This paper presents the design and modeling of a square inductor for its integration in Buck converter
DC-DC. The first, we calculate the value of inductance. The second, we descript our inductor; dimensioning
and electrical model. A buck micro converter schematic simulation coupled with ideal and integrated
inductor was presented. This conceptual model of the buck is best understood in terms of the relation
between current and voltage of the inductor. Finely, we have simulated the electromagnetic effects in two
cases. The first case, an inductor in the air, the second case with substrate. Our geometry is created en 3D
space dimension

Benhadda, Y.

Derkaoui, M.

Hamid, A.

Lebey, T.

This paper presents the design and modeling of a square inductor for its integration in Buck converter DC-DC. The first, we calculate the value of inductance. The second, we descript our inductor; dimensioning and electrical model. A buck micro converter schematic simulation coupled with ideal and integrated inductor was presented. This conceptual model of the buck is best understood in terms of the relation between current and voltage of the inductor. Finely, we have simulated the electromagnetic effects in two cases. The first case, an inductor in the air, the second case with substrate. Our geometry is created en 3D space dimension

Y. Benhadda

A. Hamid

T. Lebey

M. Derkaoui

CiteSeerX

Design and Modeling of an Integrated Inductor in a Buck Converter DC-DC

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 7 No 2, 02006(6pp) (2015) Том 7 № 2, 02006(6cc) (2015)   2077-6772/2015/7(2)02006(6) 02006-1  2015 Sumy State University Design and Modeling of an Integrated Inductor in a Buck Converter DC-DC  Y. Benhadda1,*, A. Hamid1, T. Lebey2, M. Derkaoui1  1 University of Sciences and Technology of Oran (USTO- MB) 31000 Algeria 2 University of Paul Sabatier, LAPLACE Laboratory, Toulouse, France  (Received 20 March 2015; revised manuscript received 05 June 2015; published online 10 June 2015)  This paper presents the design and modeling of a square inductor for its integration in Buck converter DC-DC. The first, we calculate the value of inductance. The second, we descript our inductor; dimensioning and electrical model. A buck micro converter schematic simulation coupled with ideal and integrated  inductor was presented. This conceptual model of the buck is best understood in terms of the relation  between current and voltage of the inductor. Finely, we have simulated the electromagnetic effects in two cases. The first case, an inductor in the air, the second case with substrate. Our geometry is created en 3D space dimension.  Keywords: Inductor, Buck converter, Integrated.   PACS number: 84.32.Hh                                                                   * benhadda_yamina@yahoo.fr 1. INTRODUCTION  In Power electronics, modeling of passive compo-nents constitute a particularly important issue. Indeed, the magnetic components, inductors and transformers are mainly used to transmit or store energy. The pas-sive elements volume reduction leads to a mounted in operating frequency, but this increase in frequency causes an increase in losses. If the behavior of some components is relatively insensitive to temperature changes, it is not the same thing for magnetic compo-nents whose characteristics depend strongly on the temperature. The losses freed in the form of heat are become a major concern due to the reduction of trade with the outside surfaces and increasing the density of losses. The aim of our work is a dimensioning a square inductor that will be integrated in a DC-DC micro-converter.  