FEM Analysis of a PCB Integrated Resonant Wireless Power Transfer

FEM Analysis of a PCB Integrated Resonant Wireless Power Transfer Žarko Martinović Danieli Systec d.o.o./vinež 601, Labin, Croatia e-mail: zmartinovic@systec.danieli.com Roman Malarić Faculty of Electrical Engineering and Computing / Department of Electrical Engineering Fundamentals and Measurements, Unska 3, Zagreb, Croatia e-mail: roman.malarić@fer.hr Martin Dadić Faculty of Electrical Engineering and Computing Department of Electrical Engineering Fundamentals and Measurements, Unska 3, Zagreb, Croatia e-mail: martin.dadic@fer.hr Željko Martinović Combis d.o.o./hektorovićeva, Zagreb, Croatia e-mail: zeljko.martinovic@combis.hr Abstract The paper presents the results of the FEM analysis of a printed-circuit-board (PCB) based wireless power transfer (WPT) receiver/transmitter. The full-wave simulations were run in HFSS. The design of the transmitter and the receiver was based on the standard double-sided PCB FR4 fiberglass-epoxy material. The WPT system was analyzed for different transmitter and receiver distances (1mm 100 mm), with and without integrated capacitance. The influence of the additional capacitance on resonant frequencies was analysed. Simulation results were compared by extracting Z parameters (impedance parameters) for different model scenarios. Keywords Wireless power transfer; Witricity; FEM, resonant coupling; resonant frequency I. INTRODUCTION Wireless resonant power transfer was originally created by Nikola Tesla. His idea was to enable distribution of energy through the Earth's ionosphere [1][][3][4]. The same concept gained a renewed interest in the last decade, mainly by the research team led by Marin Soljacic at MIT, who had described its physical behaviour and coined the term Witricity [5][6]. Wireless resonant power transfer from Fig. 1. consists of four main parts: Power Source - Amplifier Resonance Loops Transmitter Receiver Loops Receiver Load Electromagnetic systems with the same specific frequency, can excite resonance due to electromagnetic coupling to transfer energy at some distance. If those systems obtain the same resonant frequency they can exchange energy. Transmitter side should have a constant supply, and receive side should have load perfectly matched [5]. In original paper [5] a separate single coil turn was introduced at the transmitter side as an impedance transformer, and later the same concept was used by other authors. In order to design the entire transmitter system in the double-sided PCB material, this concept is in this paper replaced by a direct excitation of the transmitter coil, which is made as a planar inductance at the one side of the board. In this way, an easy integration of the transmitter coils and the electronics is allowed, which further simplifies assembling of the whole system. The resonant frequency of the planar coil is determined by its inductance and the inter-turn capacitance. The resonant frequency can be additionally tuned applying the rectangular plates in the copper on the opposite side of the PCB material, which serve as the additional parallel capacitances and lowers the overall resonant frequency. Since the resonant frequencies of the system depend of the distance of the transmitter and receiver coils, while the accurate analytical calculation of the overall lumped inductances and capacitances of the coils is very difficult, the full-wave FEM simulation was performed as an initial step in defining the demands for the drive electronics of the system. The model was created in High Frequency Structure Simulator (HFSS) according to the similar models in papers [7][8][9]. The purpose of this paper is the development of full wave Finite Element Method (FEM) model of our electromagnetic system. Verified and simulated model will enable us development of different optimization technic and processes. By extracting of FEM model, it will be created quadrupole network (Z - parameters). Figure 1. Wireless power transfer components II. COUPLED RESONATORS Fig. depicts a system of two coupled resonators. Here, denotes voltage source, is angular frequency, R is internal s U s

