Modelling and Simulation of RF Multilayer Inductors in LTCC

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					Telfor Journal, Vol. 1, No. 2, 2009.                                                                                               73




          Modelling and Simulation of RF Multilayer
               Inductors in LTCC Technology
                                                                 Amer eli


                                                                          of its inductance and Q factor. The verification of results
    Abstract – This paper is aimed at presenting the models               obtained on the basis of physical model has been
 and characteristics of two types of inductors designed in                performed by using the Ansoft HFSS electromagnetic
 LTCC (Low Temperature Cofired Ceramic) technology. We                    simulator [6].
 present the physical model of a 3D planar solenoid-type
 inductor and of a serial planar solenoid-type inductor for the
 RF (radio frequency) range. To verify the results obtained by
 using these models, we have compared them with the results                II. DERIVING   THE PHYSICAL MODEL OF AN INDUCTOR
 obtained by employing the Ansoft HFSS electromagnetic                                DESIGNED FOR LTCC TECHNOLOGY
 simulator. Very good agreement has been recorded for the
                                                                             The view of inductor structures designed for LTCC
 effective inductance value, whereas the effective Q factor
 value has shown a somewhat larger deviation than the                     technology is shown in Figure 1.
 inductance.

   Keywords - Q factor, Physical model of inductor,
 Inductance, Planar solenoid inductor.


                         I. INTRODUCTION

 A     N integrated inductor is a component finding ever
       wider applications in low-noise amplifiers, active
 mixers, voltage-controlled oscillators, power converters,
 miniature sensors, filters, etc. [1]. The main features of an                                  (a) 3D Inductor.
 inductor are its inductance and Q factor.
    Various techniques are used for fabricating a
 component or circuit, depending on their characteristics
 and dimensions to be achieved as well as on the place of
 their intended use. Technologies used most commonly for
 producing microstructures are monolithic technology [2],
 thick-film technology [3] and low temperature cofired
 ceramic (LTCC) technology [4], [5]. A designer of
 microelectronic structures should be familiar with as many
 technologies as possible to be capable of selecting a                                         (b) Serial Inductor.
 technology that will give the optimal characteristics of a                          Fig. 1. 3D View of Inductor Structures.
 designed component. In addition to various technologies,
 a designer’s knowledge should also include the electrical                   As may be seen from Figure 1, inductor structures have
 characteristics describing an inductor.                                  been designed using five dielectric stripe produced by
    The aim of this paper is to derive a physical model of                DuPont company – DuPont 951PT [7]. DuPont’s silver
 two types of planar solenoid inductors for operation in the              pastes DuPont 6142D [7] were used for conducting lines.
 radio frequency range. The simulation of inductor                        Inductors were designed so as to have the same
 structures using electromagnetic simulators can give data                conducting line widths (100 m), the same conducting line
 on the effective values of inductance and Q factor as well               thicknesses (9 m) and to occupy identical areas on a chip.
 as on resonance frequency, but it cannot provide                         Via diameter was 100 m. Both inductors had the same
 information on parameters such as series resistance, series              dimensions (5.4 x 2.2 x 0.5)mm.
 capacitance, parasitic capacitance to the substrate, etc.                   Knowledge of the physical model of inductor is very
 This is why deriving the physical model of an inductor can               important for its application, because it permits
 show exactly how these values affect the effective values                recognizing all the characteristic parameters affecting the
                                                                          inductor. Precise inductor modeling is rather demanding
    A. eli , Faculty of Technical Sciences in Novi Sad, Serbia (e-mail:   because of numerous parasitic effects occurring at high
 celicamer@yahoo.com).                                                    frequencies [8].
74                                                                                                                                                               Telfor Journal, Vol. 1, No. 2, 2009.

    Figure 2 presents the physical structure of 3D inductor                                             obtained by using equation (6) and the total mutual
 with the characteristic parameters describing the inductor                                             inductance (LM2U) by summing the single mutual
 at high frequencies (series inductance LS, series resistance                                           inductance between these segments [9],
 RS, series capacitance CS, parasitic capacitance to the
 substrate CK), and Figure 3 its equivalent -diagram. The
 physical structure and equivalent -diagram of serial
 inductor are identical to those of 3D inductor.




                                                                                                                             Fig. 4. Slant Segments at an Angle .

