Design and Evaluation of High Current PCB Embedded Inductor for High Frequency Inverters

Transcription

1 Design and Evaluation of High Current PCB Embedded Inductor for High Frequency Inverters Mehrdad Biglarbegian, Neel Shah, Iman Mazhari, Johan Enslin and Babak Parkhideh Electrical and Computer Engineering Department Energy Production and Infrastructure Center (EPIC) University of North Carolina at Charlotte Charlotte, USA s: {mbiglarb, nshah49, imazhari, Abstract This paper describes the design and evaluation of high current toroidal Printed Circuit Board (PCB) embedded inductor applicable for high frequency DC/AC converters (lower than 10MHz). The equivalent circuit model of the inductor is presented and the filtering effectiveness is verified by testing three different geometries with its own characteristics and function through a GaN converter. Besides, the temperature rise analysis is provided for all the prototypes by using finite element methods, and the obtained results are also verified by experiments. The reason behind asymmetric trend of temperature rise for the toroidal PCB embedded inductor is also discussed through both simulation and experiment, and the capability of using a heat sink to lower the temperature increment for different geometries is explained. Keywords air-core PCB embedded inductor; temperature rise analysis; high frequency; GaN I. INTRODUCTION The demand for ever-increasing switching frequency using wide band gap devices, higher power density, keep driving the development of passive integration technologies in the modern power electronics. With increasing the frequency to the MHz range, magnetic core loss increases drastically [1]. So, air core PCB embedded inductors become a viable solution, as the sizes are shrinking, and the core losses are avoided [], [3]. It will also lead to a cost reduction, as smaller passive components are less expensive. In general, the advantages of passive components integration will be size reduction, better thermal conduction, high parameter repeatability, high reliability, and cost reduction [3], [4]. Among several structures for the design of PCB embedded inductors described in the previous literature [3], [5], toroidal inductors are chosen in this paper due to their internal encapsulation of the magnetic field avoiding EMI problems. Also, compared to other common structures for a PCB embedded inductor, toroid has some drawbacks addressed in this paper such as relatively lower quality factor and inductance per area, less flexibility, and high resistance caused by thin petals, and the poor fill factor of the vias used in both inner and outer edges [3], [6]. Previous researches have been conducted combining RF circuits and power electronics to design switch mode power supplies (SMPSs) operable at very high switching frequencies (VHF) in the range of (30-300MHz), but this range of frequency is more suitable for resonant DC/DC converters [7]. Contrarily, this paper conducts a comprehensive analysis, and design investigations for three different high efficient toroidal PCB embedded inductors suitable for smoothing the AC current of high frequency hard switched inverters. Moreover, temperature Rise analysis including asymmetric distribution, proximity and skin effect, total harmonic distortion (THD), and thermal resistance are investigated and formulation for the built designs are presented. In section II, the equivalent circuit model of a toroidal PCB embedded inductor is expressed and its temperature rise profile is formulated. Section III shows all the three implemented designs, and their main characteristics such as filtering capability in THD reduction, AC resistance, and temperature profile variations. In section IV, temperature rise analysis including asymmetric distribution, proximity and skin effect, and effective factors are discussed and how it can be affected by using a heat sink will be explained. II. TEMPERATURE RISE FORMULATION FOR THE PCB EMBEEDEDD INDUCTOR A. Equivalent Circuit Model of Toroidal PCB Embedded Inductor For the full bridge inverters, it has been assumed that current and voltage ripples set to be 1%. Designing an inductor with the above specifications, not only limit the ripple amplitude, it also helps to effectively filter our high frequency harmonics [3]. Following equation shows the resonant frequency of parallel LC circuit: f cutoff 1 1 = = π L C 4π ( V V ) D ID Δ I f f ΔV min min in out max Δ max Typically, in order to be far enough from the high frequency harmonics and decrease the output noise at 10MHz switching frequency, the cutoff frequency is set to be lower than 1/10 th of the switching frequency. In (1), shows the maximum duty cycle, is the switching frequency of the inverter and sw sw (1) /16/$ IEEE 998

