A metasurface for conversion of electromagnetic radiation to DC

At the end of the 18th century, Nicola Tesla successfully demonstrated the practicality of Wireless Power Transfer (WPT). Sixty years later, the first WPT system operating at the microwave regime was demonstrated by Brown.¹ In a WPT system, DC power is fed to a transmitting circuitry which convert it to AC. The AC signal is then fed to an antenna which transmits the energy through space to a distant receiving system (rectenna), which collects the RF energy and converts it to usable DC power. A rectenna is the receiving constituent of a WPT system used to convert microwave energy into DC power. A rectenna, in general, consists of an antenna, a diode, an RF filter and a DC filter to smooth the rectified energy.^2,3 Rectennas are used in a number of applications such as remote sensing,⁴ RFID tags⁵ and energy harvesting.⁶ One critical and promising application of rectennas is Space Based Solar Power (SBSP) advocated by Glaser In 1968. In an SBSP system, a large array of solar cells in space is used to collect solar energy around the clock and then converts it to microwave power. Using high directive antennas, the power is transmitted to earth where large rectenna arrays receive the microwave power and convert it back into DC power.^7,8

Utilizing rectenna to harness the energy from the space in WPT systems has attracted much interest especially in the aspect of improving the conversion efficiency.^9–11 Since the conversion efficiency of the WPT mainly depends on the receiving system (collectors), extensive research has been carried out on the subject of rectenna. Figures of merit that are used to evaluate rectenna systems are the Radiation to AC power and Radiation to DC power conversion efficiencies. To improve the efficiency of the rectenna system, a careful design procedure including matching networks is used to minimize the losses of each rectenna component. In most previous works, heavy focus was on improving the AC to DC power conversion efficiency which was mainly attributed to the diode, RF filter and DC filter. The antenna, which is the main energy collector component of the rectenna system, and its Radiation to AC power conversion efficiency, however, were seldom discussed when calculating the overall power conversion efficiency.

Classical antennas have been used for more than a century as they play a crucial role in receiving RF energy. Therefore, different antenna types have been placed used in rectennas for harvesting electromagnetic energy. Examples include dipole antennas,^12,13 ring slot antennas,^14,15 microstrip patch antennas,¹⁶ cross dipole antennas,¹⁷ and coplanar strip line antennas.¹⁸ Most of these antennas were used because of their ability to harness the energy either over a broad band^17,19 or a duel band frequency.^14,15,20 To supply a practical system with feasible amount of power, an array composed of multiple antennas is needed.^13,19 Recently, much attention has been paid to metamaterial cells as collectors instead of classical antennas with the goal of increasing the Radiation to AC conversion efficiency in both microwaves^21,22 and infrared regimes.²³ 

The ability to tune the effective permittivity and permeability of metamaterials have led to the possibility of full absorption and near-unity energy harvesting by matching the material or surface impedance to the free space impedance. Metasurface collectors reported earlier demonstrated high radiation collection efficiency,^24,25 however, full integration of the metasurface with rectification circuitry was not presented. In earlier work, each element of the metasurface was connected to a resistive load and the AC power across the load was measured. The idea in these earlier works was that in a practical implementation, rectification circuitries would be replacing each load. In this paper, we introduce a metasurface harvester array that harvests the microwave energy and then channels the AC energy collected from all metasurface elements into a single rectification circuit through a corporate feed network. The importance of the new design is not only the novelty of the load feed network, but rather the requirement of less power density per metasurface element to activate the rectification circuit since the contribution from each individual cell is added constructively. Therefore, the threshold for the power density at the metasurface antenna needed to activate the rectification circuitry (diode turn-on) will be minimized. Of course, reducing the number of rectification circuits has the added advantage of reducing the fabrication cost and fabrication complexity.

For example, Fig. 1(a) and (b) show two panels occupying the same footprint where each panel contains 64 antenna elements. In Fig. 1(a) each antenna is connected to a diode while in Fig. 1(b) all antennas are connected together to feed one single diode. If a one mW of real power falls on both panels, each element will receive 1/64=0.015 mW. In the first scenario (Fig. 1), the power available at the feed of each diode terminals is approximately 0.015 mW under the assumption that all elements have unity efficiency. In the case shown in Fig. 1(b), however, since all power is combined through a feed network to a single diode, the power available at the feed of the diode terminal is one mW. If the diode requires one mW of power to turn on, the diode in the case of Fig. 1(b) will turn on while the diodes in the case of Fig. 1(a) will remain turned off. Therefore, in general, a power channeling strategy that maximizes the power density per diode ensures higher probability of diodes turn-on time.

