The 7th International Conference on Modern Power Systems (MPS 2017)
The Analysis of the Multilayer Spiral Inductors
Parameters at High Frequency
Sergiu Andreica, Claudia Pacurar, Vasile Topa, Adina Racasan, Claudia Constantinescu, Marian Gliga
Electrotechnics and Measurement Department
Technical University of Cluj-Napoca
Cluj-Napoca, Romania
Sergiu.Andreica@ethm.utcluj.ro
Abstract—Implementing the spiral inductors in the
radiofrequency micrometric integrated circuits is complicated,
therefore some prior studies in order to determine their optimum
configurations for the circuit in which they will be implemented
are necessary. This study is a step forward in the study of spiral
inductors, aiming at comparing the monolayer to the multilayer
spiral inductors in order to determine their advantages,
disadvantages and to reach an efficient configuration. For this
purpose, the electric and magnetic phenomena in the spiral
inductors, along with their inductance, quality factor, and
scattering parameters at high frequency in the 1 – 20 GHz
frequency range will be presented and analyzed.
Keywords—spiral inductors;
inductance; scattering parameters
I.
multilayer;
quality
factor;
INTRODUCTION
The usual operating frequency for the multilayer spiral
inductors are in the MHz and GHz frequency range. The
increase of the interest in communications and wireless
telecommunications on the commercial market generated a
continuous development of the radiofrequency integrated
circuits [1], [8].
The applicability domains for these spiral inductors exceed
the classical domains such as electric and electronic circuits, in
present times being integrated in radiofrequency integrated
circuits (RFIC), like Micro-Electro-Mechanical System
(MEMS), printed circuit board (PCB), Complementary metal
oxide semiconductor (CMOS), being designed through
performant technologies and processes such as electromagnetic
technology, Low temperature Co-Fired Ceramic (LTCC).
The variety of the spiral inductors advantages are: fiability,
durability, resistence, the possibility of mass production, their
implementation on flexible layers, sublayers, small production
costs and others [9].
The multilayer spiral inductors are especially used in the
miniature wireless power supply devices (like chargers for the
mobile phones, wireless routers), wireless monitoring and
control devices, communication devices, information transfer,
radiofrequency amplifiers, radiofrequency converters, filters,
antennas. They are indispensable also in integrated inductive
and capacitive sensors such as: temperature, pressure,
acceleration and light sensors [2].
The correct, fastest, more precise analysis of the multilayer
spiral inductors is necessary from the design phase and in the
checking phase, in order to minimize the disruptive effects
which can be caused by these inductors in the integrated
circuits [2].
The determination of the multilayer spiral inductors
inductance value for the case in which they are used at low
frequency is relatively simple, but when the spiral inductors are
used in applications which operate at high frequencies from the
GHz frequency range and must be embedded in the integrated
circuits, namely in small spaces in the micrometer order, some
difficulties occur in the analysis of the phenomena and effects
present at high frequency.
II.
LAYOUT OF THE MONOLAYER AND MULTILAYER
PLANAR SPIRAL INDUCTORS
Square spiral inductors are the most frequently used due to
their simple configuration. The square inductors are easily
generated even with simple modeling programs. However, in
the circuits design some other spiral shapes are also used.
The transition from the monolayer spiral inductors to
multilayer ones leads to the increase of their inductances. For
this the increase of the turn number must lead to the increase of
the inductance value, quality factor value and the scattering
parameters value.
In this study, the software program used for modeling and
simulating the spiral inductors is ANSYS HFSS – High
Frequency Structural Simulator, which is a well-known
software worldwide and is a reference in the 3D numerical
analysis of the field in high frequency [6], [7]. The component
parts of the geometrical model of the square spiral inductor are
presented as it can be seen in Fig. 1.
The copper spiral inductor has the width of the turn, w,
10 μm, the distance between turns, s, 5 μm, the thickness of the
turn, t, 2 μm, the exterior diameter 500 μm; the number of turns
is considered as a varied parameter in this study.
The spiral inductor is placed on a square shaped
FR4_Epoxy (εr=4.4) layer with a thickness of 10 μm and a
width of 530 μm. Under the FR4_Epoxy a silicon (εr=11.9)
substrate with the thickness of 250 μm and a width of 10 μm is
placed.
978-1-5090-6565-3/17/$31.00 ©2017 IEEE
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.
The analysis was made for the entire configuration of the
considered spiral inductor, namely the one with one layer and
two turns, considering the spiral inductor, the FR4_Epoxy,
silicon and air layer.
