Novel wireless power transmission based on Maxwell displacement current

Highlights

• Propagation characteristics of wireless power transmission (WPT) based on Maxwell displacement current were explored.

• A new model inspired by reservoir for explaining the propagation characteristics of WPT was presented.

• This new discovery may also offer a new research direction for WPT based on Maxwell displacement electric field.

Abstract

Wireless power transmission (WPT) is vitally important for portable electronics. Recently, wireless energy delivery via Maxwell displacement current from triboelectric nanogenerator may open new routes to develop novel technologies especially for implantable medical devices and sensor network due to its flexibility, adaption, convenience and safety. In this paper, the propagation characteristics of WPT are explored, which are based on displacement current from a spherical high frequency electric field. The results showed that the spherical surfaces with the same radius from the center have equal value of electric field intensity. When the receiver has a larger area or workload, the output has a higher value, which is subject to the electric field intensity. However, the current is almost unchanged with increasing output power below 15 kΩ of load resistance in series, which may have potential applications for sensors. Furthermore, the receiver circuit of wireless energy is in accordance with the traditional serial and parallel circuit regularity. Based on these, we are going to assume that the electric field source is a reservoir, and water flow is analogous to current. The assumption is suitable for studying propagation characteristics. This new discovery may also offer a new research direction for WPT based on Maxwell displacement electric field.

Introduction

Energy is the foundation of today's society. Electromagnetic generator (EMG) has been the dominant technology to generate commercial power since the first discovery of the electromagnetic induction phenomenon [1]. Electricity has propelled the world-wide economical development and changed the world. However, it is desperately needed to find new energy sources as alternatives to fossil fuels due to energy shortage, environmental pollution and depletion of the fossil fuel increasing. Recently, triboelectric nanogenerator (TENG) has attracted more and more attention owing to its lightweight, low cost and environmentally friendliness [[1], [2], [3], [4], [5]]. It has been proved to be a new energy harvesting device to efficiently scavenge ambient mechanical energy for self-powered micro/nanosystem applications, blue energy and even big data [[6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]]. Unlike the EMG, TENG is based on the coupling of the contact-electrification effect and electrostatic induction to convert the ambient mechanical energy into electricity [17,18]. Moreover, the fundamental theory of the TENG starts from the Maxwell equations [19,20], which are among the top 10 most important equations for physics. Displacement current as one of the most greatest creative ideas was first postulated by Maxwell in 1861 [21]. The displacement current is a time-varying electric field (vacuum or media), plus a contribution from the slight motion of charge bound in atoms, dielectric polarization in materials, which differs from conduction current depending on moving free charges. It is defined as:

$${\mathit{J}}_D=\frac{\partial \mathit{D}}{\partial t}=\epsilon \frac{\partial \mathit{E}}{\partial t}+\frac{\partial {\mathit{P}}_s}{\partial t}$$

where the ε is the permittivity of free space, D is displacement field, E is the electric field intensity, and P_s is the polarization density introduced by the surface electrostatic charges owing to contact-electrification effect.

In Eq. (1), the first component $\epsilon \frac{\partial \mathit{E}}{\partial t}$ gives the birth of electromagnetic wave, which establishes foundation to develop wireless communication, radio, radar, TV, microwave, light theory, space technology, photonics, and many more [21]. It has driven the development of world in communication and laser technology in the last century, which has changed people's way of life. Meanwhile, the newly added term ∂Ps/∂t is the application of Maxwell displacement current in energy and sensors, which was first proposed by Wang for the nanogenerators [22]. It is important to note that the P_s term is different from medium polarization P which induced by the electric field. The P_s is the polarization created by the electrostatic surface charges owing to mechanical triggering, and is simply called Wang term. This excellent work provides the theoretical rational for further study of piezoelectric nanogenerator and triboelectric nanogenerator. It can quantify the nanogenerators' output and provide theoretical guidance for performance improvements [20,21,23]. Furthermore, the electromagnetic radiation from nanogenerator systems can be calculated if they have high operating frequency [21]. Therefore, it may expand the scope of nanogenerators' application in wireless power transmission using displacement current.

It is generally known that metal wires are the primary medium of power transmission. However, with the development and improvement of the technology in recent years, wireless power transmission (WPT) technology is getting more concern because of its advantages of its high flexibility, adaption, convenience and safety for charging handhold electronics and devices for the internet of things [[24], [25], [26]]. At present, wireless transmission mainly includes electromagnetic induction, magnetic resonance, and radio wave, which mainly depends on the EMG relying on the Lorentz force driven flow of free electrons in a metal coil. As a new environmental energies harvester, TENG based on the Maxwell displacement current has also been designed for wireless energy delivery [[27], [28], [29]]. These studies show the applications of wireless energy delivery by TENG in areas of portable and wearable electronics. As depicted in previous studies [20,21], nanogenerator systems can produce electromagnetic radiation when the nanogenerator systems operating at high frequency. So, it is significant to explore the propagation characteristics based on Maxwell displacement current at high operating frequency.

Here, a high frequency electric field was applied to explore the wireless power transmission characteristics based on displacement current. Tin-foils with different areas are served as receivers for receiving wireless power from the electric field. Meanwhile, oscilloscopes are applied to measure the receiving-end voltages. It shows that the test points with same radius from the center have the equal value of electric field intensity. The receiving voltage and power from spherical electric field will nonlinearly increase along with the increase of receiving area and workload. However, the current is almost unchanged below 15 kΩ of load resistance. It may have potential applications for sensors. Most importantly, we have presented a new model inspired by reservoir for explaining the propagation characteristics of WPT based on displacement current.