resistance of the source, inductance, capacitance, M 1, C is source current and L 1 is source inductance, is mutual inductance, is device capacitance, I is load current. R L C 1 L is device is source is load resistance, I 1 d avg. 5d out din d d d d 0, and the fill ratio is /. out in out in Fig. 3. Square realization of the spiral inductor Figure. Equivalent circuit for coupled resonator system If we denote overall resistance at the transmitting side as the input power can be expressed as [10]: P IN R S ' R RL L M 1 R RL U S R S ' R RL L1L M1 RS ' L R RL while the output power can be expressed as: P O M 1 ' R R L L M L S L R S L 1 1 RS ' L R RL U R L 1 1 R S ' Based on the equations (1) and (), the system efficiency is [10]: R ' S M 1 R R L L L M 1 R RL The transferred power splits into two peak values when the coupling coefficient of the coils is large, where the lower frequency corresponds to the odd mode. The higher frequency corresponds to the even mode. At splitting frequencies, the transferred power reaches its maxims. The odd mode allows larger efficiency, and therefore it is mostly chosen as the operating frequency of the system. The system efficiency reaches its maximum at the natural resonant frequency [10]. R III.PLANAR COILS The inductance of the printed planar spiral inductors can be estimated using several analytical expressions. Fig. 3 depicts the square realization of the planar inductor. The planar inductor is specified by the number of turns n, the turn width w, the turn spacing s, the outer diameter d out, the inner diameter d in. Furthermore, the average diameter, (1) () (3) Based on the work of Mohan et al. [11], the modified Wheeler formula for the inductance of the square realization of the spiral inductor is n davg L mw.340. (4) 1.75 There is also an expression based on current sheet approximation and mean distances [11]: 1.7 0n davg L gmd ln.07/ 0.18 0.13 (5) The natural resonant frequency of a RLC system is determined by Thompson equation where L represents lumped inductance and C is lumped capacitance: r 1 f= (6) π LC Capacitance value [9] is dependent on conductor dimension area (A), insulator thickness (d) and permittivity of the substrate ( ) and includes both inter-turn capacitance and capacitances between turns and additional plates on the opposite side of the substrate. Inductance value is dependent on loop characteristics (e.g. lengths, width, and thickness). For a large number of turns it is increasingly difficult to calculate accurately the parasitic capacitance, due to the nonlinear adjacent winding capacitance [13]. This capacitance is typically on the order of a few pf. An estimation of the parasitic capacitance of the circular spiral inductors can be deduced from [14]: ε C S h 0K Koff (7) R i ln R 10 where h denotes height of the traces, is permittivity of vaccum, R i is the inner radius of the second winding, R i is the outer radius of the first winding. K is a constant of 0.3 and K off is an offset of about.6 pf. Due to the very small height of the traces compared to their distance the results of this 0

analytical estimation are very inaccurate. Analytical expressions is especially inaccurate with the added rectangular elements, and the capacitance calculations should rely on the numerical models. IV. Z-PARAMETERS Fig. 4. Two-port Figure 5. Developed Wireless Power Transfer model in HFSS Fig. 4 presents a two-port connected to a source with the source impedance Z 1, terminated with load impedance Z. The input and output voltages can be generally expressed as U z I z (6) U 1 11 1 1I z1i1 zi (7) where z 11 and z are open-circuit driving point impedances and z 1 and z 1 are open circuit transfer impedances of the twoport [1]. The impedance parameters (Z parameters) can be easily extracted from the FEM solver for a fixed distance of the receiving and transmitting coil, and further applied in the calculation of the transferred power and system efficiency using standard method of two-port analysis. Figure 6. Wireless power transfer model spiral turns V. WPT MODEL OVERVIEW Developed model is based on two identical PCB coils. At the top side is the receiver, and the bottom one is transmitter (Fig. 5). Transmitter and receiver plate has dimensions 80 x 80 mm with thickness 1 mm. They consist of spiral turns with 80 loops with 1 mm distance between them. The loops are made of cooper with thickness 0.035 mm (Fig. 6.). The capacitor is presented with four rectangular elements, which electrically breaks the path for the induced currents in the ground plane and allows easy implementation of the return conductor in the PCB. Strip length is 35 mm and width is 1 mm. Capacitor layers were made of copper. The insulator is FR-4 type. Advantages of FR-4 material are low cost and good integration properties related to PCB design development in electronic applications. Two external separate copper conductors are connected for the feed and the load of the system. Based on the equations (4) and (5), the inductance of the coils was estimated as L mw=07 μh and L gmd=18 μh. Figure 7. Wireles power transfer model in HFSS with air box around the model On transmitter and receiver sides the appropriate lumped ports were assigned, and the whole system was placed into an air box with radiating boundaries (Fig. 7). First 30 simulations were run for transmitter and receiver distances between 1 30 mm and after that we continued simulations with distances equal to 40, 60, 80 and 100 mm. Analysis of resonant frequency was the main output of simulations which were conducted between 1 and 100 MHz. Maximum number of