Interpreting and analyzing the obtained representations
after modeling the spiral inductors, the effects and phenomena
at high frequency in the case of micrometric spiral inductors
can be noticed.
The phenomena and effects which appear are chaotic, the
end effects, pellicular effects and proximity effects occur due
to the fact that we work in the high frequency domain.
Fig. 1. Monolayer spiral inductor, component parts, 3D view.
As it was mentioned above, the analysis targets the
monolayer and multilayer spiral inductors. So, in Fig. 2 the
geometrical model of the square spiral inductor with two layers
and two turns on each layer can be observed. Also, in Fig. 3 the
way in which the connection between the copper layers was
made through connection pathways can be observed [3], [4],
[5].
III.
THE ANALYSIS OF THE EFFECTS AND PHENOMENA IN
THE SPIRAL INDUCTORS
The 3D numerical modeling for this study was made with
the help of ANSYS HFSS. Its main objectives were the
graphical and vectorial representation of the electric field
intensity, magnetic field intensity and current density.
In conclusion, it can be noticed that the field distributions
don’t have linear variations, the direct and indirect
dependencies between the used quantities do not comply,
depending on the frequency at which the case analysis is made.
In Fig. 4 the vectorial distribution of the electric field
intensity in the analyzed spiral inductor is presented. It can be
noticed that in the terminals the end effect is present, as it can
be seen in the vectorial representation the value of the electric
field being at the minimum value. Also, in the corner area a
maximum electric field intensity value can be seen.
In Fig. 5 the vectorial representation of the magnetic field
in the spiral inductor is presented. It can be observed that the
current in the corner area of the spiral has minimum values.
In Fig. 6 the vectorial representation of the current density
through the spiral inductor with one layer and two turns per
layer is presented.
Fig. 2. Spiral inductor with 2 layers and two turns per layer.
Fig. 4. Vectorial representation of the electric field intensity in the spiral
inductor.
Fig. 3. Detail view of the connection path between the copper layers.
Fig. 5. Vectorial representation of the magnetic field in the spiral inductor.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.
For the silicon sublayer, the electric and magnetic field
representations are not so conclusive as it can be seen in
Fig. 10 and Fig. 11. Their values are the lowest so far
considering the layers mentioned above.
IV.
Fig. 6. Vectorial representation of the current density in the spiral inductor.
After the spiral inductor was analyzed, the study continued
with the representations of the phenomena in the FR4_Epoxy
layer. The vectorial representations of the electric field (Fig. 7),
magnetic field (Fig. 8), and current density (Fig. 9) are
presented as follows.
THE ANALYSIS OF SPIRAL INDUCTORS CONSIDERING
THE VARIATION OF TURNS
A. Spiral inductor with 2 layers, 2 turns
The structure modeled and simulated for this case can be
seen in Fig. 12, while in Fig. 13 the inductance variation graph
depending on the frequency, in Fig. 14 the quality factor
depending on the frequency and in Fig. 15 the scattering
parameters are presented.
Fig. 10. Vectorial representation of the electric field intensity in the Si layer.
Fig. 7. Vectorial representation of the electric field intensity in the
FR4_Epoxy layer.
Fig. 11. Vectorial representation of the magnetic field in the Si layer.
Fig. 8. Vectorial representation of the magnetic field in the FR4_Epoxy
layer.
Fig. 9. Vectorial representation of the volumetric current density in the
FR4_Epoxy layer.
Fig. 12. Geometrical model of the spiral inductor with 2 layers and 2 turns per
layer.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.
previous cases, this model will also be analyzed in a frequency
range between 1 – 20 GHz.
The characteristic parameters for this type of spiral
inductors, namely the inductance values, the quality factor
values and the scattering parameters, all depending on the
frequency, are represented in the graphs from Fig. 17 to
Fig. 19.
Fig. 13. Inductance variation graph depending on the frequency values.
Fig. 16. Geometrical model of the spiral inductor with 2 layers and 4 turns per
layer.
Fig. 14. Quality factor graph depending on the frequency values.
Fig. 17. Inductance variation graph depending on the frequency values.
Fig. 15. Scattering parameters graph depending on the frequency values.
In the case of the analyzed geometrical model, the
maximum inductance, 65.540 µH, was obtained at the
resonance frequency of 6.202 GHz, the quality factor
maximum value is 236.306 at a frequency value of
approximately 1 GHz and is zero at the resonance frequency.
The scattering parameters S for this model intersect at the value
of approximately 1 GHz.
