pith. sign in

arxiv: 2604.18387 · v1 · submitted 2026-04-20 · 🪐 quant-ph

Engineered broadband Purcell protection using a shared Pi-filter for multiplexed superconducting qubits

Samuel D. Escribano , Yael Kriheli , Samuel Goldstein , Daniel Dahan , Nadav Katz This is my paper

Pith reviewed 2026-05-10 04:17 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Purcell protectionsuperconducting qubitsmultiplexed qubitsΠ-filterbroadband filtermicrowave interferencequbit coherencequantum circuits
0
0 comments X

The pith

A single shared Π-filter integrated in the feedline protects multiple superconducting qubits from Purcell decay across a wide band.

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

The paper establishes that a compact Π-shaped filter made from two open-ended stubs and an in-line transmission line can be shared among qubits to suppress the real part of the environmental admittance via passive microwave interference. This approach protects several qubits simultaneously without dedicated hardware per qubit and preserves the readout and reset modes needed for multiplexed operation. If the simulated suppression holds, the design would deliver relaxation times longer than 1 ms over roughly 1.5 GHz for typical device parameters, with further widening possible through simple adjustments. A sympathetic reader would care because it offers a low-overhead way to improve coherence in scaled-up superconducting processors that rely on frequency multiplexing.

Core claim

The authors demonstrate through circuit simulations and finite-element modeling that the shared Π-filter suppresses transmission within the qubit frequency band while leaving readout and reset modes intact, yielding Purcell-limited relaxation times exceeding 1 ms over an approximately 1.5 GHz span for realistic parameters, with straightforward modifications able to extend that span further.

What carries the argument

The Π-filter geometry consisting of two open-ended stubs connected by an in-line transmission line, which creates passive microwave interference to suppress the real part of the environmental admittance over a broad frequency window.

If this is right

  • Multiple qubits can share one compact filter for broadband protection, reducing hardware overhead in multiplexed architectures.
  • Purcell-limited relaxation times exceed 1 ms over an approximately 1.5 GHz frequency span for realistic device parameters.
  • The filter preserves the readout and reset modes required by standard dispersive protocols.
  • Straightforward modifications of the design can extend the protected frequency span beyond 1.5 GHz.

Where Pith is reading between the lines

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

  • This shared-filter approach could simplify wiring and reduce footprint in larger qubit arrays by minimizing per-qubit components.
  • If fabrication tolerances prove compatible, the same interference principle might be adapted to protect other microwave elements such as resonators or couplers.
  • Experimental tests could compare measured admittance suppression directly against the finite-element models to quantify any fabrication-induced deviations.

Load-bearing premise

The passive interference engineered by the Π-filter will suppress the real part of the environmental admittance in actual fabricated devices to the same degree shown in simulations without introducing unmodeled losses or crosstalk that degrade readout fidelity.

What would settle it

Fabricate the device with the shared Π-filter, measure qubit relaxation times at multiple frequencies across the target 1.5 GHz band, and check whether the observed times reach or exceed the simulated 1 ms values while readout fidelity remains high.

Figures

Figures reproduced from arXiv: 2604.18387 by Daniel Dahan, Nadav Katz, Samuel D. Escribano, Samuel Goldstein, Yael Kriheli.

