Power Integrity Simulation for SiP Using GTLE
6
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP) 978-1-4244-4659-9/09/$25.00 ©2009 IEEE Power Integrity Simulation for SiP Using GTLE Yunyan Zhou, Lixi Wan, Jun Li Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China Email: [email protected] Abstract Power integrity (PI) simulation for system-in-package (SiP) is a bottleneck in SiP design flow. This paper presents a novel numerical algorithm for PI simulation in packaging structures. This algorithm is based on 2D Generalized Transmission Line Equation (GTLE), Finite Difference Frequency Domain (FDFD) and mesh division technique. The power distribution network is simulated using mesh division technique where the model of power distribution network is obtained by regarding each cell as a 2D transmission line. 2D GTLE is a group partial equation about voltage and current density distribution on a power/ground plane pair. After reduction, the voltage equation for 2D GTLE is obtained, which is a Helmholtz equation. One method to solve the Helmholtz equation is by the finite-difference scheme. The 2D Laplace operator can be approximated to solve the voltage equation. In this paper, the fringe effect is modeled by the addition of cells around edges which is efficient and easy to implement. Finally, the methodology described in prior sections has been implemented in a CAD tool. The results from our method were compared to those from a full-wave simulator to show efficiency in power integrity simulation. Introduction The density of transistors dramatically increases with the down-sizing in semiconductor technology. High-level integration with more functionality has been achieved through 3D packaging technique i.e. system-on-chip (SOC) and system-in-package (SiP). Novel electrical modeling technologies are highly demanded to tackle the challenges posed by the complexity of nano-scale integrated circuits(IC) as well as its package integration. Usually, the whole package system can be divided into two networks: signal distribution network (SDN) and power distribution network (PDN), where the PDN is often designed as power-ground planes structure to reduce the groundâs impedance. The global coupling effects such as the simultaneous switching noise (SSN) demand a system-level modeling methodology and co-simulation of signal and power integrities. Such a system level packaging EMC simulation is a great challenge to all available electromagnetic simulators [1], [2]. Based on the special features of the package structure, we propose to simulate the PDN by Generalized Transmission Line Equations (GTLE), Finite Difference Time Domain (FDTD) and Finite Difference Frequency Domain (FDFD) [3]. For the power/ground planes, the numerical methods, mesh division technique and finite difference method are used to solve these transmission lines equations and get their equivalent RLCG parameters. The transmission line equation technique is well known for its capability in treating a wide range of electromagnetic problems with a great flexibility in terms of geometrical irregularity and material parameters. The equivalence between Maxwell's equation and circuit network allows this technique to solve complex problems in both time- and frequency- domains. It is known that the derivation of conventional transmission line equation (CTLE) is based on such an assumption of an infinite-length transmission line. Unfortunately, practical transmission lines are finite-length. When the CTLE are used in a finite-length unmatched uniform transmission line or arbitrary length nonuniform transmission line, the description of the CTLE for such line discontinuities needs further scrutiny [4], [5]. The reason is that when the nonuniform transmission line is generally treated as a cascading of many short uniform transmission lines, the discontinuities between any two neighboring segments are not only generate reflections, but also produce radiations. Furthermore, the equation is a one- dimensional approximation for a pair of conductor lines. This canât satisfy the simulation for power integrity (PI) in Sip. So it is necessary for extending the one-dimensional equation to 2- or 3-dimensions [6]. In this paper, based on the finite-length line concept and vector partial differential equation, we derive generalized transmission line equation (GTLE) by using circuit theory. However, the coefficients of the GTLE need to be determined by numerical methods, such as differential algebraic equations (DAE). With this equation, the power integrity in PCBs and SiP can be simulated easily and quickly. The GTLE can be solved in time domain or frequency domain. In this paper, a frequency domain solution is discussed with the Finite Difference Frequency Domain (FDFD) technique. Comparing with the methods based on Maxwellâs equation, an obvious advantage of using GTLE is reduction of memory usage and saving processing time since the voltage and current density is only computed on the conductor and not in the entire volume space [7]. The rest of this paper is organized as follows: 1) A description of the GTLE for modeling 2-dimensionla plane is provided. 