In comparison with the monolayer spiral inductor with 2
turns, the inductance value increased, as expected, from
39.77 µH to 65.540 µH, due to the fact that the spiral inductor
inductance varies proportional to the number of turns and their
number of layers. The resonance frequency decreased with
approximately 1.3 GHz in the case of the spiral inductor with 2
layers and 2 turns per layer. The quality factor significantly
increased, and it was 12 times higher than the one for the
monolayer spiral inductor, which has the value of 18.670, for
the multilayer spiral inductor with 2 turns per layer.
B. Spiral inductors with 2 layers, 4 turns
The geometrical model of the spiral inductor with 2 layers
and 4 turns per layer can be observed in Fig. 16. As in the
Fig. 18. Quality factor graph depending on the frequency values.
Fig. 19. Scattering parameters graph depending on the frequency values.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.
The results in the case of the multilayer spiral inductor with
2 layers and 4 turns per layer, through numerical analyzing the
obtained data, shows that the direct proportional variation of
the inductance with the number of turns and layers is
maintained, thus we obtain a maximum inductance of
66.505 µH at a resonant frequency of 3.479 GHz. Compared to
the monolayer spiral inductor with 4 turns, it can be noticed
that the frequency value is 23 µH higher, for the monolayer
spiral inductor the maximum inductivity value being
43.528 µH at a frequency of 4.264 GHz. Also, it can be noticed
that the multilayer spiral inductor has the resonance frequency
0.7 GHz higher than the monolayer spiral inductor.
The quality factor has a maximum value of 163.861 at a
frequency of 1 GHz, a lot higher than the value for the
monolayer spiral inductor, 25.38.
C. Spiral inductors with 2 layers, 16 turns
The multilayer spiral inductor with 16 turns per layer can
be seen in Fig. 20. The characteristic parameters for this
structure are also presented in Fig. 21 – Fig. 23.
Fig. 23. Scattering parameters graph depending on the frequency values.
The results obtained in the case of the analyzed model, the
one of the spiral inductor with 2 layers and 16 turns per layer,
show that a maximum value for the inductance of 62.748 µH
was obtained at the resonance frequency of the inductor,
7.308 GHz. Comparing the results with the monolayer spiral
inductor, it can be stated that the maximum inductivity value is
higher for the monolayer structure, 138.431 µH, while for the
resonance frequency it can be noticed that the monolayer
structure has a lower value, namely 2.279. For the quality
factor a maximum value of 92.881 was obtained at the
frequency of 1 GHz, value a lot higher than the one obtained
for the monolayer spiral inductor, namely 29.152.
In order to reach a general conclusion, in Table 1 the
results obtained for the spiral inductor with 2 layers and a
variable number of turns per layer, between 2 and 16, namely
the inductance value, the maximum quality factor value and
the resonance frequency of the analyzed spiral inductor are
presented.
Fig. 20. Geometrical model of the spiral inductor with 2 layers and 16 turns
per layer.
Fig. 21. Inductance variation graph depending on the frequency values.
Fig. 22. Quality factor graph depending on the frequency values.
TABLE I.
RESULTS OBTAINED AFTER THE SIMULATIONS, FOR THE
SPIRAL INDUCTOR WITH TWO LAYERS
Analyzed
structure
Resonance
frequency
[GHz]
Maximum
inductance
[µH]
Quality factor
2 turns
6.203
65.54
236.306
4 turns
3.479
66.502
163.861
16 turns
7.308
62.748
92.881
In the case of the inductance a variation which does not
follow the direct proportionality between the number of turns
and the inductance can be observed. These variations are due to
the fact that some parasitic capacitance appear between the
layers. The quality factor varies inversely proportional with the
number of turns, and the resonance frequency shows no
linearity.
The spiral coil with two layers and two turns per layer has
an inductance value higher with approximately 25µH than in
the case of the monolayer spiral inductor with the same number
of turns, the quality factor is much higher with a value of
236.306 while in the case of the monolayer spiral inductor, the
quality factor being 18.67. The multilayer spiral inductor
reaches the resonance frequency at 6.203 GHz, and the
obtained frequency value is with approximately 1.3 GHz lower
than the one obtained for the monolayer spiral inductor, where
a resonance frequency alue of 7.57 GHz was obtained.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.
The two-layered spiral inductor with 4 turns has a
maximum inductance value of 66.502 µH, this value being
higher with approximately 30 µH than the inductance value
obtained for the monolayer spiral inductor with the same
number of turns. For the quality factor a significant increase
can be also noticed, this value being approximately 138 times
higher than the one for the monolayer spiral inductor with 4
turns. The resonance frequency is reached at a value of
3.479 GHz, while the monolayer spiral inductor has its
resonance frequency at 4.264 GHz.
