Bionic Fractal Topology for Wireless Power Transfer: A Technical Scheme of Stereo-to-Stereo Coupling and Dimensionality-Reduced Distribution

Abstract

Aiming at the problems of difficult coil alignment, narrow spatial coverage, and low efficiency of mobile reception in conventional wireless power transfer, this paper proposes a wireless power transmission scheme based on bionic fractal topology. Both the transmitter and receiver adopt a root-like three-dimensional mesh structure, which realizes wide-area radiation and efficient capture of spatial electromagnetic energy through three-dimensional fractal topology, forming an optimal stereo-to-stereo coupling. After capturing energy, the receiver completes dimensionality conversion and impedance matching from 3D to 2D via a gradual transition layer, and finally distributes electric energy to the load through a planar vein-like topology. This scheme maintains the advantages of high fault tolerance and blind-spot-free coverage of stereo coupling, while achieving seamless integration with planar electronic devices, providing a new path for global wireless power supply.

1. Introduction

Wireless power transfer has long been restricted by the face-to-face coupling mode of planar coils. Positional shifts and angular deflections lead to a sharp drop in coupling coefficient, making it difficult to meet the requirements of mobile devices, unmanned aerial vehicles, IoT sensors and other scenarios. In nature, tree roots efficiently absorb water and nutrients in the three-dimensional soil space in a fractal mesh structure. Its topological characteristics of three-dimensional divergence and multi-level convergence precisely correspond to the physical requirements of spatial radiation and wide-area capture in wireless power transfer.

This paper draws on the three-dimensional mesh topology of tree roots to construct a wireless power transfer system with symmetrical transmitter and receiver, and solves the engineering connection problem from stereo to planar through a transition layer.

2. System Architecture: Stereo-to-Stereo Coupling

2.1 Transmitter: Root-like Three-dimensional Mesh Structure

The transmitter adopts a three-dimensional fractal network imitating the morphology of tree roots:

- Main root: feeding input port, carrying total energy;
- Lateral roots and fibrous roots: multi-level branching, extending in all directions of space;
- Overall morphology: space-filling three-dimensional topology.

Physical function: According to the reciprocity theorem, the root mesh structure, in the transmitting state, can convert the input high-frequency electric energy into an electromagnetic field radiating diffusely to the whole space. Compared with the unidirectional radiation of traditional planar coils, the three-dimensional mesh transmitter achieves wide-angle, multi-polarization and blind-spot-free magnetic field coverage.

2.2 Receiver: Identical Root-like Three-dimensional Mesh Structure

The receiver adopts a fully symmetrical root-like three-dimensional mesh topology with the transmitter:

- Fibrous roots capture electromagnetic energy from all directions of space;
- Lateral roots converge step by step;
- Main root outputs the converged electric energy.

The symmetrical design brings two major advantages:

1. Optimal coupling: the magnetic field spatial distributions of the transmitter and receiver are highly matched. No matter the receiver translates or rotates, there are always multiple root-overlapping areas between them to maintain stable coupling;
2. Strong fault tolerance: local failure of fibrous roots does not affect the overall energy transmission.

2.3 Physical Essence of Stereo-to-Stereo Coupling

Conventional coil coupling can be regarded as point-to-point or face-to-point, while root-to-root coupling is the overlap between diffuse fields in space. Energy transmission no longer relies on a single alignment direction, but is completed through spatial interleaving of countless branches. This fundamentally solves the alignment problem of traditional wireless power transfer.