Figure 1
Figure 1. Figure 1: Isolated Purcell Π-filter. (a) Schematic of the Purcell Π-filter, consisting of two open-ended stubs of lengths ℓ+ and ℓ− connected by an in-line transmission line of length ℓ (all in gray). An output capacitor Cout connects the potential input circuit with the filter. (b) Magnitude of the effective, series impedance |Zeff | as a function of frequency. Results obtained from SPICE simulations (dark blue), f… view at source ↗
Figure 2
Figure 2. Figure 2: Quantum interference. Sketch of the minimal model used to describe the quantum interference mechanism underlying the Purcell filter. A qubit with transition fre￾quency ωq is coupled to a feedline with an effective strength g, along which two stubs of different lengths, ℓ1 and ℓ2, are connected at positions x = d1 and x = d2. Under certain geometrical conditions, the signals reflected from the stubs (green … view at source ↗
Figure 3
Figure 3. Figure 3: Purcell Π-filter protection. (a) Circuit archi￾tecture: a qubit with a dedicated readout resonator is capac￾itively coupled to a transmission line (feedline). Input and output capacitors regulate the coupling to the external en￾vironment. A Π-filter (in gray) is placed after the output capacitor and consists of two open-ended stubs separated by an in-line transmission line. (b) Simulated transmission coef￾… view at source ↗
Figure 4
Figure 4. Figure 4: Alternative Π-filter architectures. (a) Top: schematic of a double Π-filter configuration, in which iden￾tical Π-filters are placed at both ends of the feedline; bot￾tom: resulting Purcell lifetime TP, with (solid line) and with￾out (dashed) the two filters. Parameters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Purcell protection in multiplexed readout architectures. (a) Multiplexed readout architecture with four qubits qi, each coupled to its own readout resonator. (b) Purcell relaxation time TP as a function of frequency for each qubit (different colors). The dashed vertical lines in the qubit frequency band (shaded in green) indicate the idle frequencies of the qubits. The black dashed line marks the 1 ms refe… view at source ↗
Figure 6
Figure 6. Figure 6: Design robustness. Purcell decay as a function of frequency (horizontal axis) and selected circuit parameters (vertical axis): (a) the separation between the stubs of the Π filter, ℓ; (b) the difference in stub lengths, ℓ− − ℓ+; (c) the feedline length, ℓf; and (d) the output coupling capacitance, Cout. The dashed contour indicates the 1 ms Purcell lifetime threshold. Within this interval, the interference… view at source ↗
read the original abstract

We propose a broadband Purcell-protection scheme based on a single shared filter integrated directly into the feedline, enabling simultaneous protection of multiple qubits in a compact architecture with minimal hardware overhead. The filter consists of two open-ended stubs connected by an in-line transmission line, forming a $\Pi$ geometry, and operates via engineered passive microwave interference that suppresses the real part of the environmental admittance over a wide frequency window. Circuit simulations and finite-element modeling show strong suppression of transmission within the target band (the qubit's frequencies) while preserving the readout and reset modes of the multiplexed architecture. For realistic device parameters, the proposed design yields Purcell-limited relaxation times exceeding $1$ ms over a frequency span of approximately $1.5$ GHz, which can be further extended with straightforward modifications of the design. Our results establish the $\Pi$-filter as a compact and scalable solution for broadband impedance engineering in superconducting quantum circuits, compatible with standard dispersive readout protocols.

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

2 major / 3 minor

Summary. The manuscript proposes a shared Π-filter (two open-ended stubs connected by an in-line transmission line) integrated directly into the feedline for broadband Purcell protection of multiplexed superconducting qubits. It relies on passive microwave interference to suppress Re[Y_env] over a wide band, with circuit simulations and finite-element modeling demonstrating transmission suppression in the qubit frequencies while preserving readout/reset modes. For realistic parameters, this yields Purcell-limited T1 > 1 ms over ~1.5 GHz, presented as a compact, scalable solution compatible with dispersive readout.

Significance. If the simulated suppression of environmental admittance holds in fabricated devices, the design offers a low-overhead, passive method to extend qubit lifetimes in multiplexed architectures without additional components per qubit. This is a practical engineering advance for scaling superconducting processors, grounded in standard microwave theory and extensible via parameter tuning.

