© The Institution of Engineering and Technology
The low- and mid-frequency model of the transformer with resistive load is analysed for different values of coupling coefficients. The model comprising of coupling-dependent inductances is used to derive the following characteristics: voltage gain, current gain, bandwidth, input impedance, and transformer efficiency. It is shown that in the low- and mid-frequency range, the turns ratio between the windings is a strong function of the coupling coefficient, i.e., if the coupling coefficient decreases, then the effective turns ratio reduces. A practical transformer was designed, simulated, and tested. It was observed that the magnitudes of the voltage transfer function and current transfer function exhibit a maximum value each at a different value of coupling coefficient. In addition, as the coupling coefficient decreases, the transformer bandwidth also decreases. Furthermore, analytical expressions for the transformer efficiency for resistive loads are derived and its variation with respect to frequency at different coupling coefficients is investigated. It is shown that the transformer efficiency is maximum at any coupling coefficient if the input resistance is equal to the load resistance. Experimental validation of the theoretical results was performed using a practical transformer set-up. The theoretical predictions were found to be in good agreement with the experimental results.
References
-
-
1)
-
1. Liu, C., Hu, A.P., Nair, N.K.C.: ‘Modelling and analysis of a capacitively coupled contactless power transfer system’, IET Power Electron., 2011, 4, (7), pp. 808–815 (doi: 10.1049/iet-pel.2010.0243).
-
2)
-
14. Jegadeesan, R., Guo, Y.X.: ‘Topology selection and efficiency improvement of inductive power links’, IEEE Trans. Antennas Propag., 2012, 60, (10), pp. 4846–4854 (doi: 10.1109/TAP.2012.2207325).
-
3)
-
8. Boys, J., Covic, G., Green, A.: ‘Stability and control of inductively coupled power transfer systems’, IEE Proc.-Electr. Power Appl., 2000, 147, (1), pp. 37–43 (doi: 10.1049/ip-epa:20000017).
-
4)
-
16. Greene, J.D., Gross, C.A.: ‘Nonlinear modeling of transformers’, IEEE Trans. Ind. Appl., 1998, 24, (3), pp. 434–438 (doi: 10.1109/28.2892).
-
5)
-
6. Lopera, J.M., Prieto, M.J., Pernia, A.M., et al: ‘A multiwinding modeling method for high frequency transformers and inductors’, IEEE. Trans. Power Electron., 2003, 18, (3), pp. 896–906 (doi: 10.1109/TPEL.2003.810839).
-
6)
-
3. McLyman, C.W.T.: ‘Transformer and inductor design handbook’ (Marcel Dekker, New York, NY, 2004, 3rd edn.).
-
7)
-
26. Ranstad, P., Nee, H.-P.: ‘On the distribution of AC and DC winding capacitances in high-frequency power transformers with rectifier loads’, IEEE Trans. Ind. Electron., 2011, 58, (5), pp. 1789–1798 (doi: 10.1109/TIE.2010.2055773).
-
8)
-
2. Musavi, F., Eberle, W.: ‘Overview of wireless power transfer technologies for electric vehicle battery charging’, IET Power Electron., 2014, 7, (1), pp. 60–66 (doi: 10.1049/iet-pel.2013.0047).
-
9)
-
24. Song, S., Liu, G., Gong, W., et al: ‘Electromagnetic analysis of a new magnetic core of transformer for a contactless electric vehicle charging’. Proc. Int. Conf. on Electrical Machines and Systems, August 2011.
-
10)
-
29. Dalessandro, L., Karrer, N., Kolar, J.W.: ‘High-performance planar isolated current sensor for power electronics applications’, IEEE Trans. Power Electron., 2007, 22, (5), pp. 1682–1692 (doi: 10.1109/TPEL.2007.904198).
-
11)
-
12. Yu, X.J., Cheng, J.M.: ‘Leakage inductance compensation for loosely coupled transformer considering parasitic resistance’, IET Electron. Lett., 2010, 46, (10), pp. 717–719 (doi: 10.1049/el.2010.0317).