2. PRESENTATION OF THE MICRO-CONVERTER  We have chosen a Buck micro-converter continuous-continuous step-down (Fig.1) [1-3]. The inductor to in-tegrate will thus be dimensioned for this type of appli-cation. Input voltage, Vin  3 V. Output voltage, Vout  1.5 V. Maximum current ILmax  0.65 A. Output power, Pout  0.6 W. Frequency of operation, f  1 MHz.    Fig. 1 – Buck converter  The converter operates in two modes of conduction discontinuous conduction when the current required by the load is low, continuous conduction for higher cur-rents (Fig. 2). The voltage and current involved are relatively low. In order to increase the efficiency of the converter, energy losses must be minimized.    Fig. 2 – Evolution of the voltages and currents with time in an ideal buck converter  The average output current Iout is calculated by formula (1)   outoutoutPIV  (1)  Iout  4 A, Iout  IL – IC, IC  0, Iout  IL. The peak am-plitude of the current through the inductor is calculat-ed by formula (2)   max minL L LI I I    (2)  The average current LI  is expressed as follows (3)   max min2L LLI II   (3)  Where  min max2L out LI I I  , min 0.15LI A , 0.5ALI   and 0.5out inV V   .   Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015)   02006-2 The current which flows through the inductor in-creases according to relation (4)   (1 ) inLVILf    (4)  We can calculate the value of the inductance L [2] according to relation (5)   (1 ) inlVLI f  (5)  The maximum energy stored in the inductor is giv-en by relation (6)   212outW LI  (6)  The volumetric energy density of the ferrite is given by the equation (7)   2maxmax02vBWr   (7) maxB : The maximum magnetic induction supported by the ferrite r : The relative permeability 0 : The magnetic permeability of the free space The volume of the ferrite is given by relation (8)   olmaxvWVW  (8)  The ferrite’s thickness is tSub  97 m, thus the vol-ume will be 32100 2100 97μm  .  3. DIMENSIONING OF THE INTEGRATED  INDUCTOR  The geometry parameters characterizing the inte-grated inductor (Fig. 3) are the number of turns n, the width of the conductor w, thickness of the conductor t, the spacing between conductor s, length of the conduc-tor l, the outer diameter dout and input diameter din.    Fig. 3 – Geometry of a square spiral integrated inductor, (a) 3D view, (a) 2D view  We find in the literature several formulas which al-low us to calculate the number of turns n according to the value of inductance L, we chose the Weeler’s [4-5] formula (9)   21 021avgmwn dL Kk (9)  Where, we define the average diameter as ( ) / 2avg out ind d d   [6]. mA the factor’s form defined as /m out in out inA d d d d   .The coefficients k1 and k2 are defined for each geometry. For a square inductor spiral, k1  2.34 and k2  2.75. The spacing between conductors is expressed as fol-lows (10)   22( 1)out ind d wnsn  (10)  The length of the trace is expressed as follows (11)   4 [ ( 1) ]outl n d n s nw s      (11)  The skin thickness is defined as (12)   f , (12)  where  represent the resistivity of the conductor,  Copper  1.710 – 8 m and  its magnetic permeability. So that the current flows in the entire conductor, it is necessary that one of the following conditions is filled, 2w  or 2t  , 92.8μm  , 40μmt  , 120μmw  . Table 1 contains the specifications and the design results of the square spiral integrated inductor.  