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: josip.bacmaga@fer.hr
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
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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