Enhancement algorithm for reverse loop technique on planar reverse loop antenna

Finding a trade-off balance between wireless transfer efficiency (WTE) and distance is a key issue in wireless energy transfer (WET). This paper presents a method of reducing the radical alteration in WTE versus distance, by using a reverse loop technique on planar reverse loop antenna (PRLA). The design focuses on 13.56 MHz Near Field Communication (NFC). The first stage uses mathematical modelling, based on an analytical approach, to determine the size of the reverse loop using Matlab. The proposed model predicts the size of the reverse loop to stabilize the WTE at a closer distance. Next, full-wave electromagnetic simulations are applied, using the computer simulation technology (CST) MICROWAVE STUDIO®, to determine the WTE effect with distance changes with mismatch condition. Planar loop antennas (PLAs) are fabricated on glass-reinforced epoxy laminated sheets (FR4). A validation of the simulation result in a real test scenario, using these PLAs and PRLA, confirms a stability enhancement in WTE at closer distance using the reverse loop technique, compared to conventional designs.


Introduction
With the evolution of high-end technology, portable devices have become widely used. Usually, these devices require power from rechargeable batteries to enable mobility. The batteries only support these devices for limited durations, after which they require recharging using wired power delivery mechanisms. Consumers usually need to wait for the completion of the charging process before the devices can be used wirelessly. In its mooted counteraction of this problem, wireless energy transfer (WET) has garnered significant research interest. However, even with the latest technologies, there are obstacles to be overcome before the full commercialization of WET can be implemented [1].
Inductive coupling of WET has attracted a great deal of attention, due to its simplicity and safety. It is already used in technologies such as RFID and NFC [2]; NFC-enabled smartphones are even now employing inductive coupling for data transfer in contactless transactions at 13.56 MHz [3]. Theoretically, NFC can also be used to transfer energy between devices using inductive coupling at a resonant frequency as shown in Figure 1.
There have been improvements in the performance of inductive coupling and strong magnetic coupling WET schemes [4][5][6]. However, as demonstrated in many studies, the wireless transfer efficiency (WTE) is reduced greatly with altered distances [6][7][8][9][10][11]. In order to increase the insensitivity to the distance of the transmitting and receiving antennas, a handful of techniques has been developed, such as using a loaded capacitor or applying more than two coils in a system [6,11,12].
Coupling coefficient is directly proportional to mutual inductance; M. M value strongly depends on the distance between the antennas. In short, closer distance will generate higher M than farther distance. Both antennas are perfectly matched at operating distance for optimum resonant effect. However, the WTE will radically drop when the transmitter and receiver become closer. This phenomenon happens because of frequency splitting condition caused by coupling  [13]. In order to maintain a constant transfer within the over-coupled region, some researchers proposed dynamic impedance matching arrangements to either track the resonance frequency [14][15][16][17] or adaptively impedance match to maintain a stated frequency [18]. These impedance matching arrangements were implemented using either lumped reactance [14,19,20] or tuning algorithms in controllers [21][22][23]. An alternative arrangement, however, is to control the range-profile of the mutual inductance within the over-coupled region.
Besides, optimal load resistance value existed, with which the coupling efficiency can be maximised [24]. To achieve this, the resonant capacitor at the load side was replaced by a more complex impedance matching network in [16,25]. This matching network tuned the receiver coil and transformed the load resistance value into one that is optimum. The matching network was also introduced into the source side in [25][26][27]. In [25], the matching network design was integrated into WET system and displayed a good performance. Matching network can be designed to maximise the output power for transfer efficiency.
This paper focuses on 13.56 MHz WET, in order to take advantage of the fact that almost all mid-and high-end smartphones are already NFC-enabled. The reverse loop technique is used to stabilize the WTE when the distance between both antennas is shorter than optimum operating distance, without any further system adjustment. The M produced is controlled by introducing a reverse loop into a planar loop antenna (PLA) to minimize the radical changes in WTE with distance variance. This method yields the development of the planar reverse loop antenna (PRLA).

Antenna Design
The inductive coupling link consists of two antennas with separate external matching circuits. Each matching circuit uses parallel and serial capacitors to tune the antennas for maximum WTE at the operating frequency. The antennas are designed to be square in order to fit into mobile phones, thereby optimizing the available area. The PLAs are single square loops, as shown in Figures 2 (a) and (b). Their side-lengths are set at 60 mm and 40 mm for the transmitter and receiver, respectively, for an operating distance d of 50 mm.