Table 1 – Design results of the square spiral integrated  inductor  Parameter Value Inductance, L (H) 1.5  External diameter, dout (mm) 2  Internal diameter, din (mm) 0.4  Number of turns, n  2 Thickness of the conductor, t (m) 40  Width of the conductor, w (m) 120  Spacing between conductor, s (m) 280  Length of the conductor, l (m) 0.0116  4. ELECTRICAL MODEL  The equivalent electrical model of the integrated inductor [6-10] [15-16] is shown in Fig. 4. The series resistance Rs, can be approximated as (13)   sR l wt  (13)  The parasitic capacitive can be modeled as Cs (14)   20sC t l s  (14)  where, ε0 is the permittivity of free space, 12 10 8.854187.10 Mm .    а b  DESING AND MODELING OF AN INTEGRATED INDUCTOR… J. NANO- ELECTRON. PHYS. 7, 02006 (2015)   02006-3   Fig. 4 – Equivalent electrical model  The substrate capacitance Csub and resistance Rsub are approximately proportional to the area occupied by the integrated inductor and can be expressed as (15), (16).   012sub rsublwCt   (15)   2 subsub subtRlw  (16)  Cox oxide capacitance SiO2 can be expressed as (17)   0 oxoxoxC lwt     , (17)  where ,r sub  represent respectively the relative permit-tivity and the resistivity of substrate and oxt the oxide thickness. In our case, 10r  , 645.10 msub   and 80µmoxt  . The geometry of a square spiral integrated inductor on substrate [13-14] is shown in Fig. 5.     Fig. 5 – Geometry of a square spiral integrated inductor on substrate, (a) 3D view, (b) 2D view  The efficiency of integrated inductor is calculated [16-20] according by relation (18)    stocked energie2dissipated energieQ   (18) Table 2 presents electrical parameters of the inte-grated inductor.  Table 2 – Electricals Parameters of the Integrated Inductor  Electricals parameters Values ( )sR   0.04 ( )subR   0.006 (pF)sC  0.014 (pF)oxC  0.598 (pF)subC  0.631 Q  98.56  Fig. 6 shows the shape of the quality factor as a function of frequency.  0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 106020406080100120140160180200Frequency (MHz)Quality Factor Q  Fig. 6 – Quality factor Q  from integrated inductor  5. SIMULATION OF THE OF THE MICRO  CONVERTER  In this simulation, the circuit of Fig. 7 contains an ideal inductor and the Fig. 8 shows the waveform of the output voltage and current of the Buck micro converter. When the switch is closed, the voltage across the induc-tor is VL  Vin – Vout. The current through the inductor rises linearly. As the diode is reverse-biased by the voltage source, no current flows through it. When the switch is opened, the diode is forward biased. The volt-age across the inductor is VL  – Vout. The Current through inductor decreases.    Fig. 7 – Schematic of buck micro converter coupled with ideal inductor а b  Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015)   02006-4   Fig. 8 – Waveforms of voltage and current of buck micro con-verter coupled with ideal inductor  Fig. 9 shows the schematic of micro converter simu-lated coupled with integrated inductor. The simulated results are indicated in Fig. 10. We observe the same result with ideal inductor.    Fig. 9 – Schematic of buck micro converter coupled with inte-grated inductor  6. SIMULATION 3D OF THE ELECTROMAG-NETIC EFFECTS IN A INTEGRATED  INDUCTOR  In this section, we present the distribution of the electromagnetic field in a inductor in the air and on substrate [21] using finite elements method [22-24]. Fig. 11 shows the distribution of magnetic field in the inductor in the air. Fig. 12 shows the distribution of magnetic field lines in the inductor in the air.   Fig. 10 – Waveforms of voltage and current of buck micro converter coupled with integrated inductor    Fig. 11 – Distribution of magnetic field in the inductor in the air    а  DESING AND MODELING OF AN INTEGRATED INDUCTOR… J. NANO- ELECTRON. PHYS. 7, 02006 (2015)   02006-5     Fig. 12 – Distribution of magnetic field lines in the inductor in the air  Fig. 13 shows the distribution of magnetic field in the inductor on substrate.    