major comments (2)
  1. [Simulations section] Simulations section: The T1 > 1 ms claim is derived from Re[Y_env] suppression in circuit simulations; the manuscript must explicitly state the formula used to convert admittance to relaxation rate (e.g., the standard Purcell formula Γ_p = Re[Y_env(ω_q)] / (2 C_q)) and confirm it is applied without additional fitted parameters.
  2. [Finite-element modeling results] Finite-element modeling results: While transmission suppression and mode preservation are shown, the modeling does not quantify sensitivity to fabrication variations in stub lengths or in-line segment (the free parameters); this is load-bearing for the 1.5 GHz bandwidth claim under realistic conditions.
minor comments (3)
  1. [Abstract] Abstract: Specify the exact frequency window (center and edges) and the numerical values of the realistic device parameters (e.g., stub lengths, characteristic impedances) that produce T1 > 1 ms.
  2. [Figure 2 (transmission plots)] Figure 2 (transmission plots): Mark the qubit frequency band, readout frequencies, and protected window explicitly on the plots for direct visual assessment of suppression and mode preservation.
  3. [Introduction] Introduction: Add citations to prior shared-filter or broadband Purcell-protection schemes in superconducting circuits to better highlight the novelty of the single shared Π geometry.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and recommendation for minor revision. We address each major comment point by point below, committing to clarifications that strengthen the manuscript without altering its core claims.

read point-by-point responses

  1. Referee: [Simulations section] Simulations section: The T1 > 1 ms claim is derived from Re[Y_env] suppression in circuit simulations; the manuscript must explicitly state the formula used to convert admittance to relaxation rate (e.g., the standard Purcell formula Γ_p = Re[Y_env(ω_q)] / (2 C_q)) and confirm it is applied without additional fitted parameters.

    Authors: We agree that an explicit statement of the conversion improves clarity and reproducibility. The T1 values are obtained directly from the standard Purcell formula Γ_p = Re[Y_env(ω_q)] / (2 C_q), where C_q is the qubit capacitance extracted from the circuit parameters; no additional fitted parameters are used. In the revised manuscript we will insert this formula and confirmation in the Simulations section. revision: yes

  2. Referee: [Finite-element modeling results] Finite-element modeling results: While transmission suppression and mode preservation are shown, the modeling does not quantify sensitivity to fabrication variations in stub lengths or in-line segment (the free parameters); this is load-bearing for the 1.5 GHz bandwidth claim under realistic conditions.

    Authors: We acknowledge that quantifying sensitivity to fabrication variations would better support the bandwidth claim under realistic conditions. The presented results use nominal parameters. In the revision we will add a brief sensitivity study using our circuit model, varying stub lengths and the in-line segment by typical fabrication tolerances (±2 %), and report the resulting bandwidth variation. This will be placed in the Finite-element modeling results section. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central claims rest on circuit simulations and finite-element modeling of a Π-filter design grounded in standard microwave circuit theory and passive interference. The reported Purcell-limited T1 > 1 ms over ~1.5 GHz for realistic parameters are direct outputs of those external computational validations rather than any equation or parameter that is defined in terms of the target performance. No self-definitional steps, fitted inputs renamed as predictions, load-bearing self-citations, or ansatz smuggling appear in the abstract or described derivation chain; the architecture is presented as an engineering proposal whose validity is to be tested by fabrication, not by internal reduction to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The proposal rests on standard microwave transmission-line theory and the assumption that finite-element models accurately capture the admittance seen by the qubits. No new physical entities are introduced; the filter is assembled from conventional open stubs and transmission lines whose lengths are chosen to place the interference nulls at the qubit frequencies.

free parameters (1)
  • stub lengths and in-line segment length
    Chosen to engineer the interference nulls over the target 1.5 GHz window; specific values are not given in the abstract but are implicit design parameters.
axioms (1)
  • standard math Standard lossless transmission-line model and frequency-independent material parameters hold for the frequency range of interest.
    Invoked implicitly when the authors state that circuit simulations and finite-element modeling predict the admittance suppression.

pith-pipeline@v0.9.0 · 5474 in / 1444 out tokens · 38853 ms · 2026-05-10T04:17:43.968781+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

37 extracted references · 1 canonical work pages · 1 internal anchor

  1. [1]