2) Discretization and numerical methods for GTLE are briefly described. 3) Modeling techniques for fringe effect and excitation is considered. 4) Results from our method are provided, and finally, conclusions are presents. Generalized transmission line equation In frequency domain, for an infinite-length nonuniform transmission line, the 1D CTLE equation can be expressed as ( ) ( ) () () () () Vz R j LIz dz Iz G j CVz dz Ï Ï â ⧠=â + âȘ âȘ âš â âȘ =â + âȘ â© (1) where, V and I are the voltage and current for the infinitely short transmission line; R and L are the per-unit-length series 425 Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
Transcript of Power Integrity Simulation for SiP Using GTLE
untitledPower Integrity Simulation for SiP Using GTLE
Yunyan Zhou, Lixi Wan, Jun Li Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
Email: [email protected]
Abstract Power integrity (PI) simulation for system-in-package
(SiP) is a bottleneck in SiP design flow. This paper presents a novel numerical algorithm for PI simulation in packaging structures. This algorithm is based on 2D Generalized Transmission Line Equation (GTLE), Finite Difference Frequency Domain (FDFD) and mesh division technique. The power distribution network is simulated using mesh division technique where the model of power distribution network is obtained by regarding each cell as a 2D transmission line. 2D GTLE is a group partial equation about voltage and current density distribution on a power/ground plane pair. After reduction, the voltage equation for 2D GTLE is obtained, which is a Helmholtz equation. One method to solve the Helmholtz equation is by the finite-difference scheme. The 2D Laplace operator can be approximated to solve the voltage equation. In this paper, the fringe effect is modeled by the addition of cells around edges which is efficient and easy to implement. Finally, the methodology described in prior sections has been implemented in a CAD tool. The results from our method were compared to those from a full-wave simulator to show efficiency in power integrity simulation.
Introduction The density of transistors dramatically increases with the
down-sizing in semiconductor technology. High-level integration with more functionality has been achieved through 3D packaging technique i.e. system-on-chip (SOC) and system-in-package (SiP). Novel electrical modeling technologies are highly demanded to tackle the challenges posed by the complexity of nano-scale integrated circuits(IC) as well as its package integration.
Usually, the whole package system can be divided into two networks: signal distribution network (SDN) and power distribution network (PDN), where the PDN is often designed as power-ground planes structure to reduce the groundâs impedance. The global coupling effects such as the simultaneous switching noise (SSN) demand a system-level modeling methodology and co-simulation of signal and power integrities. Such a system level packaging EMC simulation is a great challenge to all available electromagnetic simulators [1], [2].
Based on the special features of the package structure, we propose to simulate the PDN by Generalized Transmission Line Equations (GTLE), Finite Difference Time Domain (FDTD) and Finite Difference Frequency Domain (FDFD) [3]. For the power/ground planes, the numerical methods, mesh division technique and finite difference method are used to solve these transmission lines equations and get their equivalent RLCG parameters.
The transmission line equation technique is well known for its capability in treating a wide range of electromagnetic
problems with a great flexibility in terms of geometrical irregularity and material parameters. The equivalence between Maxwell's equation and circuit network allows this technique to solve complex problems in both time- and frequency- domains. It is known that the derivation of conventional transmission line equation (CTLE) is based on such an assumption of an infinite-length transmission line. Unfortunately, practical transmission lines are finite-length. When the CTLE are used in a finite-length unmatched uniform transmission line or arbitrary length nonuniform transmission line, the description of the CTLE for such line discontinuities needs further scrutiny [4], [5].
The reason is that when the nonuniform transmission line is generally treated as a cascading of many short uniform transmission lines, the discontinuities between any two neighboring segments are not only generate reflections, but also produce radiations. Furthermore, the equation is a one- dimensional approximation for a pair of conductor lines. This canât satisfy the simulation for power integrity (PI) in Sip. So it is necessary for extending the one-dimensional equation to 2- or 3-dimensions [6].
