Analysis and design of high frequency gapped transformers and planar transformers in LLC resonant converters

The magnetic shunt is generally inserted in a planar transformer to increase the leakage inductance which can be utilized as the series inductor in resonant circuits such as the LLC resonant converter. This paper presents a calculation methodology for the leakage inductance of the transformer with a magnetic shunt by means of the stored magnetic energy in the primary and secondary sides of the transformer using the magnetomotive force (MMF) variation method, as well as the stored energy in the shunt based on the reluctance model. The detailed calculation method is described. Both the FEA simulation and the experimental results have proven the validity of the proposed calculation method for leakage inductance. [J.2] Z. Ouyang, J. Zhang and W. G. Hurley, “Calculation of Leakage Inductance for High Frequency Transformers,” IEEE Trans. Power Electron. , PP(99):1. (In press) Abstract: Frequency dependent leakage inductance is often observed. High frequency eddy current effects cause a reduction in leakage inductance. The proximity effect between adjacent layers is responsible for the reduction of leakage inductance. This paper gives a detailed analysis of high frequency leakage inductance and Frequency dependent leakage inductance is often observed. High frequency eddy current effects cause a reduction in leakage inductance. The proximity effect between adjacent layers is responsible for the reduction of leakage inductance. This paper gives a detailed analysis of high frequency leakage inductance and APPENDIX E. PUBLICATIONS 169 proposes an accurate prediction methodology. High frequency leakage inductances in several interleaved winding configurations are also discussed. Interleaved winding configurations actually give a smaller degree of reduction of leakage induction at high frequency. Finite Element Analysis (FEA) simulation and measurement validate the models. [J.3] C. Feeney, J. Zhang and M. Duffy, “Ac Winding Loss of Phase-Shifted Coupled Windings”, IEEE Trans. Power Electron. , 2015. (In press) Abstract: In circuits where there is an inherent phase shift angle between coupled winding currents such as in coupled inductors, it is important to accurately calculate the ac winding loss at the correct phase shift and frequency. Phase shift between winding currents can cause the ac winding loss to vary significantly due to changes in the magnetic field distribution. This paper presents an analysis of winding loss for the general case of coupled windings with arbitrary phase shifted currents and its effect in a number of practical devices. A detailed approach to analytically calculate ac winding loss in microfabricated coupled stripline inductors is presented along with a derivation of the resistance matrix for the device. The analysis and methodology is then validated using finite element analysis and experimental results. In circuits where there is an inherent phase shift angle between coupled winding currents such as in coupled inductors, it is important to accurately calculate the ac winding loss at the correct phase shift and frequency. Phase shift between winding currents can cause the ac winding loss to vary significantly due to changes in the magnetic field distribution. This paper presents an analysis of winding loss for the general case of coupled windings with arbitrary phase shifted currents and its effect in a number of practical devices. A detailed approach to analytically calculate ac winding loss in microfabricated coupled stripline inductors is presented along with a derivation of the resistance matrix for the device. The analysis and methodology is then validated using finite element analysis and experimental results. [J.4] W. G. Hurley, M. C. Duffy, J. Zhang, I. Lope, B. Kunz and W. H. Wölfle, “A Unified Approach to the Calculation of Self and Mutual Inductance for Coaxial Coils in Air”, IEEE Trans. Power Electron. , 2015. (In press) Abstract: This paper extends a previous formula for the mutual inductance between single turn coils to include all coils in air with rectangular cross-sections, without any restrictions on the dimensions (including overlapping coils). The formula is compared with a wide spectrum of examples from the literature and agreement is excellent in every case. Experimental results are presented to validate the formula for both solenoid and disk coils. The formula is relevant to coreless transformers, inductive coupling, wireless power transfer and leakage inductance in resonant converters. This paper extends a previous formula for the mutual inductance between single turn coils to include all coils in air with rectangular cross-sections, without any restrictions on the dimensions (including overlapping coils). The formula is compared with a wide spectrum of examples from the literature and agreement is excellent in every case. Experimental results are presented to validate the formula for both solenoid and disk coils. The