuning Range and Phase Noise of a 20–28GHz LCVCO and a 51–62GHz Self-Mixing LCVCO,”IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 69, no. 6, pp. 2351–2363, 2022

    work page 2022

  28. [32]

    A Single-Turn Inductor based Compact and Wide-Tuning LC-VCO using Dual-Resonant Modes,

    R. Sachdeva and A. Kumar, “A Single-Turn Inductor based Compact and Wide-Tuning LC-VCO using Dual-Resonant Modes,” in2023 21st IEEE Interregional NEWCAS Conference (NEWCAS), 2023, pp. 1–5

    work page 2023

  29. [33]

    A 12.1-16.5GHz Resistance Self-biased Inverse Class-F23 VCO Achieving 20-54kHz 1/f3 Corner Frequency,

    J. Jing, W. Li, R. Yuan, and H. Xu, “A 12.1-16.5GHz Resistance Self-biased Inverse Class-F23 VCO Achieving 20-54kHz 1/f3 Corner Frequency,” in2023 IEEE International Symposium on Circuits and Systems (ISCAS), 2023, pp. 1–5

    work page 2023