Fig. 13 – Distribution of magnetic field in the inductor on substrate  Fig. 14 shows the distribution of magnetic field lines in the inductor on substrate. When we insert a sub-strate, the majority of the magnetic field lines are con-centrated at the walls of the magnetic block. So, we conclude that the substrate layer is required to have a good electromagnetic compatibility in the case of the integration inductor.       Fig. 14 – Distribution of magnetic field lines in the inductor on substrate  7. CONCLUSION  In this paper, we have presented the dimensioning, the modeling and the simulation of a square inductor. We have visualized the electromagnetic phenomenon in inductor in the air and on substrate. The aim of this simulation is to study the electromagnetic compatibility of the inductor integrated in Buck micro converter  DC-DC.  b c a b c  Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015)   02006-6 REFERENCES  1. P. Reimann, Phys. Rep. 361, 57 (2002). 2. G.S. Vorobjov, V.O. Zhurba, A.S. Krivets, J. Nano- Elec-tron. Phys. 2 No 4, 47 (2010). 3. L. Xian, Y. Wang An, 11th IEEE Int. Conf. Control Auto-mation (ICCA) 1067 (2014). 4. A. Allaoui, A. Hamid, P. Spiterri, V. Bley, T. Lebey, J. Low Power Electron. 11 No 1, 63 (2015). 5. M. Derkaoui, A. Hamid, T. Lebey, R. Melati, Telkomnika 11 No 4 (2013). 6. S.S. Mohan, M.D.M. Hershenson, S.P. Boyd, T.H. Lee, IEEE J. Solid-State Circuits 34 No 10, 1419 (1999). 7. N. Arbabi, M. Najmabadi, V. Devabhaktuni, M. Yagoub, Canadian Conf. Electrical Computer Eng. (CCECE), 99 (Vancouver, BC: Canada: 2007). 8. E.D. Gadjeva, V.P. Durev, M.H. Hristov, D.I. Pukneva, Proc. of the 13th Int. Conf. Mixed Desing of Integrated Cir-cuits  and Systems MIXDES, 518 (Gdynia: Poland: 2006). 9. R. Guo, C. Wang, T. Li, 8th IEEE Conference on Industrial Electronics and Applications (ICIEA 2013) (2013). 10. C.P. Yue, C. Ryu, J. Lau, T.H. Lee, S.S. Wong, IEEE Elec-tron Dev. Meeting, 155 (1996). 11. H. Fuketa, Shinozuka, K. Ishida, M. Takamiya, T. Sakurai, IEEE Power Electron. Conf., 2228 (2014). 12. M. Kaluża, A. Napieralski, Bulletin of the Polish Academy of Sciences Technical Sciences 56 No 1, 21 (2008). 13. A. Tasic W.A. Serdijn, IEEE Int. Symp. on Circuits and Systems, II-819 (2002). 14. C.P. Yue, S.S. Wong, IEEE T. Electron Dev. 47 No 3, 560 (2000). 15. M.K. Yapici, J.M. Hong, J. Zou, K. Balareddy, IEEE 17th Int. Conf. Transducers and Eurosensors XXVII, 128 (2013). 16. C.-H. Liu, H.-D. Chang, K.-H. Li, C.H. Lin, C.-J. Hsu, T.-Y. Lin, H.-H. Chou, H.-C. Huang, H.-Y. Liao, IEEE Elec-tron. Components Technol. Conf. 1675 (2013). 17. C.P. Yue, S.S. Wong, IEEE J. Solid-State Circuits 33 No 5, 743 (1998). 18. T.G. Imre, U. Viscarret, I.E. Otadui, A. Rufer, IEEE (2008). 19. C. Wang, H. Liao, C. Li, R. Huang, W. Wong, X. Zhang, Y. Wang, IEEE T. Electron Dev. 56 No 4, 609 (2009). 20. S.Y. Lee, L. Zhao, J.T. Strydom, W.G. Odendaal, J.D. Van Wyk, IEEE 33rd Annual Power Electronics Specialists Conf., 1009 (2002). 21. R. Petkov, IEEE T. Power Electron. 11 No 1, 33 (1996). 22. P. Viarouge, J.C. Fagundes, E. Tourkhani, H. Le-Huy, IEEE Canadian Conference on Electrical and Computer Engineering, 582 (1995). 23. P. Sharma, M. Mehta, Int. J. Sci. Eng. Res. 3 No 2, (2012). 24. Q. Qian, Y. Liu, IEEE (2013). 25. M.-C. Hsieh, IEEE T. Components, Packaging Manufac-turing Technol. 4 No 3, 451 (2014). 26. L. Ying, H. Chunyue, Z. Xin, L. Tianming, G. Guangkuo, X. Guoji, T. Wenliang, IEEE 15th Int. Conf. Electronic Packaging Technol. (ICEPT), 577 (2014).  