-
12)
-
17. Boys, J.T., Covic, G.A., Yong, X.X.: ‘Modeling and controller design of ICPT pick-ups’. Proc. Int. Conf. Power System Technology, 2002, vol. 3, pp. 1602–1606.
-
13)
-
34. Kondrath, N., Kazimierczuk, M.K.: ‘Inductor winding loss owing to skin and proximity effects including harmonics in non-isolated pulse-width modulated dc-dc converters operating in continuous conduction mode’, IET Power Electron., 2010, 3, (6), pp. 989–1000 (doi: 10.1049/iet-pel.2009.0299).
-
14)
-
35. Smeets, J.P.C., Krop, D.C.J., Jansen, J.W., et al: ‘Optimal design of a pot core rotating transformer’. Proc. IEEE Energy Conversion Congress and Exposition, September 2010, pp. 4390–4397.
-
15)
-
4. Ayachit, A., Kazimierczuk, M.K.: ‘Thermal effects on inductor winding resistance at high frequencies’, IEEE Magn. Lett., 2013, 4, (1).
-
16)
-
37. Kazimierczuk, M.K., Sekiya, H.: ‘Design of AC resonant inductors using area product method’. Proc. IEEE Energy Conversion Congress and Exposition, September 2009, pp. 994–1001.
-
17)
-
20. Dalessandro, L., Odendaal, W.G., Kolar, J.W.: ‘HF characterization and non-linear modeling of a gapped toroidal magnetic structure’, IEEE Trans. Power Electron., 2006, 21, (5), pp. 1167–1175 (doi: 10.1109/TPEL.2006.880357).
-
18)
-
5. Liu, X.C., Wang, G.F., Ding, W.: ‘Efficient circuit modelling of wireless power transfer to multiple devices’, IET Power Electron., 2014, 7, (12), pp. 3017–3022 (doi: 10.1049/iet-pel.2013.0969).
-
19)
-
11. Dalessandro, L., Cavalcante, F.S., Kolar, J.K.: ‘Self-capacitance of high-voltage transformers’, IEEE Trans. Power Electron., 2007, 22, (5), pp. 2081–2092 (doi: 10.1109/TPEL.2007.904252).
-
20)
-
36. Howard, T.O., Carpenter, K.H.: ‘A numerical study of the coupling coefficients for pot core transformers’, IEEE Trans. Magn., 1995, 31, (3), pp. 2249–2253 (doi: 10.1109/20.376237).
-
21)
-
25. Lee, S.-H., Lorenz, R.D.: ‘Development and validation of model for 95%-efficiency 220 W wireless power transfer over a 30 cm air gap’, IEEE Trans. Ind. Appl., 2011, 47, (6), pp. 2495–2504 (doi: 10.1109/TIA.2011.2168555).
-
22)
-
10. Sanghoon, C., Yon-Hae, K., Kang, S.-Y., et al: ‘Circuit-model-based analysis of a wireless energy-transfer system via coupled magnetic resonances’, IEEE Trans. Ind. Electron., 2010, 58, (7), pp. 2906–2914.
-
23)
-
15. Faiz, J., Abed-Ashtiani, B., Byat, M.R.: ‘Lumped complete equivalent circuit of a coreless high-frequency transformer’, IEEE Trans. Magn., 1997, 33, (1), pp. 703–707 (doi: 10.1109/20.560102).
-
24)
-
14. Kondrath, N., Kazimierczuk, M.K.: ‘Bandwidth of current transformers’, IEEE Trans. Instrum. Meas., 2009, 58, (6), pp. 2008–2016 (doi: 10.1109/TIM.2008.2006134).
-
25)
-
2. Boys, J.T., Covic, G.A., Elliott, G.A.J.: ‘Pick-up transformer for ICPT applications’, Electron. Lett., 2002, 38, (21), pp. 1276–1278 (doi: 10.1049/el:20020874).
-
26)
-
7. Youssef, M.Z., Jain, P.K.: ‘Series-parallel resonant converter in self-sustained oscillation mode with the high-frequency transformer-leakage-inductance effect: analysis, modeling, and design’, IEEE Trans. Ind. Electron., 2007, 54, (3), pp. 1329–1341 (doi: 10.1109/TIE.2007.892742).