3. Core Challenges: From Stereo Reception to Planar Distribution

The receiver root structure outputs electric energy converged by a three-dimensional network, but most electrical equipment uses planar circuits (PCB, flexible printed circuit). Directly connecting the 3D main root output to a planar circuit faces three major obstacles:

- Topological dimensionality mismatch: The convergence point (end of main root) of the 3D network is three-dimensional, while the input of a planar circuit is a 2D pad or microstrip line, resulting in stress and unreliable contact in direct connection.
- Impedance mismatch: The stereo transmitting/receiving system operates in the near-field coupling region, with an equivalent output impedance usually ranging from several ohms to tens of ohms, while the standard impedance of planar circuits is 50Ω or 75Ω. Mismatch will cause reflection loss.
- Electromagnetic mode mismatch: Electromagnetic energy exists in the form of spatial magnetic field in the stereo structure, while planar circuits transmit in quasi-TEM mode, leading to low efficiency in direct conversion.

4. Solution: Gradual Transition Layer

The transition layer is located between the main root of the receiver and the planar vein distribution network, performing three major conversion functions.

4.1 Topological Dimensionality Reduction

Structural design: The transition layer adopts a three-dimensional structure of tapered gradual change and branch fusion:

- Upper end face: matches the cross-section of the main root, maintaining a three-dimensional shape;
- Middle part: gradually flattened, the 3D contour slowly compresses into a 2D planar contour;
- Lower end face: physically connects with the main vein of the planar leaf vein.

Principle: Progressive dimensional compression avoids stress concentration and electromagnetic discontinuity caused by abrupt changes, achieving a smooth transition from 3D to 2D.

4.2 Impedance Matching

Electrical design: A gradual microstrip line or stepped impedance transformer is embedded in the transition layer:

- Input impedance: set to the equivalent output impedance of the receiver root (obtained by measurement or simulation, assumed as Z₁);
- Output impedance: set to 50Ω (standard planar circuit impedance);
- Gradient length: ≥ 1/4 of the operating wavelength to ensure broadband matching.

LC resonant networks can be paralleled for narrowband compensation when necessary.

4.3 Electromagnetic Mode Conversion

Field-circuit collaboration: The internal structure of the transition layer completes the conversion from magnetic field mode to quasi-TEM mode simultaneously:

- Upper end: magnetic field energy exists in the form of eddy current in the stereo branches;
- The gradual conductors and dielectric layers in the transition layer gradually straighten the magnetic lines of force to be parallel to the transmission direction;
- Lower end: energy enters the planar veins in the form of voltage/current waves.

5. Energy Distribution: Planar Leaf Vein Topology

After output from the transition layer, electric energy enters the planar leaf vein distribution network:

- Main vein: connected to the transition layer output, carrying the total current;
- Secondary fine veins: spreading around, distributing energy evenly to multiple load points or energy storage units.

The advantage of vein topology lies in low loss and coplanar integration, which can be fully embedded in equipment circuit boards without additional thickness.

6. Engineering Feasibility and Core Advantages

6.1 Feasibility

- Root-like 3D mesh structure (transmitter/receiver): 3D printed conductive materials, 3D winding technology, flexible PCB three-dimensional assembly;
- Gradual transition layer: 3D printing with gradual permittivity, multi-layer PCB stepped structure;
- Planar leaf vein network: standard PCB or flexible printed circuit technology.

6.2 Core Advantages

- No alignment requirement: stereo-to-stereo coupling, position shift and angle deflection do not significantly affect efficiency;
- Global coverage: the transmitter radiates to the whole space, eliminating blind spots;
- High fault tolerance: mesh parallel structure, local damage does not affect the whole;
- Device-friendly: the final output of the receiver is planar, which can be directly integrated in consumer electronic products.

7. Conclusion

This paper proposes a wireless power transmission scheme in which both the transmitter and the receiver adopt a root-like three-dimensional mesh topology. It realizes wide-area transmission of spatial electromagnetic energy through peer-to-peer stereo coupling, then uses a gradual transition layer to complete the dimensional, impedance and mode conversion from 3D to 2D, and finally supplies power through a planar leaf vein distribution network. The scheme theoretically solves the alignment dependence of traditional wireless charging without increasing the integration difficulty of terminal equipment, providing a natural and feasible bionic path for ubiquitous wireless power supply.