2 is the cutoff frequency of the AC filter, respectively. Therefore, the inductance can be calculated in () after simplifying (1): ( Vin Vout ) D () max L = Δ V f C By choosing a low ceramic capacitor (<1µF) to have a low equivalent series resistance (ESR), the nH range of the inductance will be obtained for DC/AC converter applications in the specified range of switching frequency ( < 10 ). The geometric parameters of a typical air-core PCB embedded inductor is shown in Fig.1. sw Top Petal Therefore, inductance and AC resistance of the toroidal PCB embedded inductor can be calculated as follow: Based on the previous studies [6], [8], in a toroidal air-core PCB embedded inductor, the inductance can be calculated in (3): Nhμ0 do do + di do + di μ0 π d i 4 do di L = ln + ln(8 ) In (3), is the number of petals, h is the height of PCB/inductor and is the permeability of the air. Furthermore, outer and inner diameters of the inductor are shown by and, respectively. As shown in [3], [9], the inductance can be simplified as below: (3) L μ k (4) 0 N h Input/output Legs where, at the defined outer/inner geometries is a constant value. As shown in [6], [10], the resistance can be expressed in (5). As shown in (5), the resistance consists of two main parts: resistance of petals and resistance of vias. R R R= N Rpetal + + Ninner N inner _ via outer _ via outer (5) Bottom Petal Fig. 1. Geometric parameters of an air-core PCB embedded inductor (yellow: bottom petals, cyan: top petals) Fig. a. depicts the equivalent electrical circuit model of the proposed embedded inductor. Due to the encapsulation of magnetic flux inside the toroid, the path of current in each petal can be represented in a LR circuit configuration. The behavior of this impedance over a wide range of frequencies has been studied through the spectrum analyzer shown in the Fig. b. As can be observed, in very high frequency (~80MHz), the inductor has a resonance, which mainly caused by the parasitic capacitance of adjacent petals and vias. The occurrence of the resonant at this range of frequency shows that the parasitic capacitance would be in the range of (~pf). As the proposed inductor is normally operating at much lower than this resonant frequency, the effect of the capacitance in the equivalent impedance can be neglected for further analysis. Via The resistance of each petal is proportional to the copper resistivity, number of turns, and outer diameter of the inductor, and it is inversely related to the skin depth, petals clearance and inner diameter of vias. On the other side, the vias resistance will be increased directly by copper resistivity and inversely with the via diameter, and the skin depth, which is a measure of the penetration of a plane electromagnetic wave into the copper. By considering the impact of skin and proximity effects on the total resistance of the vias, the current tends to pass through the edges of the conductor (copper) as the current density is largest near the surface. Also, proximity effect due to the relatively bigger size of each petal respect to their clearance can be ignored. By simplifying the equations and applying the skin effect relation with switching frequency, the AC resistance can be expressed in (6) as shown also[3], [9]: Rac kn 1 f where, is constant factor which depends on the geometry of the inductor. B. Temperature Rise Formulation of Toroidal PCB Embedded Inductor As shown in [11], the temperature rise in convection mode at the steady-state conditions can be defined as (7): (6) P Rth =Δ T (7) (a) (b) Fig.. Equivalent circuit model and the impedance spectrum vs. frequency In this formula, is the total dissipative power of the inductor, and is the total thermal resistivity between the board and the environment. 999