In the case of the spiral inductor with two layers and 16
turns an inductance value of 62.748 µH was obtained, value
which is lower than the one obtained for the monolayer spiral
inductor, due to the fact that parasitic capacitances appear
between the layers and the turns. The two layered spiral
inductor reaches the resonance frequency at a value of 7.308
GHz, while the monolayer spiral inductor’s resonance
frequency has a value of 2.279 GHz. The quality factor has a
value of 92.881 which is approximately 3 times higher than
the value obtained in the case of the monolayer spiral inductor
where the quality factor has a value of 29.152.
V.
CONCLUSIONS
After analyzing the phenomena and effects which appear in
the studied structure, it can be said that the end effects,
pellicular effects and proximity effects occur in the high
frequency domain. The field distributions don’t have linear
variations, the direct and indirect dependencies between the
used quantities do not comply, depending on the frequency at
which the case analysis is made.
The inductance in the case of the multilayer spiral inductor
increases significantly in comparison with the monolayer
spiral inductors with the same number of turns, varying
proportional to the number of turns and number of layers. The
same conclusion can be drawn in the case of the quality factor.
The resonance frequency for the multilayer spiral inductors
decreases in comparison with the same value obtained for the
monolayer spiral inductors.
Considering only the multilayer spiral inductors with 2, 4
and 16 turns, it can be said that in the case of the inductance a
variation which does not follow the direct proportionality
between the number of turns and the inductance can be
observed. These variations are due to the fact that some
parasitic capacitance appear between the layers. The quality
factor varies inversely proportional with the number of turns,
and the resonance frequency shows no linearity.
ACKNOWLEDGMENT
This work was supported by a grant of the Romanian
National Authority for Scientific Research and Innovation,
CNCS – UEFISCDI, project number PN-II-RU-TE-2014-40199.
This work was supported by CEMIVA: PN II - PT - PCCA
- 2013 - 4 - 1019 –CEMIVA.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
C. Pacurar, V. Topa, A. Racasan, C. Munteanu, C. Hebedean, “Spiral
Inductors Inductance Computation and Layout Optimization”, 2012
International Conference and Exposition on Electrical and Power
Engineering (EPE 2012), 25-27 October, Iasi, Romania, pp. 699-704, 25
Octombrie 2012.
C. Wang, B-Q. Gao, C.-P. Deng, “Accurate Study of Q-factor of
Resonator by a Finite-DifferenceTime-Domain Method”, IEEE
Transaction on Microwave Theory and Techniques, vol. 3, Issue 7,
pp. 1524-1529, August 2002.
V. Topa, A. Racasan, C. Munteanu, C. Pacurar, “Inductance Calculation
and Layout Optimisation for Planar Spiral Inductors”, Inductance
Calculation and Layout Optimisation for Planar Spiral Inductors, pp. 6,
25 October 2012.
A. M., Niknejad, R. G. Meyer, ”Analysis, design and optimisation of
spiral inductors and transformers for Si RF ICs”, IEEE Journal of SolidState Circuits, 1998, Vol. 33, Issue 10, pp. 1470-1481.
Z. I. K. Hanisah Muhamed NAdzar, “RF circuit design features of spiral
inductors using multilayer structure”, IEEE, 2008, pp. 5.
R. V. Ciupa, Laura Darabant, Mihaela Plesa, O. Cret, D. D. Micu,
“Design of Efficient Magnetic Coils for Repetitive Simulation”, Revue
Roumaine d’Electrotechnique, vol. 55, 2010, pp. 251-260.
W. Roshen, “Superconducting Inductors for Ultra-High Frequency
Power Conversion,” SSU Power Technology, pp. 2075-2081, June 2007.
A. Ammouri, H. Belloumi, T. B. Salah1, F. Kourda, “Experimental
Analysis of Planar Spiral Inductors”, CISTEM 2014, pp. 1-5, 2014
S.Rasidah; M. H. Siti Maisurah; E. F. Nazif; K. Norhapizin, A. I. A.
Rahim, ”The design of ground shield spiral inductor using 0.13 μm
CMOS technology for millimeter-wave radio over fiber applications”,
RSM2015 Proc. 2015, K. Terengganu, Malaysia, p. 4, 15 March 2015.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY WARANGAL. Downloaded on November 15,2022 at 02:58:33 UTC from IEEE Xplore. Restrictions apply.