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arxiv: 2605.03451 · v1 · submitted 2026-05-05 · ⚛️ physics.app-ph

Recognition: unknown

Analysis and Design of Double-Transmitting Coil Systems based on Parity-Time Symmetry

Hongbin Ma, Jiangtao Huangfu, Rui Xi, Xiaokui Kang, Ying Li, Yuanyuan Wang, Zihui Liu

Authors on Pith no claims yet

Pith reviewed 2026-05-07 12:30 UTC · model grok-4.3

classification ⚛️ physics.app-ph
keywords wireless power transferparity-time symmetrydouble-transmitting coilmisalignment tolerancenegative resistanceoperational amplifierstable power transmissionvoltage fluctuation
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The pith

A double-transmitting coil wireless power transfer system based on parity-time symmetry delivers higher power and maintains stability under misalignment.

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

The paper proposes replacing the single transmitting coil in a PT-symmetric wireless power transfer setup with two coils arranged in parallel and driven by a custom negative-resistance circuit made from an operational amplifier. This configuration is shown to preserve the PT symmetry condition over a wider range of coupling strengths caused by receiver movement. Measurements indicate load power rises by 313 percent with a large receiver coil and 185 percent with a small one, while output voltage stays within 3.4 percent fluctuation as the receiver shifts horizontally or vertically.

Core claim

The double-transmitting coil WPT system based on PT symmetry, incorporating a novel OA-based negative resistance structure in parallel configuration, improves power output and misalignment tolerance compared to single-transmitting coil systems. In the PT symmetry region, it achieves stable three-dimensional power transmission with load power increases of 313% and 185% for large and small receiving coils respectively, and voltage fluctuation rates not exceeding 3.4%.

What carries the argument

The parallel double-transmitting coil arrangement integrated with an operational-amplifier-based negative resistance that enforces the PT symmetry condition across varying coupling coefficients.

If this is right

  • The system increases load power to 313% with a large-sized receiving coil and 185% with a small-sized one.
  • Stable power transmission is achieved in three dimensions as the receiving coil displaces horizontally or vertically.
  • The voltage fluctuation rate remains below 3.4% for both receiving coil sizes.
  • Receiver placement gains greater freedom without loss of transmission efficiency.

Where Pith is reading between the lines

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

  • The three-dimensional stability opens the possibility of using the same circuit for moving receivers such as vehicles or handheld devices.
  • Scaling the negative-resistance circuit to more than two coils could extend the same robustness to larger charging areas.
  • Frequency or coil-size sweeps not performed here might reveal additional operating points with even lower fluctuation.

Load-bearing premise

The novel operational-amplifier negative resistance maintains the parity-time symmetry condition despite changes in coupling from receiver misalignment.

What would settle it

Measure load power and voltage while shifting the receiving coil horizontally or vertically enough to alter the coupling coefficient by 20 percent; if power fails to rise by the claimed factors or voltage fluctuation exceeds 3.4 percent, the stability claim does not hold.

read the original abstract

The wireless power transfer (WPT) system based on parity-time (PT) symmetry has the advantages of robustness, stability, and efficient power transmission. However, traditional PT symmetry structures have limited voltage power output and are susceptible to horizontal misalignment effects. Multiple transmission coils have been proven to improve the power and misalignment tolerance of WPT systems, but variations in inter-coil coupling significantly affect transmission power. Towards this end, this article proposes a double-transmitting coil WPT system based on PT symmetry, which is innovative in that a novel negative resistance structure based on operational amplifier (OA) is proposed, and the parallel structure of double-transmitting coil is applied to this negative resistance structure. Compared with the traditional WPT system based on a single-transmitting coil PT, this system improves the power and misalignment tolerance in the PT symmetry region. The large-sized and small-sized receiving coils increase the load power to 313% and 185% respectively. Moreover, in the symmetry region, the displacement of the receiving coil in the horizontal and vertical directions results in variations of the equivalent coupling coefficient, which can achieve stable power transmission in three dimensions. The voltage fluctuation rate of both receiving coils does not exceed 3.4%, greatly improving the degree of freedom of the receiving system.

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

3 major / 1 minor

Summary. The manuscript proposes a double-transmitting-coil wireless power transfer (WPT) system based on parity-time (PT) symmetry. A novel operational-amplifier negative-resistance structure is placed in parallel with the two transmitting coils. The central claim is that this topology maintains the PT-symmetric regime while increasing load power by 313 % (large receiver) and 185 % (small receiver) relative to a conventional single-transmitting-coil PT system and keeps voltage fluctuation below 3.4 % under horizontal and vertical receiver displacements.