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 7 No 2, 02006(6pp) (2015) Том 7 № 2, 02006(6cc) (2015) 
 
 
2077-6772/2015/7(2)02006(6) 02006-1  2015 Sumy State University 
Design and Modeling of an Integrated Inductor in a Buck Converter DC-DC 
 
Y. Benhadda1,*, A. Hamid1, T. Lebey2, M. Derkaoui1 
 
1 University of Sciences and Technology of Oran (USTO- MB) 31000 Algeria 
2 University of Paul Sabatier, LAPLACE Laboratory, Toulouse, France 
 
(Received 20 March 2015; revised manuscript received 05 June 2015; published online 10 June 2015) 
 
This paper presents the design and modeling of a square inductor for its integration in Buck converter 
DC-DC. The first, we calculate the value of inductance. The second, we descript our inductor; dimensioning 
and electrical model. A buck micro converter schematic simulation coupled with ideal and integrated  
inductor was presented. This conceptual model of the buck is best understood in terms of the relation  
between current and voltage of the inductor. Finely, we have simulated the electromagnetic effects in two 
cases. The first case, an inductor in the air, the second case with substrate. Our geometry is created en 3D 
space dimension. 
 
Keywords: Inductor, Buck converter, Integrated. 
 
 PACS number: 84.32.Hh 
 
 
                                                                
* benhadda_yamina@yahoo.fr 
1. INTRODUCTION 
 
In Power electronics, modeling of passive compo-
nents constitute a particularly important issue. Indeed, 
the magnetic components, inductors and transformers 
are mainly used to transmit or store energy. The pas-
sive elements volume reduction leads to a mounted in 
operating frequency, but this increase in frequency 
causes an increase in losses. If the behavior of some 
components is relatively insensitive to temperature 
changes, it is not the same thing for magnetic compo-
nents whose characteristics depend strongly on the 
temperature. The losses freed in the form of heat are 
become a major concern due to the reduction of trade 
with the outside surfaces and increasing the density of 
losses. The aim of our work is a dimensioning a square 
inductor that will be integrated in a DC-DC micro-
converter. 
 
2. PRESENTATION OF THE MICRO-
CONVERTER 
 
We have chosen a Buck micro-converter continuous-
continuous step-down (Fig.1) [1-3]. The inductor to in-
tegrate will thus be dimensioned for this type of appli-
cation. Input voltage, Vin  3 V. Output voltage, 
Vout  1.5 V. Maximum current ILmax  0.65 A. Output 
power, Pout  0.6 W. Frequency of operation, f  1 MHz. 
 
 
 
Fig. 1 – Buck converter 
 
The converter operates in two modes of conduction 
discontinuous conduction when the current required by 
the load is low, continuous conduction for higher cur-
rents (Fig. 2). The voltage and current involved are 
relatively low. In order to increase the efficiency of the 
converter, energy losses must be minimized. 
 
 
 
Fig. 2 – Evolution of the voltages and currents with time in an 
ideal buck converter 
 
The average output current Iout is calculated by 
formula (1) 
 
 outout
out
P
I
V
  (1) 
 
Iout  4 A, Iout  IL – IC, IC  0, Iout  IL. The peak am-
plitude of the current through the inductor is calculat-
ed by formula (2) 
 
 max minL L LI I I    (2) 
 
The average current LI  is expressed as follows (3) 
 
 max min
2
L L
L
I I
I

   (3) 
 
Where 
 
min max2L out LI I I  , min 0.15LI A , 0.5ALI   and 
0.5out inV V   .  
 Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015) 
 
 
02006-2 
The current which flows through the inductor in-
creases according to relation (4) 
 
 
(1 ) in
L
V
I
Lf
 
   (4) 
 
We can calculate the value of the inductance L [2] 
according to relation (5) 
 
 
(1 ) in
l
V
L
I f
 


 (5) 
 
The maximum energy stored in the inductor is giv-
en by relation (6) 
 
 
21
2
outW LI  (6) 
 
The volumetric energy density of the ferrite is given 
by the equation (7) 
 
 
2
max
max
02
v
B
W
r 
  (7) 
maxB : The maximum magnetic induction supported 
by the ferrite 
r : The relative permeability 
0 : The magnetic permeability of the free space 
The volume of the ferrite is given by relation (8) 
 
 ol
maxv
W
V
W
  (8) 
 
The ferrite’s thickness is tSub  97 m, thus the vol-
ume will be 32100 2100 97μm  . 
 
