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

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

Problem Statement
Wireless Power Transfer (WPT) systems based on magnetic resonance often suffer from a lack of robustness when mutual inductance changes due to spatial misalignment, leading to fluctuations in transmission power and efficiency. While Parity-Time (PT) symmetry offers a solution by enabling automatic frequency selection and robust power transmission without active feedback, traditional PT-WPT systems face specific limitations. Existing designs are typically restricted to one-to-one configurations with single transmitting coils, resulting in limited voltage power output and weak tolerance to horizontal misalignment. Furthermore, methods to increase power often rely on adding more amplifiers or complex inverter-based gain circuits, which increase cost, complexity, and are unsuitable for miniaturized applications like implantable medical devices.

Methodology
The authors propose a novel WPT system utilizing a double-transmitting coil and single-receiving coil configuration based on PT symmetry. The methodology involves three core components:

1. Novel Negative Resistance Structure: Instead of traditional linear operational amplifier (OA) circuits or complex inverter-based gain elements, the authors propose a negative resistance structure using an OA (LM6171) operating in a nonlinear, forward saturation region. By configuring the feedback resistors such that the amplification factor is high (A=10), the OA oscillates and outputs energy, providing the necessary gain for PT symmetry while maintaining circuit simplicity and stability.
2. System Topologies: Two specific configurations are analyzed and modeled:
   • System A: A "two-to-one" system where a single receiving coil (same size as transmitting coils) couples with two parallel transmitting coils. The receiving coil couples fully with only one transmitting coil at a time.
   • System B: A "two-to-one" system where a larger receiving coil (twice the diameter of the transmitting coils) is positioned to couple simultaneously with both transmitting coils.
3. Theoretical Modeling: The authors derive equivalent circuit models for both systems using Kirchhoff's laws. They establish conditions for PT symmetry, calculate critical coupling coefficients, and analyze operating frequencies. The models demonstrate that the double-transmitting structure increases the magnetic field coupling range and allows for stable power transmission across three-dimensional displacements.

Key Contributions

• Circuit Innovation: The introduction of a nonlinear OA-based negative resistance circuit that supports a double-transmitting coil parallel structure, avoiding the complexity of external control loops required by inverter-based systems.
• Dual-Coil Architecture: The application of a double-transmitting coil topology to PT symmetry systems, which expands the magnetic coupling range and improves misalignment tolerance compared to single-transmitting designs.
• Scalable Design: The demonstration that the receiving coil size can be tailored to the application (System A for compactness, System B for extended range), with the system maintaining PT symmetry conditions regardless of the specific coil dimensions.
• Comprehensive Analysis: Theoretical derivation and experimental verification of transmission characteristics, including critical coupling coefficients, voltage ratios, and efficiency under varying load resistances and spatial displacements.

Experimental Results
The authors built an experimental prototype using Litz wire coils (140 mm diameter for transmitters and System A receiver; 290 mm for System B receiver) and an LM6171 OA. Key findings include:

• Power and Voltage Enhancement:
  • System A (Small Receiver): Increased load voltage to 136% and output power to 185% compared to a traditional one-to-one system.
  • System B (Large Receiver): Increased load voltage to 177% and output power to 313% compared to the one-to-one system.
  • System B achieved a receiving voltage approximately 1.95 times the transmitting voltage, while System A achieved 1.37 times.
• Misalignment Tolerance:
  • System A: Maintained stable voltage output with a vertical (Z) range of 12 cm, horizontal (Y) offset of 15 cm, and (X) offset of 7 cm.
  • System B: Maintained stable voltage output with a vertical (Z) range of 14 cm, horizontal (Y) offset of 17 cm, and (X) offset of 13 cm.
• Stability and Efficiency:
  • In the PT symmetry region, the voltage fluctuation rate for both receiving systems did not exceed 3.4%.
  • Actual transmission efficiency remained above 94.4% for System A and 95.1% for System B.
  • The system operated stably across a wide load resistance range (from tens of ohms to tens of kilohms), with a maximum output power of 510 mW.

Significance and Claims
The paper claims that the proposed double-transmitting coil system significantly improves the robustness of PT-WPT systems against spatial misalignment in three dimensions without increasing the number of amplifiers or relying on complex external control circuits. By utilizing a nonlinear OA structure, the system achieves high power output and stability suitable for small-scale applications (e.g., implantable devices) where space is constrained. The authors emphasize that the system effectively decouples the receiving coil size from the stability of the PT symmetry condition, allowing for flexible design choices to maximize power transfer or misalignment tolerance based on specific application needs. The work demonstrates that increasing the number of transmitting coils, rather than amplifiers, is an effective strategy for enhancing the performance of PT-symmetric WPT systems.