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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 [1] Ch. M. Tai, Ch. N. Liao, “A Physical Model of Solenoid Inductors on Silicon Substrates,” IEEE Transactions on Microwave Ttheory and Techniques, vol. 55, no. 12, Decebmer 2007. [2] A. M. Niknejad, R. G. Mayer, "Analysis, design, and optimization of spiral inductors and transformers for Si RF IC's ," IEEE Journal of Solid-State Circuits, vol.3, no. 10 , pp. 1470-1481, October 1998. [3] V. Desnica, Lj. Živanov, O. Aleksi , S. Jenei, "Modeling and optimization of thick film solenoid-bar type inductors and transformers," COMPEL(Computation and Mathematics in Fig. 8. Q Factor of 3D Inductor. Electrical and Electronic Engineering), vol. 19, no. 2, pp. 615-622, 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, The maximum Q factor value obtained by simulation was vol. 54, no. 2, pp. 221-331, 2006. 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. comparison with the 3D inductor. This is so because there Živanov, “Fizi ki model planarnog i 3D induktora projektovanih za 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.

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