3 8-turn 6-turn Fig. 3. Equivalent thermal circuit model without heatsink In order to quantitatively demonstrate and compare the temperature rise variations of the inductor, the temperature rise can be normalized to the specific reference. The temperature rise of the PCB embedded inductor is normalized per quality factor, which can be obtained regardless of the current conditions: ΔTP.U = P Rth Q I ( f + k5 ) I Z = k 4 x3 x3 f (9) In (9), defines the ratio of the surface area to the effective length and describes the inductor geometry for heat transferring, is the rms current,,, are the constant values depicts AC resistance depending on inductor geometry and variation of the inductor. In the PCB embedded inductor, is defined as a degree of freedom of a design which would be area divided by the perimeter of the inductor with considering the outer diameter. Larger corresponding to bigger surface can bring benefits for better heat transferring capability; however, it exacerbates achieving higher power density/efficiency [3]. III. Fig. 4. Prototyped PCB inductor designs with 6-turn (60 mm outer diameter), 13-turn (60 mm outer diameter), and 8-turn (30mm outer diameter) (8) Therefore,. is the temperature rise per the quality factor. After simplifying the equations (4)-(8): ΔTP.U = k3 13-turn By considering (9), the proposed inductor has been tested with relatively lower continuous current (5A) to keep the temperature rise limited in the predefined range. The second prototype with 13-turn (L: 150nH/ R(DC): 3mΩ/ R(AC): 50mΩ-5MHz), is proposed such that by decreasing the number of turns and increasing the height of the inductor, the inductance value is high enough to filter out the high frequency ripples and decrease the DC conduction losses simultaneously. It can be shown that because of its relatively high resistance, the temperature rise for continuous currents bigger than 10A will be increased to 50. Finally the third prototype with 8-turn (L: 50nH/ R(DC):.4mΩ/ R(AC): 8mΩ-5MHz) is designed and implemented in 4-oz copper to decrease the resistance and increase the continuous current capacity of inverter to enhance power density. The 50nH has been tested with GaN converter (EPC9033) in a Half-Bridge mode with.5mhz switching frequency, as shown in Fig. 5: IMPLEMENTED PCB EMBEDDED INDUCTOR DESIGNS By considering the initial constraints and imposing the equations from (3)-(9), different designs of PCB embedded inductors are simulated through using finite element methods in JMAG. The finite element simulations verify the predicted results for temperature distributions, current density, AC resistance, and inductance of the PCB embedded inductor. Then, after evaluation of various parameters of toroid inductors in the specified range of frequency ( < 10 ), three patterns are selected for prototyping as shown in Fig. 4. In all implemented patterns, allocating a minimum surface area for high power density, and keeping the temperature rise lower than 45 at the rated current are considered as the main design objectives, and the pros and cons of each design are investigated. In the first model with 6-turn (L: 40nH/ R(DC): 160mΩ/ R(AC): 00mΩ-5MHz), the inductor is designed such that the highest inductance to filter out the high frequency ripples is provided. Based on (3), the higher number of turns makes via s diameter smaller and also increases the petals resistance drastically. Fig. 5. Experimental Results: Voltage/Current of Inductor design-3 with Half Bridge GaN converter The total harmonic distortion (THD) of the inductors has been calculated for all the three samples to evaluate how effective they can filter out high frequency switching harmonics. Table I summarizes the THD calculated for all three prototypes and their frequency spectrums have been shown in Fig

4 In order to evaluate the impact of the resistance on the temperature rise, two different analyses are investigated from different aspects: copper thickness, and via diameters. The temperature rise variations of the petals in each design have been simulated in JMAG as shown in Fig. 7. The continuous current of each inductor is selected such that the maximum temperature rise cannot exceed 45. For the second analysis, by changing the diameter of via, the trend of total AC resistance respects to the frequency is shown for the 8-turn inductor in Fig. 8. As it can be seen, with increasing the diameter of via, the total AC resistance of inductor will be notably reduced. The slope of resistance variations in high frequencies drops significantly due the considerable reduction in skin depth variations. Fig. 6. Experimental Results: THD waveforms of the current for all three designs before (dash lines) and after (solid lines) filtering. TABLE I. THD CALCULATION OF THREE PROTOTYPES THD Design-1 Design- Design-3 Before Filtering After Filtering 49.81% 5.84% 58.9% 6.78% % 9.51% (a) (b) (c) Fig. 9. Experimental Results: Temperature rise variations of PCB embedded inductors in three different prototypes. a) design-1:6-turn