    M. D. Reed, B. R. Johnson, A. A. Houck, L. DiCarlo, J. M. Chow, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, Fast reset and suppressing spontaneous emis- sion of a superconducting qubit, Applied Physics Letters 96, 203110 (2010)

    2010

  2. [2]

    E. A. Sete, J. M. Gambetta, and A. N. Korotkov, Purcell effect with microwave drive: Suppression of qubit relax- ation rate, Phys. Rev. B89, 104516 (2014)

    2014

  3. [3]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, A quantum enginee’s guide to superconducting qubits, Applied Physics Reviews6, 021318 (2019)

    2019

  4. [4]

    A. A. Houck, J. A. Schreier, B. R. Johnson, J. M. Chow, J. Koch, J. M. Gambetta, D. I. Schuster, L. Frunzio, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Con- trolling the spontaneous emission of a superconducting transmon qubit, Phys. Rev. Lett.101, 080502 (2008)

    2008

  5. [5]

    E. A. Sete, J. M. Martinis, and A. N. Korotkov, Quan- tum theory of a bandpass purcell filter for qubit readout, Phys. Rev. A92, 012325 (2015)

    2015

  6. [6]

    Jeffrey, D

    E. Jeffrey, D. Sank, J. Y. Mutus, T. C. White, J. Kelly, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. Megrant, P. J. J. O’Malley, C. Neill, P. Roushan, A. Vainsencher, J. Wenner, A. N. Cleland, and J. M. Martinis, Fast accurate state measurement with super- conducting qubits, Phys. Rev. Lett.112, 190504 (2014)

    2014

  7. [7]

    N. T. Bronn, E. Magesan, N. A. Masluk, J. M. Chow, J. M. Gambetta, and M. Steffen, Reducing spontaneous emission in circuit quantum electrodynamics by a com- bined readout/filter technique, IEEE Transactions on Applied Superconductivity25, 1 (2015)

    2015

  8. [8]

    F. m. c. Swiadek, R. Shillito, P. Magnard, A. Remm, C. Hellings, N. Lacroix, Q. Ficheux, D. C. Zanuz, G. J. Norris, A. Blais, S. Krinner, and A. Wallraff, Enhanc- ing dispersive readout of superconducting qubits through dynamic control of the dispersive shift: Experiment and theory, PRX Quantum5, 040326 (2024)

    2024

  9. [9]

    A. Yen, Y. Ye, K. Peng, J. Wang, G. Cunningham, M. Gingras, B. M. Niedzielski, H. Stickler, K. Serniak, M. E. Schwartz, and K. P. O’Brien, Interferometric pur- cell suppression of spontaneous emission in a supercon- ducting qubit, Phys. Rev. Appl.23, 024068 (2025)

    2025

  10. [10]

    Heinsoo, C

    J. Heinsoo, C. K. Andersen, A. Remm, S. Krinner, T. Walter, Y. Salath´ e, S. Gasparinetti, J.-C. Besse, A. Potoˇ cnik, A. Wallraff, and C. Eichler, Rapid high- fidelity multiplexed readout of superconducting qubits, Phys. Rev. Appl.10, 034040 (2018)

    2018

  11. [11]

    H. Yan, X. Wu, A. Lingenfelter, Y. J. Joshi, G. Anders- son, C. R. Conner, M.-H. Chou, J. Grebel, J. M. Miller, R. G. Povey, H. Qiao, A. A. Clerk, and A. N. Cleland, Broadband bandpass purcell filter for circuit quantum electrodynamics, Applied Physics Letters123, 134001 (2023)

    2023

  12. [12]

    Y. Zhou, X. Cai, Y. Zheng, B. Zhou, Y. Wang, K. Xiong, and J. Feng, High-suppression-ratio and wide bandwidth four-stage purcell filter for multiplexed superconducting qubit readout, Journal of Applied Physics135, 024402 (2024)

    2024

  13. [13]