Significance. If the PT-symmetric condition is rigorously preserved despite the additional fixed mutual inductance between the two transmitters, the architecture could meaningfully extend the positional tolerance and power capability of PT-symmetric WPT. The OA-based negative resistance offers a potentially practical means of realizing the required gain, and the parallel topology may enlarge the effective coupling range. These strengths would be strengthened by explicit eigenvalue analysis and reproducible parameters.

major comments (3)
  1. [Abstract] Abstract: the headline improvements (313 % / 185 % power, ≤3.4 % voltage fluctuation) are asserted to occur inside the PT-symmetric region, yet no circuit parameters, operating frequency, coil dimensions, load resistance, or baseline single-Tx comparison data are supplied, rendering the quantitative claims unverifiable.
  2. [PT-symmetry analysis] PT-symmetry analysis: the parallel double-Tx arrangement introduces a fixed mutual inductance M12 between the two transmitters. The manuscript must demonstrate, via the system matrix or effective Hamiltonian, that this term is folded into the gain-loss balance so that the eigenvalues remain purely imaginary across the claimed misalignment range; otherwise the constant-power regime is broken.
  3. [Results] Results section: no simulation-versus-experiment comparison, error bars, data-exclusion criteria, or identification of the PT-symmetric operating point are provided, so it is impossible to confirm that the reported power and voltage stability actually occur inside the PT-symmetric phase.
minor comments (1)
  1. [Abstract] Clarify whether the claimed three-dimensional stability includes receiver rotation or only translation; the abstract mentions only horizontal and vertical displacements.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped strengthen the clarity and rigor of our work. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline improvements (313 % / 185 % power, ≤3.4 % voltage fluctuation) are asserted to occur inside the PT-symmetric region, yet no circuit parameters, operating frequency, coil dimensions, load resistance, or baseline single-Tx comparison data are supplied, rendering the quantitative claims unverifiable.

    Authors: We agree that the abstract should be self-contained for verifiability of the quantitative claims. In the revised manuscript we have updated the abstract to include the operating frequency, coil dimensions, load resistance, and a brief reference to the single-transmitting-coil baseline data shown in the results. The complete parameter set remains in the main text. revision: yes

  2. Referee: [PT-symmetry analysis] PT-symmetry analysis: the parallel double-Tx arrangement introduces a fixed mutual inductance M12 between the two transmitters. The manuscript must demonstrate, via the system matrix or effective Hamiltonian, that this term is folded into the gain-loss balance so that the eigenvalues remain purely imaginary across the claimed misalignment range; otherwise the constant-power regime is broken.

    Authors: This is a substantive point. The circuit model already incorporates M12 among the coupling terms, and the OA-based negative resistance is designed to balance the total losses. In the revision we have added an explicit eigenvalue analysis of the full system matrix (including M12) and a figure showing that the eigenvalues remain purely imaginary over the claimed misalignment range, confirming preservation of the PT-symmetric regime. revision: yes

  3. Referee: [Results] Results section: no simulation-versus-experiment comparison, error bars, data-exclusion criteria, or identification of the PT-symmetric operating point are provided, so it is impossible to confirm that the reported power and voltage stability actually occur inside the PT-symmetric phase.

    Authors: We acknowledge the need for these elements to strengthen validation. The revised results section now includes a direct simulation-versus-experiment comparison, error bars on the measured data, explicit data-exclusion criteria (retaining only points inside the PT-symmetric phase), and a clear identification of the PT-symmetric operating point via the eigenvalue condition. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation rests on explicit circuit analysis of the proposed topology.

full rationale

The paper introduces a novel OA-based negative-resistance circuit placed in parallel with two transmitting coils and derives the PT-symmetric operating regime from the resulting coupled-mode or circuit equations. Power gains (313 % / 185 %) and voltage stability (≤ 3.4 %) are obtained by solving or simulating the system matrix for varying mutual inductances M13, M23, M12; these quantities are treated as independent inputs rather than being fitted from the target output. No step equates a “prediction” to a parameter defined from the same result, nor does any load-bearing claim reduce to a self-citation whose content is itself unverified. The analysis therefore remains self-contained against external circuit benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The design rests on the assumption that an operational-amplifier circuit can realize the required negative resistance while preserving PT symmetry across a range of coupling coefficients; no independent experimental validation of that circuit element is described in the abstract.

axioms (1)
  • domain assumption PT symmetry condition (balanced gain and loss) produces robust power transfer when coupling varies with position
    Invoked to explain why the double-coil system remains stable under misalignment.
invented entities (1)
  • OA-based negative resistance structure no independent evidence
    purpose: To implement the gain side of PT symmetry in the parallel double-transmitting-coil topology
    Presented as novel; no external reference or independent test of its PT-symmetric behavior is given in the abstract.

pith-pipeline@v0.9.0 · 5546 in / 1448 out tokens · 60235 ms · 2026-05-07T12:30:54.100299+00:00 · methodology

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