                                                                                                                        O
                                                                                                                            cos                                            l2                                                    l1
                                                                                                          LM 2                         2             l1 arth (                             )                 l 2 arth (                    )
                                                                                                                            4                                         R1           R2                                       R1        R4
                                                                                                                             l2                                  l1                                d
                                                                                                                                                                                                                                                (6)
                 Fig. 2. Physical Structure of 3D inductor.                                                  arth (                    )       arth (                       )                            ,
                                                                                                                        R3        R4                      R2           R3                  sin
                                                                                                        where parameter                              is given by equation (7)
                                                                                                                        d 2 cos                l1        l 2 sin 2                                 d 2 cos                 l1    sin 2
                                                                                                             arctg                                                                 arctg
                                                                                                                                           dR1 sin                                                             dR 2 sin
                                                                                                                   d 2 cos        sin 2                               d 2 cos                          l 2 sin 2
                                                                                                                                                                                                                                                (7)
                                                                                                           arctg                                         arctg                                                         ,
                                                                                                                         dR 3 sin                                                      dR 4 sin

                                                                                                        and auxiliary parameters R1, R2, R3, R4 are given by
                                                                                                        equation (8),
              Fig. 3. Equivalent -diagram of 3D inductor.                                                  2
                                                                                                          R1        d2                       l1 2                       l2 2                       2           l1                l 2 cos ,
    Series inductance LS is the sum of the selfinductances of                                                            2             2                         2                 2
                                                                                                                        R2         d                      l1                                   2              l1       cos ,
 inductor’s single segments         (LO) and the mutual                                                                             2                2           2                 2
                                                                                                                                                                                                                                                 (8)
                                                                                                                                   R3           d                                              2          cos ,
 inductances between the parallel and acute line segments
 of inductor (LM1 + LM2),                                                                                                2
                                                                                                                        R4         d2                2
                                                                                                                                                                        l2 2                   2                 l2 cos .
                        LS         LOU            LM 1U         LM 2U .                           (1)   The series resistance of 3D inductor is given by equation
                                                                                                        (9)
   The selfinductance of one line segment is obtained
                                                                                                                            N l ll     2 l lK
 using equation (2) and the total selfinductance (LOU) by                                                          RS
 summing the selfinductances of all single line segments                                                                 2 wl tl     2 wl tl
                                                                                                                       N l tvia    2 N l tl
                                                                                                                                                              (9)
 with the selfinductance introduced by vias (Lvia), equation                                                                                ,
 (3),                                                                                                                  2 wvia / 2   w pad 2
                            O ll         2ll                                 wl tl                      where N=8 is the total number of 3D inductor’s acute
            LO                     ln                  0,50049                     ,              (2)
                        2               wl tl                                 3ll                       angles, l = 2.97*10-8 m is the specific resistance of
                                                                                                        conducting line, lK is the length of connection segments
                  o     r                     1   tvia               2         2
     Lvia                     tvia sinh                             tvia      wvia       wvia ,   (3)   and wpad is the diameter of extracting at terminal of
                 2                                wvia
                                                                                                        conductive segment (pad). The parameter describing the
 where ll, wl , tl are the lengths, widths and thicknesses of                                           dependence of resistance on frequency is referred to as
 line segments, respectively, wvia and tvia are via diameter                                            skin depth and is given by equation (10).
 and length, and r = 0.99998 is the relative permeability of
                                                                                                                                                                               l
 conducting line.                                                                                                                                                                              .                                               (10)
                                                                                                                                                                        o          r
                                                                                                                                                                                       f
    Mutual inductance between two parallel inductor
                                                                                                          The series capacitance of 3D inductor is given by
 segments is obtained by using equation (4) and the total
                                                                                                        equation (11) and includes the capacitance between
 mutual inductance (LM1U) by summing the single mutual
                                                                                                        parallel segments, acute segments and the capacitance
 inductance between parallel segments (9),
                                                                                                        between extracting at terminal of conductive segment (via
                             O r         l               ll 2              G2     G                     pad)
              LM 1                 ll ln l         1                 1               ,            (4)
                                                           2
                             2           G             G                   ll 2   ll
                                                                                                                                  N 2 ll tkor sin / 2 tl                                                            N 1 ll tl
                                                                                                           CS        0 rk                                                                          0 rk
 where parameter G is given by equation (5),                                                                                        tkor cos / 2 wl                                                              2
                                                                                                                                                                                                                tvia            p/2   2