In this paper, based on the finite-length line concept and vector partial differential equation, we derive generalized transmission line equation (GTLE) by using circuit theory. However, the coefficients of the GTLE need to be determined by numerical methods, such as differential algebraic equations (DAE). With this equation, the power integrity in PCBs and SiP can be simulated easily and quickly. The GTLE can be solved in time domain or frequency domain. In this paper, a frequency domain solution is discussed with the Finite Difference Frequency Domain (FDFD) technique. Comparing with the methods based on Maxwellâs equation, an obvious advantage of using GTLE is reduction of memory usage and saving processing time since the voltage and current density is only computed on the conductor and not in the entire volume space [7].
The rest of this paper is organized as follows: 1) A description of the GTLE for modeling 2-dimensionla plane is provided. 2) Discretization and numerical methods for GTLE are briefly described. 3) Modeling techniques for fringe effect and excitation is considered. 4) Results from our method are provided, and finally, conclusions are presents.
Generalized transmission line equation In frequency domain, for an infinite-length nonuniform
( )
( )
( ) ( )
( ) ( )
Ï
Ï
(1)
where, V and I are the voltage and current for the infinitely short transmission line; R and L are the per-unit-length series
425
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
resistor and inductance, respectively; C and G are per-unit- length shunt capacitance and conductance, respectively; Ï is angular frequency.
Extending (1) to the GTLE:
( ) ( )
( )
Ï
Ï
(2)
where, Cuc, Guc, Luc, Ruc are the parameters of capacitance, conductance, inductance and resistance per-unit-area for 2- dimensional problem or per-unit-volume for 3-dimensional problem. For a non-isotropic material in the structure, the Luc and Ruc are tensors. Unlike CTLE, V and J in GTLEs are voltage and current density vector flowing through the domain. Vâ and Jââ are the grads and divergence for voltage and current density vector, respectively. Equation (2) can also be deduced from electromagnetic field analysis, Maxwell equation. Same as CTLE, the GTLE describe the voltage and current density on a conductor with reference to a âgroundâ conductor. Therefore, the study will focus on the conductor instead of a pair of conductors.
By applying divergence to both sides of the first equation in equation (2), and replace Jââ by the second equation, a new equation can be written as the following:
2 2
0 ( )( )uc uc uc uc
â + =
ui,j
ui,j-1
Figure 1 Mesh division of a PCB or substrate and
discretization of voltage Obviously, Equation (3) is a Helmholtz equation. In PI
analysis, the2 is the transverse Laplace operator parallel to the planar structures. One method to solve the Helmholtz equation is by applying the finite-difference scheme. Using mesh division technique, the PCB or substrate in SiP is divided into many cells as shown in Figure 1. The 2- dimensional Laplace can be approximated as
( )2 2 1, , 1 1, , 1 ,4 /i j i j i j i j i jV u u u u u hâ â + +â = + + + â (4)
where, h is the mesh length and uij is the voltage at node (i, j) for the cell-centered discretization as shown in Figure 1. Equation (4) is completed by assigning homogenous voltage and current density in one cell.
The discretization results in a well-known bedspring model for plane consisting of per-unit-cell resistance (Ruc) and
inductance (Luc) between neighboring nodes, capacitance (Cuc) and conductance (Guc) from each node to ground. For a parallel-plate transmission line of equal length and width (h), the resistance, inductance, capacitance and conductance per- unit-cell can be obtained as
12
2
2 /
(5)
where, Ï is the resistivity of the conductor, Δr, ÎŒr and tgα are the relative dielectric constant, relative permittivity and loss tangent of the material inside power plane and ground respectively, dC is the distance between two planes, c is the light velocity in the material, dR is the thickness of power plane, and f is the work frequency. The factor of â2â in resistance equation is because there are two conductor planes in this problem. The geometry and electrical model of a unit cell for a single plane pair is shown in figure 2.