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A coupled pair of one-turn square loops in a wireless energy transfer link can be illustrated in a simplified equivalent circuit, as shown in Figure 3 [28]. The inductance of each PLA can be calculated using (1), also stated in [29]: where µ is the conductor (copper) permeability, and Figure 3. Equivalent circuit for antennas [28] The average side length of the PLA is given by with la and lb denoting the largest and smallest side lengths, respectively. Taking the skin effect into consideration, the resistance of the PLA, R at f = 13.56 MHz, can be computed as: where ρ is the resistivity of copper (1.7 × 10 -8 Wm), A is the cross-sectional area of the loop and l is the total length of the PLA. t is the thickness of the conductor. Ar and l can be determined by using where w, ls, g and p are the width, side length, gap length and port line length of the conductor respectively. The WTE of the established link is calculated as [11]: where QTX is the quality factor of the transmitting antenna and QRX is the quality factor of the receiving antenna; both are defined as = 2 (10) k is the coupling coefficient between both antennas and can be determined using: = 2 2 2 2 + 2 + 2 (14) rmin and rmax are the corresponding smaller and larger side lengths of the square antennas, respectively. Here, X is the half side length of the transmitter antenna and Y is the half side length of the receiver antenna. d denotes the distance between the transmitter and receiver of the PLA system. In terms of mutual inductance between transmitter and receiver PLA, M is inversely proportional to the distance, as shown in Figure 4. In theory, high values of M will produce high WTE; however, this is only true if both PLAs are perfectly matched. In fixed matching circuits for inductive WET, the highest WTE will be obtained at a matching operating distance, which in this case is 50 mm. Deviation from this operating distance will greatly reduce the WTE of the system. Further distance from the operating point will reduce M value, also causing WTE reduction. Meanwhile, a closer distance from the operating point will increase the M between PLAs and create the over-coupling condition, as characterized by frequency splitting [13]. The over-coupling phenomena will decrease the WTE greatly, even when M is high at that point. In theory, the WTE can be stabilized by maintaining a constant M, irrespective of the distance. This can be achieved by introducing a reverse loop in the transmitter antenna, producing a PRLA, as shown in Figure 5 (a). The receiver antenna will be using initial single square loop antenna as presented in Figure 5 (b). This reverse loop will generate an opposite M, as shown in Figure 6. The net result will be a reduction in the alteration of M as the coupled antennas are brought closer together. The first stage in obtaining the side length of the reverse loop requires the choice of two points of distance. The first point is an optimum operating distance, while the second is a closer distance than the former. Based on (13), maintaining the value of M at these two points will result in a stable WTE. The size of the reverse loop to maintain a constant M at both points can be obtained by solving (15). Matlab is used to solve the proposed equation.
M1,2 are calculated using: where A1,2, B1,2 and d1,2 are the half-side length of the transmitter, the half-side length of the receiver and the distance between PRLAs at different points, respectively. If A1, B1, d1, A2 and d2 are known, the optimum size of the reverse loop side length, B2 can be calculated. The calculated value of B2 is an optimum value of reverse loop side length that produces highest and most stable WTE at a distance between antennas closer than matching distance. To tune the system for optimum performance at f = 13.56MHz, both PLAs and PRLAs were matched to 50Ω impedances using external capacitor networks, as shown in Figure 6. Full-wave simulations were carried out in CST to ascertain the effect on WTE with distance. The antennas were then fabricated to validate the simulated results.

Results and Analysis
Simulated antennas are matched using Mini Match matching technique in CST. Two capacitors are used at each antenna to eliminate the reactance component and get a resonance at 13.56 MHz, as shown in Figure 3. This matching stage is very important to ensure the maximum possible output power will be delivered. The fabricated transmitter's PLA and PRLA are shown in Figure 7, with the matching circuit shown in the inset. The capacitance values are shown in Table 1, while Figure 8 shows the lab measurement setup.  The M of the system using PRLA is shown in Figure 9. Even though the PRLA has a lower M compared to the PLA, the M for the PRLA loop is much more stable over distance. This ensures the reduction of the over-coupling effect at closer distances; accordingly, frequency-splitting phenomena can be minimized. The WTE alteration, with shorter coupling distances than the matching distance, is thus reduced.
In Figure 9, the total M produced by the PLRA is shown. Total M is decreased because the reverse loop in PRLA introduced negative M. The maximum M obtained indicates that the optimum WTE can be achieved at perfectly matched conditions. Here, the maximum WTE can be reached at a matching distance equal to 25 mm. Figure 10 shows the WTE alteration of both PLAs and PRLAs antennas for various distances. Even though the WTE for PRLA is lower than PLA at matching distance, WTE for PRLA has better stability than PLA. Frequency splitting phenomena has been reduced greatly by introducing reverse loop into PRLA. As a result, WTE for PRLA at closer distance from matching distance is higher than PLA.  Figure 11 compares the WTE performance of the PRLA and conventional PLA as the operating distance is varied. Differences in capacitor values within a 5% tolerance contribute to differences between the simulation and measurement results. Non-existent values for required capacitors in the market also led to this dissimilarity.
However, there is acceptable agreement between the measured and simulated profiles of WTE. Overall, the PLRA is shown to stabilise the WTE at closer distances. An improvement of 150% for S21 at a distance of 10mm is recorded. In addition, the PLRA is able to maintain S21 over 0.5 at a greater distance than the conventional PLA. PLA has S21 larger than 0.5 from 25 mm to 75 mm while PRLA manage to maintain S21 above 0.5 from 0 up to 60 mm, which produce range improvement of 20%. Figure 11. Transfer efficiency with varied distances

Conclusion
WTE can be stabilised over shorter coupling distances by using the reverse loop technique at a closer distance. By controlling the increase in mutual inductance between a pair of coupled antennas at shorter distances, the alteration of WTE is reduced. This leads to an improvement in the stability of WET.