The metasurface unit cell of the proposed energy harvester is the Electric Ring Resonator (ERR) shown in Fig. 2. This element was first proposed for developing highly absorbent surfaces in the infrared frequency regime²⁶ and was used in the design of a metasurface antenna.²⁷ Without loss of generality, the ERR element was designed to resonate at 3 GHz. The ERR is backed by a ground plane which plays an important role in maximising radiation to AC power efficiency but also provides electromagnetic isolation from the additional circuitry and transmission line traces that are needed for energy channeling. Arranging a periodic array of these symmetric ERR elements will create a class of subwavelength particles which exhibit a strong resonance response to the incident electrical field. The geometric dimensions of the ERR were optimized to achieve the desired resonance at 3 GHz where the maximum power absorption occurs. The meatasruface energy collector designed here is similar to the one used for feeding the metasurface antenna reported earlier.²⁷ 

The commercial full wave simulator ANSYS^$®$ HFSS^TM28 was used to design and optimize the proposed harvester element. To measure the level of transmission and reflection of the incident wave at the unit cell surface, the proposed unit cell was placed in the center of a waveguide with perfect magnetic wall in the yz planes, perfect electric wall in the xz planes, and two excitation ports along the z-axis (see Fig. 2). These boundary conditions were applied to force the electrical and magnetic fields to be parallel to the element surface and to ensure that a transverse electromagnetic wave is incident on the unit cell surface. When the electric field of the incident wave is polarized such that it is parallel to the ERR arm containing the via (Fig. 2), the ERR exhibits a strong resonance and thus maximum energy absorption potential.

An important considerations when maximizing the power delivery to the load is the via position (see Fig. 2) and the resistive load value. These two parameters were optimized to yield maximum conversion efficiency. The optimal resistance value that resulted in maximum power transfer from the ERR cell to the resistive load is found to be 200 $Ω$ (the spacing between the elements strongly affects the input impedance of each cell). Next, an array of $8×8$ ERR elements arranged periodically on a square substrate was designed. The array was first numerically simulated to ensure that it provides good absorption of the incident power. The numerical simulation was performed by positioning the array at the center of an open radiation box and excited by an incident plane wave such that the electric and magnetic fields were parallel to the element surface. Since the purpose of the simulation is to gage the absorption efficiency of the metasurface panel, each individual ERR cell was terminated by the optimal resistive load of 200 $Ω$ and the power received by all 64 cells was numerically computed. A maximum radiation to AC absorption efficiency of 92% was achieved. Scattering from the panel and dielectric absorption accounted for the remaining 8%. This simulation was a first step to ensure the potential of the design.

Since the metasurface cells need to be closely spaced to achieve good impedance balance, it is impossible to include the feed network at the copper plane where the elements are positioned. Therefore, a third copper plane was added to host the required feed network for channelling the energy to a single load as shown in Fig. 3(b). Since the input impedance of each ERR cell is $200Ω$⁠, very thin transmission lines would be needed to impedance match the ERR cell to a $50Ω$ load. Of course, for energy harvesting applications, one need not design energy harvesting system for a $50Ω$ system as one may channel the power to an energy storage device such as a battery. Here, a $50Ω$ load was chosen to facilitate AC measurement of the channeled power using a power meter with $50Ω$ input impedance. To host the feed network, low loss Rogers RT5880LZ^$®$, with a dielectric constant of 1.96 and a loss tangent of 0.0019, was used to allow for maximizing the transmission line width while maintaining the required characteristic impedance for each stage in the channeling network. Fig. 3 depicts the board architecture of the proposed metasurface harvester array and the channeling network.