3. DIMENSIONING OF THE INTEGRATED  
INDUCTOR 
 
The geometry parameters characterizing the inte-
grated inductor (Fig. 3) are the number of turns n, the 
width of the conductor w, thickness of the conductor t, 
the spacing between conductor s, length of the conduc-
tor l, the outer diameter dout and input diameter din. 
 
 
 
Fig. 3 – Geometry of a square spiral integrated inductor, (a) 
3D view, (a) 2D view 
 
We find in the literature several formulas which al-
low us to calculate the number of turns n according to 
the value of inductance L, we chose the Weeler’s [4-5] 
formula (9) 
 
 
2
1 0
21
avg
mw
n d
L K
k




 (9) 
 
Where, we define the average diameter 
as ( ) / 2avg out ind d d   [6]. mA the factor’s form defined 
as /m out in out inA d d d d   .The coefficients k1 and k2 
are defined for each geometry. For a square inductor 
spiral, k1  2.34 and k2  2.75. 
The spacing between conductors is expressed as fol-
lows (10) 
 
 
2
2( 1)
out ind d wns
n
 


 (10) 
 
The length of the trace is expressed as follows (11) 
 
 4 [ ( 1) ]outl n d n s nw s      (11) 
 
The skin thickness is defined as (12) 
 
 
f



 , (12) 
 
where  represent the resistivity of the conductor,  
Copper  1.710 – 8 m and  its magnetic permeability. 
So that the current flows in the entire conductor, it 
is necessary that one of the following conditions is 
filled,
 
2w 
 
or 2t  , 92.8μm  , 40μmt  , 
120μmw  . Table 1 contains the specifications and the 
design results of the square spiral integrated inductor. 
 
Table 1 – Design results of the square spiral integrated  
inductor 
 
Parameter Value 
Inductance, L (H) 1.5  
External diameter, dout (mm) 2  
Internal diameter, din (mm) 0.4  
Number of turns, n  2 
Thickness of the conductor, t (m) 40  
Width of the conductor, w (m) 120  
Spacing between conductor, s (m) 280  
Length of the conductor, l (m) 0.0116 
 
4. ELECTRICAL MODEL 
 
The equivalent electrical model of the integrated 
inductor [6-10] [15-16] is shown in Fig. 4. 
The series resistance Rs, can be approximated as (13) 
 
 sR l wt  (13) 
 
The parasitic capacitive can be modeled as Cs (14) 
 
 20sC t l s  (14) 
 
where, ε0 is the permittivity of free space, 
12 1
0 8.854187.10 Mm .
   
 
а 
b 
 DESING AND MODELING OF AN INTEGRATED INDUCTOR… J. NANO- ELECTRON. PHYS. 7, 02006 (2015) 
 
 
02006-3 
 
 
Fig. 4 – Equivalent electrical model 
 
The substrate capacitance Csub and resistance Rsub 
are approximately proportional to the area occupied by 
the integrated inductor and can be expressed as (15), 
(16). 
 
 0
1
2
sub r
sub
lw
C
t
   (15) 
 
 2 subsub sub
t
R
lw
  (16) 
 
Cox oxide capacitance SiO2 can be expressed as (17) 
 
 0 oxox
ox
C lw
t
  
  
 
, (17) 
 
where ,r sub  represent respectively the relative permit-
tivity and the resistivity of substrate and oxt the oxide 
thickness. In our case, 10r  , 
645.10 msub
   and 
80µmoxt  . 
The geometry of a square spiral integrated inductor 
on substrate [13-14] is shown in Fig. 5. 
 
 
 
 
Fig. 5 – Geometry of a square spiral integrated inductor on 
substrate, (a) 3D view, (b) 2D view 
 
The efficiency of integrated inductor is calculated 
[16-20] according by relation (18)  
 
 
stocked energie
2
dissipated energie
Q   (18) 
Table 2 presents electrical parameters of the inte-
grated inductor. 
 