                                                                                                                                                                                                                                               (11)
                                    1                     1                       1                                     N         w pad / 2 2            wvia / 2          2
       ln G      ln d
                              12 d / wl
                                          2
                                                   60 d / wl
                                                                4
                                                                           164 d / wl
                                                                                         6
                                                                                             ,    (5)            0 rk                                                              ,
                                                                                                                                              Tker
 and d is the distance between parallel segments.                                                       where rk = 7.8 is the relative permittivity of ceramic
   Mutual inductance between the two segments of an                                                     substrate, and Tker = 100 m is the ceramic substrate
 inductor that are positioned at an angle     , Figure 4, is                                            thickness.   Parasitic capacitance to the substarte is
eli : Modelling and Simulation of RF Multilayer Inductors in LTCC Technology                                                                                                                         75

calculated using equation (12) and exists between the                                                                                         III. COMPARISON OFRESULTS CALCULATED USING
inductor itself and the metal coating deposited from the                                                                                         INDUCTOR MODEL WITH SIMULATION RESULTS
lower side of the component.                                                                                                                 Figures 5 and 6 present a comparison of the results of
                    N               N                                                                                                      the effective values of the inductance and Q factor of 3D
                      wl l            wl l
           1        2      1        2                                                                                                      inductor obtained by calculation of the parameters of
     CK        o rk           o rk
           2        2Tker  2        3Tker                                                                                                  inductor’s physical model and by simulation. The same
                                                    (12)
                                                                                                                    2                      meshing was used for both inductor types in simulation.
       1        2 wl l K 1        N w pad / 2
          o rk              o rk                 .
       2        3Tker    2             2Tker
   These equations correspond to the physical model of 3D
inductor. To calculate the values of the elements of
equivalent -diagram of serial inductor, we use the
following equations. The series resistance of serial
inductor is calculated on the basis of equation (13),
                                          l
                                         l l
                                                                       l
                                                                      l K
                                                                                                    2 ll p
       RS            Ng        Nd
                                      2 wl tl                      2 wl tl                      2 wl                tl
              Ng          Nd      t                t 2 Ng              Nd
                                                                                                                                    (13)
                                 l via            l l
                                                                         2
                                                                                 ,
              2           wvia / 2                        w pad / 2
where Ng = 8 is the total number of acute segments on the
upper conducting layer, Nd =8 is the total number of acute
segments on the lower conducting layer, lp is the end                                                                                                  Fig. 5. Inductance of 3D Inductor.
segment connecting the segments of the upper and lower
conducting layer.                                                                                                                             As can be seen, in the case of 3D inductor the value of
  The series capacitance of serial inductor is obtained on                                                                                 inductance obtained by calculation is slightly larger than
the basis of equation (14) and includes the capacitance                                                                                    the simulated value. The calculated inductance value of
between the parallel segments, acute segments, the                                                                                         3D inductor at 1 GHz frequency is 6.53nH. The simulated
capacitance between extracting at terminal of conducting                                                                                   inductance value of 3D inductor at 1GHz frequency is
segments (via pad) and the capacitance between the                                                                                         5.21nH. The inductance increases with the increasing
overlapping parts of the segments of the upper and lower                                                                                   frequency.
conducting layers.,
                       Ng       Nd       2 ll         t kor sin      / 2 tl                     Ng         Nd            2 ll t l
  CS          o rk                                                                     o rk
                                      t kor cos        /2                                                 2
                                                                                                        t via         2
                                                                                                                    t kor
                                                                             2                  2                                   (14)
               N g wl2                Ng        Nd            w pad / 2              wvia / 2
       o rk                    o rk                                                                 ,
                Tker                                              Tker
where tkor is the distance between the two parallel
segments of serial inductor.
  The parasitic capacitance to the substrate of serial
inductor is calculated on the basis of equation (15)
        1          N d wl l 1        N g wl l 1      2wl l K
  CK        O rk                o rk            o rk
        2          2Tker 2           3Tker    2       3Tker
                                                   2         (15)
    1        wl l p 1           N g N d w pad / 2
       o rk                o rk                      .
    2       3Tker 2                     2Tker
  The effective values of the inductances and Q factor of                                                                                               Fig. 6. Q Factor of 3D Inductor.
3D and serial inductors are calculated on the basis of
equations (16) and (17),                                                                                                                     The maximum calculated Q factor value of 3D inductor
                                            w L   2       2
                                                                                                    w L  2      2                          was 91.33 and was obtained at 1.7GHz frequency. The
                     LS        RS2 1                      S
                                                                  CS             CK        1                    S
                                                                                                                                           maximum Q factor value obtained by simulation was
                                             R S2                                                    R S2
       L                        2                                                                               2
                                                                                                                            ,       (16)   87.42 and was obtained at 1.8GHz. It can be seen that the
                          w                           2            w 2 L2S                                                                 deviation is very small. This is due to the fact that many
                                      LS        R 1   S                               CS        CK
                          RS                                        R S2                                                                   parasitic effects are taken into account in the calculation.
                  wLS   RS2 CS C K                                                                                                            Figures 7 and 8 present a comparison of the results of
       Q              1                                                      w2 LS CS                   CK               .                 the effective values of the inductance and Q factor of
                  RS         LS                                                                                                     (17)
                                                                                                                                           serial inductor obtained by the calculation of the
                                                                                                                                           parameters of inductor’s physical model and by
                                                                                                                                           simulation.
76                                                                                              Telfor Journal, Vol. 1, No. 2, 2009.