Figure 2 Geometry (a) and electrical model (b) of a unit cell for a single plane pair
The unit cell model shown in Figure 2(b) uses a common
ground node. In a multilayered structure consisting of more than two planes, we use the nearest ground plane from the power plane as the reference common ground node.
Easily, boundary condition and connection condition between cells in GTLE can be confirmed by Kirchhoff laws. The boundary condition is current behavior on the boundary. The connection condition is that a voltage should keep in same at the connection region if two or more conductors connected together.
Fringe effect model The model and solution discussed in the previous sections
assumes that each unit cell plane-pairs of infinite extent along the lateral directions. However, fringing fields occur at edge discontinuities. This implies that both the per-unit-length inductance and capacitance will be different from that obtained from parallel plate formulae. This problem has been considered in [8], which proposes building a library that maps various geometries to model elements, and interpolating between these values. However, this technique requires the development of a large database that accounts for variations in dielectric height and permittivity, trace width and metal height, and can suffer from interpolation errors. The technique proposed in [9] modified the fringe fields by adding additional elements to edges, which is easy to implement.
(a) (b)
426
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
. . .
. . .
. . .
. . .
Figure 3 Sketch map of additional cells
( ) ( )
( )
J G j C V z I
Ï
Ï
( )
V k V hI
k j L R j C G h j L R
Ï Ï Ï
(7)
The same as above, equation (7) can also be approximated by Laplace operator.
Results The methodology described in prior sections has been
implemented in a CAD tool. Simulations were performed to compare the methodology against full-wave simulations. Full- wave simulations were performed with finite-element-method based solver, HFSS. The above equations were applied to three test cases to illustrate the application of the GTLE method.
Test case 1: bared power/ground plane pair At first, a bare power/ground plane pair of 1Ă1cm2 square
conductor pair with a dielectric of 20 Όm thickness is tested. The dielectric was FR4 with Δr=4.4. The current excitation and testing port are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm), respectively. There is no component on the plane pair.
The insertion loss (S21) of the plane is shown in figure 4. In all cases, it can be seen that the accuracy of GTLE is comparable with HFSS. The reason of deviation between GTLE and HFSS is mainly about the modal difference between exciting and testing port. In HFSS, the excitation
port is one via resulting parasitic capacitance and inductance. Otherwise, in GTLE, the excitation is processed under equation (7).
This example was discretized using a cell size of 0.2 mm, resulting in about 2700 nodes, and required 34s of computation time for 100 frequencies simulated. But HFSS requires about 16 minutes of CPU time for 100 frequencies, resulting in a speed up of 28Ă.
0 2 4 6 8 10
x 109
Figure 4 S21 for bared power/ground plane pair
Test case 2: low-pass filter A novel low-pass filter of 1Ă1cm2 square is shown in
Figure 5(a). The thickness between power and ground was only 14um with high DK=16. The âwideâ and âgapâ are equal to 0.5mm as shown in Fig. 5(a). âaâ, âbâ, âcâ figure 5(a) are equal to 9, 3.75, 4.75 respectively. The port 1 and 2 are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm). The insertion loss (S21) of this low-pass filter is shown in Figure 5(b). In all cases, it can also be seen that the accuracy of GTLE is comparable with HFSS. And it is also resulting in a speed up of about 28Ă.
b
c
wide
a
gap
(a)
427
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
0 2 4 6 8 10
x 109
Frequency (Hz)
S2 1
(d B)
GTLE HFSS
Figure 5 Simulation of the low-pass filter: (a) the top view of structure; (b) insertion loss (S21).
Test case 3: multilayered structure consisting of four
planes At last, a multilayered structure consisting of four planes
is simulated, that is two power/ground pairs. The up two planes is 1Ă1 cm2, and the down two planes is 2Ă2cm2. In up power/ground pair, the dielectric is FR4 with Δr=4.4 and 130 ÎŒm thickness. In down power/ground pair, the dielectric is Δr=3.2 and 90 ÎŒm thickness. The distance between two power/ground pairs is 150 ÎŒm. The current excitation and testing port are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm) in up power planes, respectively. The power and ground point connecting are at (2, 3) mm and (1, 6) mm.