Table 2 – Electricals Parameters of the Integrated Inductor 
 
Electricals parameters Values 
( )sR   0.04 
( )subR   0.006 
(pF)sC  0.014 
(pF)oxC  0.598 
(pF)subC  0.631 
Q  98.56 
 
Fig. 6 shows the shape of the quality factor as a 
function of frequency. 
 
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
x 10
6
0
20
40
60
80
100
120
140
160
180
200
Frequency (MHz)
Q
u
a
lit
y
 F
a
c
to
r 
Q
 
 
Fig. 6 – Quality factor Q  from integrated inductor 
 
5. SIMULATION OF THE OF THE MICRO  
CONVERTER 
 
In this simulation, the circuit of Fig. 7 contains an 
ideal inductor and the Fig. 8 shows the waveform of the 
output voltage and current of the Buck micro converter. 
When the switch is closed, the voltage across the induc-
tor is VL  Vin – Vout. The current through the inductor 
rises linearly. As the diode is reverse-biased by the 
voltage source, no current flows through it. When the 
switch is opened, the diode is forward biased. The volt-
age across the inductor is VL  – Vout. The Current 
through inductor decreases. 
 
 
 
Fig. 7 – Schematic of buck micro converter coupled with ideal 
inductor 
а 
b 
 Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015) 
 
 
02006-4 
 
 
Fig. 8 – Waveforms of voltage and current of buck micro con-
verter coupled with ideal inductor 
 
Fig. 9 shows the schematic of micro converter simu-
lated coupled with integrated inductor. The simulated 
results are indicated in Fig. 10. We observe the same 
result with ideal inductor. 
 
 
 
Fig. 9 – Schematic of buck micro converter coupled with inte-
grated inductor 
 
6. SIMULATION 3D OF THE ELECTROMAG-
NETIC EFFECTS IN A INTEGRATED  
INDUCTOR 
 
In this section, we present the distribution of the 
electromagnetic field in a inductor in the air and on 
substrate [21] using finite elements method [22-24]. 
Fig. 11 shows the distribution of magnetic field in 
the inductor in the air. 
Fig. 12 shows the distribution of magnetic field lines 
in the inductor in the air. 
 
 
Fig. 10 – Waveforms of voltage and current of buck micro 
converter coupled with integrated inductor 
 
 
 
Fig. 11 – Distribution of magnetic field in the inductor in the air 
 
 
 
а 
 DESING AND MODELING OF AN INTEGRATED INDUCTOR… J. NANO- ELECTRON. PHYS. 7, 02006 (2015) 
 
 
02006-5 
 
 
 
 
Fig. 12 – Distribution of magnetic field lines in the inductor in 
the air 
 
Fig. 13 shows the distribution of magnetic field in 
the inductor on substrate. 
 
 
 
Fig. 13 – Distribution of magnetic field in the inductor on 
substrate 
 
Fig. 14 shows the distribution of magnetic field lines 
in the inductor on substrate. When we insert a sub-
strate, the majority of the magnetic field lines are con-
centrated at the walls of the magnetic block. So, we 
conclude that the substrate layer is required to have a 
good electromagnetic compatibility in the case of the 
integration inductor. 
 
 
 
 
 
 
Fig. 14 – Distribution of magnetic field lines in the inductor 
on substrate 
 
7. CONCLUSION 
 
In this paper, we have presented the dimensioning, 
the modeling and the simulation of a square inductor. 
We have visualized the electromagnetic phenomenon in 
inductor in the air and on substrate. The aim of this 
simulation is to study the electromagnetic compatibility 
of the inductor integrated in Buck micro converter  
DC-DC. 
 
b 
c 
a 
b 
c 
 Y. BENHADDA, A. HAMID, ET AL. J. NANO- ELECTRON. PHYS. 7, 02006 (2015) 
 