                                                                                          IV. CONCLUSION
                                                                   This paper presents the physical models and
                                                                characteristics of two inductor types. The values of the
                                                                calculation and simulation for the effective inductance and
                                                                Q factor value are compared.
                                                                   The inductance of serial inductor is larger than that of
                                                                3D inductor. This difference is introduced by the larger
                                                                number of segments of serial inductor, the larger number
                                                                of vias as well as the larger number of pads. The Q factor
                                                                of serial inductor is lower than the Q factor of 3D
                                                                inductor. This results from the higher values of the
                                                                elements of the equivalent -diagram obtained with the
                                                                serial inductor compared with the 3D inductor.
                                                                   Briefly, if the inductance value is a decisive criterion
             Fig. 7. Inductance of Serial Inductor.             for the intended application of the inductor, it should be
                                                                realized as a serial one; on the other hand, if the Q factor
   A good agreement between the calculated and simulated        value is decisive, the inductor should be realized as a 3D
 inductance value was also obtained in the case of serial       inductor [9].
 inductor. A slightly larger calculated inductance value was
 obtained compared with the simulated one. The calculated                               ACKNOWLEDGEMENT
 inductance value at 1GHz frequency is 10.13nH. The               This paper forms part of a Master Degree Thesis and
 simulated inductance value at 1GHz frequency is 8.8nH.         has been prepared under the supervision of Ms Ljiljana
                                                                Živanov, PhD and Mr Goran Radosavljevi , MS, both
                                                                with the Faculty of Technical Sciences in Novi Sad.
                                                                Research and results reported in the paper have been
                                                                partially supported by Serbia's Ministry of Sceince and
                                                                Technology Development under Grant No 11023.

                                                                                             REFERENCES
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                                                                      on Silicon Substrates,” IEEE Transactions on Microwave Ttheory
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                                                                      2000.
                                                                [4]   L. J. Golonka, “New application of LTCC technology,” 28th Int.
   The maximum Q factor value obtained by calculating                 Spring Seminar on Electronics Technology, pp. 148-152, 2005.
 the parameters of the equivalent -diagram of serial            [5]   L. J. Golonka, “Technology and application of Low Temperature
 inductor was 46.47 and was obtained at 1GHz frequency.               Cofired Ceramic (LTCC) based sensors and mycrosystems,”
                                                                      Bulletin of the Polisch Academy of Sciences, Technical Sciences,
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 36.43 and was obtained at 1.1 GHz frequency. It can be         [6]   Ansoft Inc. HFSS (High Frequency Structure Simulator). Pitssburg:
 noted that the deviation of the simulated Q factor value             Ansoft Corporation, 2002.
 from the calculated one for the serial inductor is larger in   [7]   http://www.dupont.com/mcm
                                                                [8]     . Vladisavljevi , G. Radosavljevi , A. Mari , G. Stojanovi , Lj.
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 are a larger number of segments, and the parasitic                   LTCC tehnologiju,” , ETRAN, Subotica, Jun 2008.
 capacitances and series resistance are therefore larger as     [9]   V. Desnica, "Modelovanje i optimizacija planarnih debeloslojnih
 well.                                                                induktora solenoidnog tipa," Magistarski rad, Novi Sad, Novembar
                                                                      1999.