The insertion loss (S21) of the plane is shown in Figure 6. From Figure 6, it can be seen the deviation of GTLE from HFSS. The reason of error is mainly about the stacking strategy to model a multilayered plane by short-circuit the cells between power and ground planes. In the future work, we will improve the GTLE in multilayered structure adapting the transmission line modal.
0 2 4 6 8 10
x 109
power/ground pairs
Conclusions Generalized Transmission Line Equation (GTLE) method
was developed for simulation of power integrity in Sip structure. The fringe effect and excitation model are presented. Also the discretization and numerical methods for GTLE is presented in order to solve the problem efficiently. The methodology has been compared with full-wave simulators. The simulation results for three test cases matched well. Under similar condition, the GTLE was much faster than HFSS.
Acknowledgments This work was supported by Hi-tech Research and
Development Program of China (863 Program) No. 2006AA01Z236, 2007AA01Z200.
References [1] S. W. Leung, et al. âA mathematical model for ground
voltage fluctuation in PCBsâ, Asia-Pacific of Conference on Environmental Electromagnetic, IEEE, vol.1, 100-104, 2000.
[2] S. W. Leung, et al. âModeling of the ground bounce effect on PCBs for high speed digital circuitsâ, IEEE International Symposium on Electromagnetic Compatibility, on Vol. 1, 110â115, 2005.
[3] Wei-Da Guo, et al, âAn Integrated Signal and Power Integrity Analysis for Signal Traces Through the Parallel Planes Using Hybrid Finite-Element and Finite-Difference Time-Domain Techniquesâ, IEEE Transactions on Advanced Packaging, Vol. 30, Issue 3, pp.558-565, 2007.
[4] Lixi Wan, et al. âDesign, simulation and measurement of embedded ecoupling capacitors for multi-GHz packages/PCBsâ, ICEPT2005 Proccedings, 108-112, 2005.
[5] Er-Ping Li, et al, âAdvanced parallel algorithm for system-level EMC modeling of high-speed electronic packageâ, EMC 2008, pp.1-5.
[6] Yuanqing Wang, et al. âAnalysis of nonuniform coupled transmission lines using generalized transmission line equationsâ, proceeding of APMC, IEEE, vol.3, 2005.
[7] Lixi Wan, et al. âSimulation of switching noise in multi- layer structures using generalized transmission line equation methodâ, IEEE International Symposium on Electromagnetic Compatibility, Vol.2, 1026â1031, 2002.
[8] Ching-Chao Huang, et al, âAccurate Analysis of Multi- Layered Signal and Power Distributions Using the Fringe RLGC Models â, IEEE 13th Topical Meeting on Electrical Performance of Electronic Packaging, 103-106, 2004.
[9] Krishna Bharath, et al, âEfficient Simulation of Power/Ground Planes for SiP Applicationsâ, ECTC '07, 1199-1205.