b) design-:13-turn Fig. 10. Simulation Results: Asymmetric temperature distribution for different (a) Simulation Reuslts: Assymetric temperature distribuition in outer petals is more than 4 Fig. 7. Simulation Results: Temperature rise variations of three prototypes respect to copper thickness at rated current at 5MHz Switching Frequency (b) Simulation Results: Temperature difference less than 1 (c) Simulation Results: Temperature difference is around 3 Fig. 8. Simulation Results: AC resistance of PCB embedded inductor vs. frequency by variable vias diameter in 8-turn (50nH) inductor at 18A current. input/output configurations in design-: 13-turn inductor at the nominal current (10A current) 3001

5 IV. TEMPERATURE RISE ANALYSIS AND RESULTS A. Asymmetrical Temperature Rise Evaluations After analyzing three fabricated PCB embedded inductors, they are tested continuously under the nominal currents (5A for 6-turns,10A for 13-turn, and 18A for 8-turn) for 0 minutes to reach the steady state conditions to extract the temperature rise profile as shown in Fig. 9. The asymmetric temperature rise distribution among the petals is observed for all three porotypes in both simulation and hardware results as described in [3]. R th _ heatsink 1 = h(a +η N A ) heatsink fin fin (10) To prove the impact of location of input/output legs, different configurations, for the 13-turn inductor are proposed in Fig. 10. As expected, similar results are also observed after simulating both design-1: 6-turn and design-3: 8-turn not presented in this paper for reasons of space. Both simulations, and experimental results verify that the temperature reaches the highest point where the output leg is bent, and the current path is forced to be distracted. So, the convention of the temperature increment in adjacent regions is observed in all provided results. It should also be noted that the spectrum range of the temperature variations is not the same for all the three implemented designs. The highest attainable temperature is expectedly related to the inductor with 6-turn, which has higher conduction losses through the petals resulting in higher temperature rise. Regardless of the electrical characteristics, this asymmetric temperature profile relates to different geometries. To prove this fact, all three designs have been tested under hard switching frequency with Fluorinert as a non-electrical conductive liquid. The FC-40 flourinert is elected because of the advantage of having a wide range of boiling temperature, and very high volume resistivity. These capabilities provide a symmetric temperature distribution, isotherms behavior, under multiple scenarios such as fully and partially immersed in the fluorinert. Due to the constant coefficient dispatch of the liquid, the heat is smoothly dissipated along the petals, and no assymetric thermal distribution is observed. B. Temperature Rise Analysis of PCB Embedded Inductor with Heat Sink Practically, using a heat sink for cooling down the converter switches due to their fast operation when the dissipative losses exceed more than 1W is inevitable. This means heat sink adds a new dimension in the converter design, and decreases the overall power density. Therefore, by designing a customized heat sink, there is a chance to make inductor smaller such that the AC resistance of the inductor is decreased, which results higher efficiency, and enhancing the power density. Considering only conduction and natural convection transferring the heat through the heat sink and air respectively, the equivalent thermal circuit model can be described as shown in Fig. 11. As the surface area of the heat sink cannot exceed the total area of the inductor, and assuming its height is 5mm, the total thermal resistance can be calculated as below [11]: Fig. 11. Equivalent Thermal circuit model without heatsink where, h is convective heat transfer coefficient, is the base surface area, is the surface area of the fins and is the total number of the heat sink (Fig. 1). So, the total thermal resistivity of the PCB embedded inductor based on Fig. 11 will be calculated as: R = R + ( R R ) th _ total th _ heatsin k th _ PCB th _ copper Fin Area Base Area Fig. 1. Heat sink geometries selected for the PCB embedded inductor R = th _ PCB 1 A h PCB inductor (11) (1) Now, by considering the designed values for the heat sink from table-ii and imposing the equations (10)-(1), there is a possibility to shrink the inductor diameter from 60mm to 39mm for the design-1 and (6-turn and 13-turn respectively) and from 30mm to 5mm for the design-3: 8-turn with the constant temperature rise (45 ). This also means that the total resistance of the PCB embedded inductor will be decreased by 0% for the design-1 and design- and 10% of the design-3, which results in higher efficiency. The analysis shows that because of the smaller size of the heat sink in design-3 and relatively smaller in (9), the rate of size reduction in design-3 is much lower than design-1 and design-. Fin 300