-
27)
-
32. Bartoli, M., Noferi, N., Reatti, A., et al: ‘Modeling litz-wire winding losses in high-frequency power inductors’, IEEE Power Electron. Spec. Conf., 1996, 2, pp. 1690–1696.
-
28)
-
48. Zierhofer, C., Hochmair, E.: ‘Geometric approach for coupling enhancement of magnetically coupled coils’, IEEE Trans. Biomed. Eng., 1996, 43, (7), pp. 708–714 (doi: 10.1109/10.503178).
-
29)
-
31. Hurley, W.G., Wȯlfle, W.H., Breslin, J.G.: ‘Optimized transformer design: inclusive of high-frequency effects’, IEEE Trans. Power Electron., 1998, 13, (4), pp. 651–659 (doi: 10.1109/63.704133).
-
30)
-
42. Magnetics, Inc.: ‘Ferrite Cores’, 2013.
-
31)
-
4. Boys, J.T., Elliott, G.A.J., Covic, G.A.: ‘An appropriate magnetic coupling coefficient for the design and comparison of ICPT pickups’, IEEE Trans. Power Electron., 2007, 22, (1), pp. 333–335 (doi: 10.1109/TPEL.2006.887590).
-
32)
-
29. Witulski, A.F.: ‘Introduction to modeling of transformers and coupled inductors’, IEEE Trans. Power Electron., 1995, 10, (3), pp. 349–357 (doi: 10.1109/63.388001).
-
33)
-
26. Wodja, R.P., Kazimierczuk, M.K.: ‘Winding resistance of litz-wire and multi-strand inductors’, IET Power Electron., 2012, 5, (2), pp. 257–268 (doi: 10.1049/iet-pel.2010.0359).
-
34)
-
40. Wojda, R.P., Kazimierczuk, M.K.: ‘Analytical winding size optimisation of solid-round-wire windings’, IEEE Trans. Ind. Electron., 2013, 60, (3), pp. 1033–1041 (doi: 10.1109/TIE.2012.2189543).
-
35)
-
33. Lavers, J.D., Bolborici, V.: ‘Loss comparison in the design of high frequency inductors and transformers’, IEEE Trans. Magn., 1999, 35, (5), pp. 3541–3543 (doi: 10.1109/20.800583).
-
36)
-
38. Cogirore, B., Keradec, J.P., Barbaroux, J.: ‘The two-winding transformer: an experimental method to obtain a wide frequency range equivalent circuit’, IEEE Trans. Instrum. Meas., 1994, 43, (2), pp. 364–371 (doi: 10.1109/19.293449).
-
37)
-
23. Myunghyo, R., Yonghwan, P., Juwon, B., et al: ‘Comparison and analysis of the contactless power transfer systems using the parameters of the contactless transformer’. Proc. IEEE Power Electronics Specialist Conf. Record, June 2006, pp. 1–6.
-
38)
-
2. den Bossche, A.V., Valchev, V.C.: ‘Inductors and transformers for power electronics’ (CRC Press, FL, USA, 2005).
-
39)
-
41. Wojda, R.P., Kazimierczuk, M.K.: ‘Analytical optimisation of solid-round-wire windings conducting dc and ac non-sinusoidal periodic currents’, IET Power Electron., 2013, 6, (7), pp. 1462–1474 (doi: 10.1049/iet-pel.2012.0347).
-
40)
-
1. Kazimierczuk, M.K.: ‘High-frequency magnetic components’ (John Wiley and Co., Chichester, UK, 2014, 2nd edn.).
-
41)
-
30. Petkov, R.: ‘Optimum design of a high-power, high-frequency transformer’, IEEE Trans. Power Electron., 1996, 11, (1), pp. 33–42 (doi: 10.1109/63.484414).
-
42)
-
13. Hayano, S., Nakajima, Y., Saotome, H., et al: ‘A new type of high frequency transformer’, IEEE Trans. Magn., 1991, 27, (6), pp. 5205–5207 (doi: 10.1109/20.278788).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cds.2015.0147
Related content
content/journals/10.1049/iet-cds.2015.0147
pub_keyword,iet_inspecKeyword,pub_concept
6
6