 
02006-6 
REFERENCES 
 
1. P. Reimann, Phys. Rep. 361, 57 (2002). 
2. G.S. Vorobjov, V.O. Zhurba, A.S. Krivets, J. Nano- Elec-
tron. Phys. 2 No 4, 47 (2010). 
3. L. Xian, Y. Wang An, 11th IEEE Int. Conf. Control Auto-
mation (ICCA) 1067 (2014). 
4. A. Allaoui, A. Hamid, P. Spiterri, V. Bley, T. Lebey, J. Low 
Power Electron. 11 No 1, 63 (2015). 
5. M. Derkaoui, A. Hamid, T. Lebey, R. Melati, Telkomnika 
11 No 4 (2013). 
6. S.S. Mohan, M.D.M. Hershenson, S.P. Boyd, T.H. Lee, 
IEEE J. Solid-State Circuits 34 No 10, 1419 (1999). 
7. N. Arbabi, M. Najmabadi, V. Devabhaktuni, M. Yagoub, 
Canadian Conf. Electrical Computer Eng. (CCECE), 99 
(Vancouver, BC: Canada: 2007). 
8. E.D. Gadjeva, V.P. Durev, M.H. Hristov, D.I. Pukneva, 
Proc. of the 13th Int. Conf. Mixed Desing of Integrated Cir-
cuits  and Systems MIXDES, 518 (Gdynia: Poland: 2006). 
9. R. Guo, C. Wang, T. Li, 8th IEEE Conference on Industrial 
Electronics and Applications (ICIEA 2013) (2013). 
10. C.P. Yue, C. Ryu, J. Lau, T.H. Lee, S.S. Wong, IEEE Elec-
tron Dev. Meeting, 155 (1996). 
11. H. Fuketa, Shinozuka, K. Ishida, M. Takamiya, 
T. Sakurai, IEEE Power Electron. Conf., 2228 (2014). 
12. M. Kaluża, A. Napieralski, Bulletin of the Polish Academy 
of Sciences Technical Sciences 56 No 1, 21 (2008). 
13. A. Tasic W.A. Serdijn, IEEE Int. Symp. on Circuits and 
Systems, II-819 (2002). 
14. C.P. Yue, S.S. Wong, IEEE T. Electron Dev. 47 No 3, 560 
(2000). 
15. M.K. Yapici, J.M. Hong, J. Zou, K. Balareddy, IEEE 17th 
Int. Conf. Transducers and Eurosensors XXVII, 128 (2013). 
16. C.-H. Liu, H.-D. Chang, K.-H. Li, C.H. Lin, C.-J. Hsu, T.-
Y. Lin, H.-H. Chou, H.-C. Huang, H.-Y. Liao, IEEE Elec-
tron. Components Technol. Conf. 1675 (2013). 
17. C.P. Yue, S.S. Wong, IEEE J. Solid-State Circuits 33 No 5, 
743 (1998). 
18. T.G. Imre, U. Viscarret, I.E. Otadui, A. Rufer, IEEE 
(2008). 
19. C. Wang, H. Liao, C. Li, R. Huang, W. Wong, X. Zhang, 
Y. Wang, IEEE T. Electron Dev. 56 No 4, 609 (2009). 
20. S.Y. Lee, L. Zhao, J.T. Strydom, W.G. Odendaal, J.D. Van 
Wyk, IEEE 33rd Annual Power Electronics Specialists 
Conf., 1009 (2002). 
21. R. Petkov, IEEE T. Power Electron. 11 No 1, 33 (1996). 
22. P. Viarouge, J.C. Fagundes, E. Tourkhani, H. Le-Huy, 
IEEE Canadian Conference on Electrical and Computer 
Engineering, 582 (1995). 
23. P. Sharma, M. Mehta, Int. J. Sci. Eng. Res. 3 No 2, (2012). 
24. Q. Qian, Y. Liu, IEEE (2013). 
25. M.-C. Hsieh, IEEE T. Components, Packaging Manufac-
turing Technol. 4 No 3, 451 (2014). 
26. L. Ying, H. Chunyue, Z. Xin, L. Tianming, G. Guangkuo, 
X. Guoji, T. Wenliang, IEEE 15th Int. Conf. Electronic 
Packaging Technol. (ICEPT), 577 (2014). 
 


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