    X.-Y. Gu, D. Feng, Z.-Y. Peng, G.-H. Liang, Y. He, Y. Xiao, M.-C. Wang, Y. Yan, B.-J. Chen, Z.-Y. Mei, Y.-Z. Bu, J.-C. Zhang, J.-C. Song, C.-L. Deng, X. Song, D. Zheng, K. Xu, Z. Xiang, and H. Fan, Engineering a multi-mode purcell filter for superconducting-qubit re- set and readout with intrinsic purcell protection (2025), arXiv:2507.04676 [quant-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  14. [14]

    Mirhosseini, E

    M. Mirhosseini, E. Kim, V. S. Ferreira, M. Kalaee, A. Sipahigil, A. J. Keller, and O. Painter, Superconduct- ing metamaterials for waveguide quantum electrodynam- ics, Nature Communications9, 3706 (2018)

    2018

  15. [15]

    J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, Charge-insensitive qubit design de- rived from the cooper pair box, Phys. Rev. A76, 042319 (2007)

    2007

  16. [16]

    T. P. Orlando, J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo, Superconducting persistent-current qubit, Phys. Rev. B60, 15398 (1999)

    1999

  17. [17]

    V. E. Manucharyan, J. Koch, L. I. Glazman, and M. H. Devoret, Fluxonium: Single cooper-pair circuit free of charge offsets, Science326, 113 (2009)

    2009

  18. [18]

    L. B. Nguyen, Y.-H. Lin, A. Somoroff, R. Mencia, N. Grabon, and V. E. Manucharyan, High-coherence flux- onium qubit, Phys. Rev. X9, 041041 (2019)

    2019

  19. [19]

    L. Ding, M. Hays, Y. Sung, B. Kannan, J. An, A. Di Paolo, A. H. Karamlou, T. M. Hazard, K. Azar, D. K. Kim, B. M. Niedzielski, A. Melville, M. E. Schwartz, J. L. Yoder, T. P. Orlando, S. Gustavsson, J. A. Grover, K. Serniak, and W. D. Oliver, High- fidelity, frequency-flexible two-qubit fluxonium gates with a transmon coupler, Phys. Rev. X13, 031035 (2023)

    2023

  20. [20]

    D. A. Rower, L. Ding, H. Zhang, M. Hays, J. An, P. M. Harrington, I. T. Rosen, J. M. Gertler, T. M. Haz- ard, B. M. Niedzielski, M. E. Schwartz, S. Gustavsson, K. Serniak, J. A. Grover, and W. D. Oliver, Suppressing counter-rotating errors for fast single-qubit gates with fluxonium, PRX Quantum5, 040342 (2024)

    2024

  21. [21]

    J. D. Teoh, P. Winkel, H. K. Babla, B. J. Chapman, J. Claes, S. J. de Graaf, J. W. O. Garmon, W. D. Kalfus, Y. Lu, A. Maiti, K. Sahay, N. Thakur, T. Tsun- oda, S. H. Xue, L. Frunzio, S. M. Girvin, S. Puri, and R. J. Schoelkopf, Dual-rail encoding with superconduct- ing cavities, Proceedings of the National Academy of Sci- ences120, e2221736120 (2023). 8

    2023

  22. [22]

    Levine, A

    H. Levine, A. Haim, J. S. C. Hung, N. Alidoust, M. Kalaee, L. DeLorenzo, E. A. Wollack, P. Arrangoiz- Arriola, A. Khalajhedayati, R. Sanil, H. Moradinejad, Y. Vaknin, A. Kubica, D. Hover, S. Aghaeimeibodi, J. A. Alcid, C. Baek, J. Barnett, K. Bawdekar, P. Bienias, H. A. Carson, C. Chen, L. Chen, H. Chinkezian, E. M. Chisholm, A. Clifford, R. Cosmic, N. Cr...