passes was 6. The resonant frequency of the system was targeted to satisfy the European regulations for the inductive loop systems in the frequency range 9 khz to 30 MHz, i.e. ETSI EN300 330 [15]. VI. RESONANT FREQUENCY ANALYSIS a) WPT model without additional capacitance b) WPT model with additional capacitance WPT coils with additional capacitance elements (Fig. 10.) have additional rectangular elements at the reverse side of the PCB board. WPT model without capacitance (Fig. 8.) consists of two coils and insulator boards with the identical dimensions. Simulation was run with distances between coils equal to 1, 0, 40, 60, 80 and 100 mm, for all simulations presented in the paper. Figure 10. WPT model with capacitive elements Figure 8. WPT model without capacitance Fig. 9 depicts the frequency response of the Z 1 parameter for all examined distances. From Fig. 9. we can conclude that the main resonant frequencies is in the band 10-30 MHz, for all examined distances, with the biggest peak at 5 MHz and 40 mm. Figure 11. Z 1-parameters of model with additional capacitance From Fig. 11. we can notice decreasing in resonant frequency by adding capacitance, which shifts main resonances below 0 MHz. The biggest resonant peak is now at 13 MHz and at a distance of 60 mm. c) WPT model with additional capacitors and lateral misalignment of the coils Figure 9. Z 1-parameters of model without capacitance In this subsection the influence of the lateral misalignment of the coils is examined, Fig. 1. depicts the examined Witricity model with lateral misalignment of the coils. Receiver and transmitter boards are shifted lateraly for 5 mm. Since the wavelength was much greater than the physiscal dimensions of the system, the adaptive meshing of all models was based on the element length based refinment, with the restricted maximum lemgth of the elements in the whole domain (including air box) equal to 17.8 mm (wavelength was always below 3 m), and using the unrestricted number of elements.

Figure 1. WPT model with lateral shift of the coils Figure 14. Conductor model of WPT From Fig. 13. we can see that the frequency of the strongest peak is again 13 MHz with distance between plates equal to 60 mm. As we can notice, the frequency responses is similar to the model with the aligned coils, both in the shape and in the magnitudes. It may be concluded that the small lateral shifts does not influence the response of the system significantly. Figure 15. Z 1-parameters of the WPT model consisted of coils only (without substrate) Figure 13. Z 1-parameters of the WPT model with the lateral shift d) WPT conductor model In the last subsection, the influence of the permittivity on the increase of the resonant frequencies of the substrate was examined for the initial model without additional rectangular capacitive elements. In this model the PCB substrate is replaced by the air. Such a conductor model represents simplified model, which is consisted of two loops with air gap distance (Fig. 14.). For model without any insulators and additional capacitances, the results are presented in Figure 15. The decrease of the permittivity increased the frequencies of the resonance peaks for approximatelly 4 MHz, which is the absolute upper bound for possible change in the resonant frequencies due to different substrate materials (FR-3, Rogers), or the frequency dependance of the permittivity. VI. CONCLUSION In order to properly design wireless power transfer system, it is necessary to carefully determine the resonant frequency of the system, as well as its frequency response. Previous papers [7]-[9] shows a similar design where resonant frequency was adjusted according to the number of turns from the receiver and transmitter side, thickness of the substrate and dimensions of capacitors. In this paper approach was on adjusting the resonant frequency but with different parameters. In order to reach specific resonance frequency limits we changed shape of the possible additional capacitive elements. As it can be seen from the FEM analysis, the main resonant peak of the system with additional capacitors is near 13 MHz, while without them it has been near to 0 MHz. Another set of simulations were run with transmitter and receiver coil axes shifted laterally for 5 mm, with no significant change in the response. For all presented scenarios, the impedance parameters (Z-parameters) were extracted, which allows easy calculation of the system response for different loads, as well as their matching regarding to the efficiency and the maximum power transfer.

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