formula is relevant to coreless transformers, inductive coupling, wireless power transfer and leakage inductance in resonant converters. APPENDIX E. PUBLICATIONS 170 Conference Papers [C.1] J. Zhang, W. G. Hurley, W. H. Wolfle and M. C. Duffy, “Optimized design of LLC resonant converters incorporating planar magnetics,” in Proc. IEEE Appl. Power Electron. Conf. Expo. (APEC), 2013, pp. 1683-1688. Abstract: The LLC resonant converter is widely applied as front-end dc-dc conversion for distributed power system and intermediate conversion for renewable energy power generation systems. A continuous miniaturization of LLC resonant converter incorporating planar magnetics is leading to higher performance, higher efficiency and decreasing costs. This paper outlines an improved design methodology for LLC resonant converters based on judicious choice of the circuit components including the resonant inductor, the transformer magnetizing inductor and the resonant capacitor as well as the dead time. Planar magnetics are playing a significant role in the low profile DC/DC converter applications. With the planar transformer employed, the parameters can be controlled precisely which is of great importance to the operating performance of the converter. Several structures of the planar transformer applied in LLC resonant converter are investigated. Finally, the comparison of the proposed structures basis on the ac resistance and the winding losses are presented The LLC resonant converter is widely applied as front-end dc-dc conversion for distributed power system and intermediate conversion for renewable energy power generation systems. A continuous miniaturization of LLC resonant converter incorporating planar magnetics is leading to higher performance, higher efficiency and decreasing costs. This paper outlines an improved design methodology for LLC resonant converters based on judicious choice of the circuit components including the resonant inductor, the transformer magnetizing inductor and the resonant capacitor as well as the dead time. Planar magnetics are playing a significant role in the low profile DC/DC converter applications. With the planar transformer employed, the parameters can be controlled precisely which is of great importance to the operating performance of the converter. Several structures of the planar transformer applied in LLC resonant converter are investigated. Finally, the comparison of the proposed structures basis on the ac resistance and the winding losses are presented [C.2] J. Zhang, Z. Ouyang, M. C. Duffy, M. A. E. Andersen and W. G. Hurley, “Leakage inductance calculation for planar transformers with a magnetic shunt,” in Proc. IEEE Energy Convers. Congr. Expo. (ECCE), 2013, pp. 643-648. Abstract: The magnetic shunt is generally inserted in a planar transformer to increase the leakage inductance which can be utilized as the series inductor in resonant circuits such as the LLC resonant converter. This paper presents a calculation methodology for the leakage inductance of the transformer with a magnetic shunt by means of the stored magnetic energy in the primary and secondary sides of the transformer using the magnetomotive force (MMF) variation method, as well as the stored energy in the shunt based on the reluctance model. The detailed calculation method is described. Both the FEA simulation and the experimental results have proven the validity of the proposed calculation method for leakage inductance. The magnetic shunt is generally inserted in a planar transformer to increase the leakage inductance which can be utilized as the series inductor in resonant circuits such as the LLC resonant converter. This paper presents a calculation methodology for the leakage inductance of the transformer with a magnetic shunt by means of the stored magnetic energy in the primary and secondary sides of the transformer using the magnetomotive force (MMF) variation method, as well as the stored energy in the shunt based on the reluctance model. The detailed calculation method is described. Both the FEA simulation and the experimental results have proven the validity of the proposed calculation method for leakage inductance. APPENDIX E. PUBLICATIONS 171 [C.3] J. Zhang, W. G. Hurley and W. H. Wolfle, “Gapped transformer design methodology and implementation for LLC resonant converters,” in Proc. IEEE Appl. Power Electron. Conf. Expo. (APEC), 2014, pp. 726-731. Abstract: In the LLC resonant converter, the air gap is generally positioned in the core of the transformer for proper magnetizing inductance. Traditional transformer design methods assume infinite permeability of the core and no energy stored in the core. The improved design methodology for the gapped transformer is proposed with the optimum relative permeability and gap selection to meet the temperature rise and the magnetizing inductance requirements. The magnetizing current influences the magnetic flux in the core leading to the core saturation and core loss, while the resonant current contributes to th