6 TABLE II. PARAMETERS FOR THE DESIGN OF HEAT SINK Parameters Design1 Design Design 3 Units Number of Fins Heat Sink Height mm Fins clearance mm Fins thickness mm Convective Coefficient of Heat Sink Convective Coefficient of Air W/m^K W/m^K V. CONCLUSION In summary, the aim of this paper is to formulate the temperature rise variations of toroidal PCB embedded inductor and evaluates the design considerations for high switching frequency inverters. Equivalent circuit model of these inductors at the range of lower than 10MHz switching frequency is presented and three different prototypes are also fabricated. These designs have been tested under.5mhz switching frequency with GaN type half bridge converter. The hardware results show that all the prototypes can effectively filter high switching frequency signals with THD lower than 10%. The outcome of the analysis shows: the design-1 with the highest filtering effect has the lowest THD, but its AC resistance is very high, which is not suitable for efficient converter design. The design- has acceptable THD, but there is a room for improvement of power density and efficiency. In the last design, the THD is slightly scarified to improve the power density and AC resistance of the inductor. Furthermore, the effective parameters to impact AC resistance of PCB embedded inductors as well as asymmetrical temperature variations of the prototypes were simulated and explained. Eventually, an approach to improve power density and efficiency through size reduction of PCB embedded inductor by adding a heat sink to the converter is also investigated. [] J. Qiu and C. R. Sullivan, Design and fabrication of VHF tapped power inductors using nanogranular magnetic films, IEEE Trans. Power Electron., vol. 7, no. 1, pp , 01. [3] M. Biglarbegian, N. Shah, I. Mazhari, and B. Parkhideh, Design Considerations for High Power Density / Efficient PCB Embedded Inductor, in 3rd IEEE workshop on Wide Band Gap Devices and Applications, Nov [4] S. Mao and Y. Zhang, Design and characterization of planar integrated passive component for power converters, Proc th Eur. Conf. Power Electron. Appl., pp. 1 6, 011. [5] S. Orlandi, B. Allongue, G. Blanchot, S. Buso, F. Faccio, C. Fuentes, M. Kayal, S. Michelis, and G. Spiazzi, Optimization of shielded PCB aircore toroids for high efficiency dc-dc converters, 009 IEEE Energy Convers. Congr. Expo., pp , Sep [6] M. Madsen, A. Knott, M. a. E. Andersen, and A. P. Mynster, Printed circuit board embedded inductors for very high frequency Switch-Mode Power Supplies, 013 IEEE ECCE Asia Downunder, pp , Jun [7] H. Schneider, T. Andersen, J. D. Mønster, M. P. Madsen, A. Knott, and M. A. E. Andersen, Investigation of a Hybrid Winding Concept for Toroidal Inductors using 3D Finite Element Modeling, pp. 1 4, 013. [8] C. R. Sullivan, W. Li, S. Prabhakaran, and S. Lu, Design and Fabrication of Low-Loss Toroidal Air-Core Inductors, 007 IEEE Power Electron. Spec. Conf., pp , 007. [9] D. J. Perreault, J. H. J. Hu, J. M. Rivas, Y. H. Y. Han, O. Leitermann, R. C. N. Pilawa-Podgurski, a. Sagneri, and C. R. Sullivan, Opportunities and Challenges in Very High Frequency Power Conversion, 009 Twenty-Fourth Annu. IEEE Appl. Power Electron. Conf. Expo., 009. [10] P. Kamby, A. Knott, and M. a E. Andersen, Printed circuit board integrated toroidal radio frequency inductors, IECON Proc. (Industrial Electron. Conf., pp , 01. [11] T. L. Bergman, A. S. Lavine, F. P. Incropera, and P. Dewitt, Heat and Mass Transfer ACKNOWLEDGMENT This work is supported by Energy Production and Infrastructure Center (EPIC), University of North Carolina at Charlotte. The authors would like to thank the JMAG Corporation for using FEA software, EPC Corporation, and 3M for their great support. The authors also would like to appreciate Ivan Chan from EPC due to his tremendous help and guidance during this work. REFERENCES [1] Y. Han, G. Cheung, A. Li, C. R. Sullivan, D. J. Perreault, and S. Member, Evaluation of Magnetic Materials for Very High Frequency Power Applications, vol. 7, no. 1, pp ,