Each individual resonator had a $200Ω$ input impedance. However, the received power by each resonator was channelled by metallic traces made of copper and collected at a single resistive load of $50Ω$⁠. A corporate feed technique was used as shown in Fig. 3(b) to design the channeling network.³¹ Three different transmission lines were used to ensure maximum impedance match to the $50Ω$ load. The width and length of the traces were calculated using microstrip transmission line equations.²⁹ The transmission line widths to achieve characteristic impedances of $50Ω$⁠, $100Ω$⁠, and $200Ω$⁠, were 3.35 mm, 1 mm, and 0.13 mm, respectively. The length of the quarter wavelength transformer used in the corporate network was $λ/4=18$ mm. After incorporating the feed network, the entire structure was numerically simulated. Fig. 4 shows the radiation to AC conversion efficiency with and without the corporate feed. Expectedly, the maximum efficiency was slightly decreased due to propagation losses in the feed network; nevertheless, the results of the numerical simulation validated the channeling network design.

Using the microstrip transmission line corporate feed network, the $8×8$ metasurface harvesting array was fabricated as shown in Fig. 5. All collectors were connected to a single feed point where a $50Ω$ SMA connector was mounted. A rectifier was then designed using Agilent Advance Design Systems (ADS) having an input impedance of $50Ω$ at the resonance frequency. Since the rectifier is non-linear, it was analyzed using the Harmonic Balance simulator. The diode was connected to the feed of the antenna through a matching network containing a short circuited stub, open circuited stub and a series transmission line. Then a DC filter containing two series transmission lines and two open circuited stubs along with a 150 pF was connected to the cathode node of a HSMS 2860 Schottky diode. The design schematic for the rectification circuit is shown in Fig. 6 and the fabricated one in Fig. 7.

The fabricated metasurface array was tested with and with out the rectification circuity. The incident field was generated using an 11.5 dBi gain commercial wideband horn antenna excited by a frequency signal generator with a power level of 13 dBm. The metasurface array was positioned a distance of one m away from the transmitting antenna such that the electric field is parallel to the ERR arm containing the via (shown in Fig. 2). A schematic of the measurements setup is shown in Fig. 8. Fig. 9 shows the actual measurement setup. The AC power at the output of the corporate feed network was measured over the 2 GHz to 4GHz frequency range. The radiation to AC harvesting efficiency was obtained using the following formula:²¹ 

where P_received is the total time-average power received by the metasurface array (dissipated in the resistive load), and P_incident is the total time average power incident on the entire metasurface. P_incident was calculated using Friis equation:³⁰ 

where P_t is the output power of the transmitting antenna, G_t is the gain of the transmitting antenna, R is the distance between the antennas, and A is the entire metasurface area. For the entire metasurface that contains N collectors, P_received is given by:

where V_L is the voltage across the resistance of the single load resistor R_L.

Fig. 10 depicts the measured radiation to AC power conversion efficiency $ηrad−AC$ of the proposed metasurface harvester before attaching the rectifier. The highest $ηrad−AC$ achieved was 78% at 2.9 GHz. The rectifier is then attached to the metasurface array using an SMA connector. The power across the DC load is then measured at the optimal frequency and incident power level. To obtain the optimal power level, the power output from the signal generator was connected to a 42 dB microwave power amplifier. It was found that the diode operate maximally at a incident power level of 12 dBm and a frequency of 2.82 GHz for a load resistance of $300Ω$⁠. The peak radiation to DC power conversion efficiency, $ηrad−DC$⁠, of the array including the rectifier was 40% at 2.82 GHz.

This work presented the design of metasurface harvester that efficiently collects electromagnetic wave radiation power and channels it to one resistive load. A corporate feed network was designed to match the input impedance of the ERR cells to one resistive load such that all cells were connected in phase to the resistive load. An ensemble of $8×8$ ERR cells was designed, fabricated and tested. The experimental results show that the metasurface in conjunction with the corporate feed network provided a maximum total radiation to DC conversion efficiency of 40%.

In this particular work, the radiation illuminating the metasurface panel was incident normally to its surface. This resulted in all the metasurface elements (ERR cells) having uniform phase and thus the propagation of the AC signal on the corporate feed network resulted in constructive interference at the rectifier input. If the incident radiation was incident at other angles, the efficiency is expected to decrease due to non-uniformity of the phase at each element. Therefore, the presented design concept is most suitable when the radiation is arriving from a specific direction known to the receiver system.

The authors would like to acknowledge the financial support of the Libyan Ministry of Higher Education, Prince Sattam University, Saudi Arabia and the Natural Sciences and Engineering Research Council of Canada.