    2024

  23. [23]

    Mirrahimi, Z

    M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: a new paradigm for universal quan- tum computation, New Journal of Physics16, 045014 (2014)

    2014

  24. [24]

    A. Z. Ding, B. L. Brock, A. Eickbusch, A. Koottan- davida, N. E. Frattini, R. G. Corti˜ nas, V. R. Joshi, S. J. de Graaf, B. J. Chapman, S. Ganjam, L. Frunzio, R. J. Schoelkopf, and M. H. Devoret, Quantum control of an oscillator with a kerr-cat qubit, Nature Communications 16, 5279 (2025)

    2025

  25. [25]

    Yamamoto, K

    T. Yamamoto, K. Inomata, M. Watanabe, K. Matsuba, T. Miyazaki, W. D. Oliver, Y. Nakamura, and J. S. Tsai, Flux-driven josephson parametric amplifier, Ap- plied Physics Letters93, 042510 (2008)

    2008

  26. [26]

    A. A. Clerk, M. H. Devoret, S. M. Girvin, F. Marquardt, and R. J. Schoelkopf, Introduction to quantum noise, measurement, and amplification, Rev. Mod. Phys.82, 1155 (2010)

    2010

  27. [27]

    Kurizki, P

    G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Pet- rosyan, P. Rabl, and J. Schmiedmayer, Quantum tech- nologies with hybrid systems, Proceedings of the National Academy of Sciences112, 3866 (2015)

    2015

  28. [28]

    Shen and S

    J.-T. Shen and S. Fan, Coherent single photon trans- port in a one-dimensional waveguide coupled with super- conducting quantum bits, Phys. Rev. Lett.95, 213001 (2005)

    2005

  29. [29]

    Shen and S

    J.-T. Shen and S. Fan, Theory of single-photon trans- port in a single-mode waveguide. i. coupling to a cavity containing a two-level atom, Phys. Rev. A79, 023837 (2009)

    2009

  30. [30]

    Blais, A

    A. Blais, A. L. Grimsmo, S. M. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Rev. Mod. Phys.93, 025005 (2021)

    2021

  31. [31]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Applied physics reviews6 (2019)

    2019

  32. [32]

    E. M. Levenson-Falk and S. A. Shanto, A review of design concerns in superconducting quantum circuits, Materials for Quantum Technology5, 022003 (2025)

    2025

  33. [33]

    Kosen, H.-X

    S. Kosen, H.-X. Li, M. Rommel, D. Shiri, C. Warren, L. Gr¨ onberg, J. Salonen, T. Abad, J. Bizn´ arov´ a, M. Ca- puto,et al., Building blocks of a flip-chip integrated su- perconducting quantum processor, Quantum Science & Technology7, 035018 (2022)

    2022

  34. [34]

    Savola,Design and modelling of long-coherence qubits using energy participation ratios, Master’s thesis, Aalto University (2023)

    N. Savola,Design and modelling of long-coherence qubits using energy participation ratios, Master’s thesis, Aalto University (2023)

    2023

  35. [35]

    Moretti, D

    R. Moretti, D. Labranca, P. Campana, R. Carobene, M. Gobbo, M. A. Castellanos-Beltran, D. Olaya, P. F. Hopkins, L. Banchi, M. Borghesi,et al., Transmon qubit modeling and characterization for dark matter search, IEEE Transactions on Quantum Engineering (2025). 9 Appendix A: Numerical methods and parameters

    2025

  36. [36]

    These were performed using a SPICE-based solver (PySpice/Ngspice) and post-processing was carried out in Python

    Circuit simulations The circuit-level response of the Purcell Π-filter and the full circuit-QED architectures presented in this work were obtained using frequency-domain simula- tions based on lumped and distributed circuit mod- els. These were performed using a SPICE-based solver (PySpice/Ngspice) and post-processing was carried out in Python. The transm...

  37. [37]

    HFSS In addition to lumped element simulations, as de- scribed above, we also prepare a finite element model (FEM) to validate the SPICE results. Implemented as a CAD and exported as a GDS file, this model is prepared as a fabrication ready layout, compatible with processing in an industrial cleanroom facility and is in fact a simpli- fied version of an a...