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High-Frequency Modelling of Surface-Mount Power Inductor Used in Switching DC-DC Converters 1 12 3 Josip Bačmaga , Raul Blečić , Renaud Gillon and Adrijan Barić 1 1 University of Zagreb Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia Tel: +385 (0)1 6129547, fax: +385 (0)1 6129653, e-mail: [email protected] 2 KU Leuven, ESAT-TELEMIC, Kasteelpark Arenberg 10, 3001 Leuven, Belgium 3 ON Semiconductor Belgium BVBA, Westerring 15, 9700 Oudenaarde, Belgium Test Procedure and Measurement Methods Abstract Introduction Two-port “series” method Two-port “shunt” method • • • • • • • • • to extract the inductor model using yij parameters and pi-network [11] port-to-port admittance: Y3 = −(y12 + y21)/2 pad-to-ground admittances: Y1 = y11 − Y3, Y2 = y22 − Y3 50 W CBCPW-1 CBCPW-2 P1 P2 0 0 P2 P1 50 W P20 P2 L–DUT P10 • model extraction: model parameters are optimized in ADS [10] to the measurement results obtained by two-port “series” method R3 • R3 — skin-effect at mid freqs • C1 — P10-to-ground capacitance • C2 — P20-to-ground capacitance • L1 — inductance • R1 — DC resistance • R2-C3 — skin-effect at high freqs C3 R2 P10 L1, nH R1, mΩ R2, Ω R3, Ω C1, pF C2, pF C3, pF 81.26 0.22 41.05 69.47 1.50 2.26 46.40 P20 R1 L1 Z = 1/Y3 C1 • model validation: model is compared to the measurement results obtained by two-port “shunt” method C2 Model extraction — “series” method Model validation — “shunt” method 40 40 10 1 10 0 10 −1 10 −2 10 −3 10 Meas. Model 1 10 100 Frequency, f [MHz] 20 Meas. Model −20 1 10 100 Frequency, f [MHz] 210 Meas. 180 Model 150 120 90 60 30 0 1 10 100 Frequency, f [MHz] 0 1 0.1 Meas. Model 1 10 100 Frequency, f [MHz] Phase(Z3 ) [deg] 40 80 60 40 20 0 −20 2 10 1 10 0 10 −1 10 −2 10 −3 10 −4 10 Meas. Model 1 10 100 Frequency, f [MHz] Inductance, L [nH] 2 60 10 Mag(Z3 ) [Ω] Meas. Model 0.1 1 10 100 Frequency, f [MHz] 100 80 Re(Z3 ) [Ω] 1 Phase(1/Y3 ) [deg] 100 10 10 90 75 60 45 30 15 0 Meas. Model 1 10 100 Frequency, f [MHz] Meas. Model 1 10 100 Frequency, f [MHz] Discussion 2 • test fixture impedance obtained from the “shunt” measurements before the de-embedding of the test fixture parasitics is performed: z12 + z21 z12 + z21 + z22 − Z1 + Z2 = z11 − 2 2 = z11 + z22 − (z12 + z21) • test fixture resistance is an order of magnitude larger than the resistance of the inductor at low frequencies for the “series” measurements • discrepancy between the two-port methods at low frequencies is caused by the test fixture parasitics included into the measured impedance • comparison of the model and “shunt” measurements, which are less sensitive to parasitics of the test fixture, shows that the “series” measurements may be used for the extraction of an accurate inductor model • “series” measurements enable the extraction of the parasitic pad-to-ground capacitances C1 and C2, while the “shunt” measurements hide either C1 or C2 10 1 10 0 “series”-DUT “shunt”-DUT test fixture Inductance, L [nH] [1] W. G. Hurley and W. H. Wölfle, Transformers and Inductors for Power Electronics: Theory, Design and Applications, John Wiley & Sons, 2013. [2] I. Jovanović, “Power Supply Technology - Past, Present and Future,” in Proc. of the Power Conversion and Intelligent Motion Conf. (PCIM China), Mar. 2013, pp. 3–15. [3] G. Zhu et al., “Modeling and Analysis of Coupled Inductors in Power Converters,” in Proc. 24th Annual IEEE Applied Power Electronics Conference and Exposition (APEC), Feb. 2009, pp. 83–89. [4] R. Wrobel et al., “Derivation and Scaling of AC Copper Loss in Thermal Modeling of Electrical Machines,” IEEE Trans. on Ind. Electronics, vol. 61, no. 8, pp. 4412–4420, Aug. 2014. [5] M. S. Perdigao et al., “Large-Signal Characterization of Power Inductors in EV Bidirectional DC-DC Converters Focused on Core Size Optimization,” IEEE Trans. on Ind. Electronics, vol. 62, no. 5, pp. 3042–3051, May 2015. [6] H. Kosai et al., “Coupled Inductor Characterization for a High Performance Interleaved Boost Converter,” IEEE Trans. on Magnetics, vol. 45, no. 10, pp. 4812–4815, Oct. 2009. [7] SMT Power Inductor: Power Beads - PA051XNL, PA121XNL, PA151XNL Series, “Power Beads - PA051XNL,” Pulse, 2007. [8] R. N. Simmons, Coplanar Waveguide Circuits, Components, and Systems, John Wiley, 2001. [9] T. Mandic et al., “Characterizing the TEM Cell Electric and Magnetic Field Coupling to PCB Transmission Lines,” IEEE Trans. on Electromagnetic Compatibility, vol. 54, no. 5, pp. 976–985, Oct. 2012. [10] ADS 2015, Simulation-Analog RF, Keysight Technologies, 2015. [11] D. M. Pozar, Microwave Engineering, John Wiley, 3rd ed., 2005. [12] I. Novak, “Measuring MilliOhms and PicoHenrys in Power-Distribution Networks,” in DesignCon 2000, Santa Clara, CA, USA, Feb. 2000. CBCPW-1 Lumped-Element Model of the Inductor −4 References 50 W Inductance, L [nH] in this paper, a frequency-domain characterization of a surface-mount power inductor [7] is performed and a lumped-element model with frequency-independent parameters is extracted extracted model allows estimation of the impedance characteristics of the inductor in a broad frequency range, which also includes the frequencies of the higher harmonics of the switching frequency of a DC-DC converter impact of the skin effect on the impedance characteristics can be also evaluated by the extracted model P1 Mag(1/Y3 ) [Ω] analyses performed in [3], [4], [5] and [6] investigate the influence of power inductors on behaviour of switching DC-DC converters, but do not estimate the impedance of the analyzed power inductors at high frequencies to validate the extracted inductor model using zij parameters and T-network [11] impedance: Z3 = (z12 + z21)/2 model compared to the measurements more effective for low-impedance DUTs [12] L–DUT Re(1/Y3 ) [Ω] one of the most important parts of the design of highfrequency switching DC-DC converters is the choice of an appropriate power inductor [1] improvements in operation of switching DC-DC converters are guided by advancements in semiconductors while much less attention is given to the analysis of power inductors [2] impedance characteristics of the inductor at high frequencies are needed to accurately determine AC power losses and power efficiency of DC-DC converters ⇒ frequency characterization manufacturers of inductors for power applications usually do not declare parameters used to predict the behaviour of inductors at high frequencies CBCPW-2 50 W Resistance [Ω] A lumped-element model of a 72-nH surface-mount power inductor used in high-frequency DC-DC converters is presented. The model parameters are optimized to fit the measured impedance characteristics. Two different topologies of the characterization set-up are used: the first one to extract the model and the second to validate its impedance characteristics up to 300 MHz. The extracted model demonstrates the impact of skin effect on the impedance characteristics. The model consists of frequency-independent components. The extracted model allows accurate estimation of AC power losses of the inductor and power efficiency of a DC-DC converter. 1) Sij parameters of the inductor are measured using the both measurement methods up to the ports P1 and P2 2) parasitics of the test fixture (SMA connectors [9] and CBCPW transmission line segments [8]) are de-embedded up to P10 and P20 from the measured Sij parameters for both set-ups to obtain the Sij parameters of the DUT 3) yij parameters of the DUT are calculated from the measured Sij parameters [11] of the DUT that are obtained by two-port “series” method 4) zij parameters of the DUT are calculated from the measured Sij parameters [11] of the DUT that are obtained by two-port “shunt” method 10 −1 10 −2 10 −3 10 1 10 100 Frequency, f [MHz] 210 180 150 120 90 60 30 0 “series”-DUT “shunt”-DUT test fixture 1 10 100 Frequency, f [MHz] Conclusion X extracted inductor model is simple, valid in a broad frequency range, built of frequency-independent lumped elements that represent the influence of skin-effect on inductor characteristics X evaluated power inductor characteristics enable to estimate accurately the inductor losses at the harmonics of the switching frequency and, consequently, the power efficiency of the DC-DC converter