(b)
428
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
http://www.edatop.com
(www.edatop.com)
ADS
ADS
ADS
http://www.edatop.com/peixun/ads/13.html
HFSS
HFSSHFSS
HFSS
CST
CST
3 âŠ
HFSS
HFSS âŠ
13.56MHz
13.56MHz
13.56MHz
<< /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.6 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize false /OPM 0 /ParseDSCComments false /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo false /PreserveFlatness true /PreserveHalftoneInfo true /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts false /TransferFunctionInfo /Remove /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true /Arial-Black /Arial-BoldItalicMT /Arial-BoldMT /Arial-ItalicMT /ArialMT /ArialNarrow /ArialNarrow-Bold /ArialNarrow-BoldItalic /ArialNarrow-Italic /ArialUnicodeMS /BookAntiqua /BookAntiqua-Bold /BookAntiqua-BoldItalic /BookAntiqua-Italic /BookmanOldStyle /BookmanOldStyle-Bold /BookmanOldStyle-BoldItalic /BookmanOldStyle-Italic /BookshelfSymbolSeven /Century /CenturyGothic /CenturyGothic-Bold /CenturyGothic-BoldItalic /CenturyGothic-Italic /CenturySchoolbook /CenturySchoolbook-Bold /CenturySchoolbook-BoldItalic /CenturySchoolbook-Italic /ComicSansMS /ComicSansMS-Bold /CourierNewPS-BoldItalicMT /CourierNewPS-BoldMT /CourierNewPS-ItalicMT /CourierNewPSMT /EstrangeloEdessa /FranklinGothic-Medium /FranklinGothic-MediumItalic /Garamond /Garamond-Bold /Garamond-Italic /Gautami /Georgia /Georgia-Bold /Georgia-BoldItalic /Georgia-Italic /Haettenschweiler /Impact /Kartika /Latha /LetterGothicMT /LetterGothicMT-Bold /LetterGothicMT-BoldOblique /LetterGothicMT-Oblique /LucidaConsole /LucidaSans /LucidaSans-Demi /LucidaSans-DemiItalic /LucidaSans-Italic /LucidaSansUnicode /Mangal-Regular /MicrosoftSansSerif /MonotypeCorsiva /MSReferenceSansSerif /MSReferenceSpecialty /MVBoli /PalatinoLinotype-Bold /PalatinoLinotype-BoldItalic /PalatinoLinotype-Italic /PalatinoLinotype-Roman /Raavi /Shruti /Sylfaen /SymbolMT /Tahoma /Tahoma-Bold /TimesNewRomanMT-ExtraBold /TimesNewRomanPS-BoldItalicMT /TimesNewRomanPS-BoldMT /TimesNewRomanPS-ItalicMT /TimesNewRomanPSMT /Trebuchet-BoldItalic /TrebuchetMS /TrebuchetMS-Bold /TrebuchetMS-Italic /Tunga-Regular /Verdana /Verdana-Bold /Verdana-BoldItalic /Verdana-Italic /Vrinda /Webdings /Wingdings2 /Wingdings3 /Wingdings-Regular /ZWAdobeF ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages false /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /ColorImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /GrayImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e55464e1a65876863768467e5770b548c62535370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002> /CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc666e901a554652d965874ef6768467e5770b548c52175370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002> /DAN <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> /DEU <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> /ESP <FEFF005500740069006c0069006300650020006500730074006100200063006f006e0066006900670075007200610063006900f3006e0020007000610072006100200063007200650061007200200064006f00630075006d0065006e0074006f0073002000640065002000410064006f00620065002000500044004600200061006400650063007500610064006f007300200070006100720061002000760069007300750061006c0069007a00610063006900f3006e0020006500200069006d0070007200650073006900f3006e00200064006500200063006f006e006600690061006e007a006100200064006500200064006f00630075006d0065006e0074006f007300200063006f006d00650072006300690061006c00650073002e002000530065002000700075006500640065006e00200061006200720069007200200064006f00630075006d0065006e0074006f00730020005000440046002000630072006500610064006f007300200063006f006e0020004100630072006f006200610074002c002000410064006f00620065002000520065006100640065007200200035002e003000200079002000760065007200730069006f006e0065007300200070006f00730074006500720069006f007200650073002e> /FRA <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> /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN <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> /KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020be44c988b2c8c2a40020bb38c11cb97c0020c548c815c801c73cb85c0020bcf4ace00020c778c1c4d558b2940020b3700020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e> /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR <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> /PTB <FEFF005500740069006c0069007a006500200065007300730061007300200063006f006e00660069006700750072006100e700f50065007300200064006500200066006f0072006d00610020006100200063007200690061007200200064006f00630075006d0065006e0074006f0073002000410064006f00620065002000500044004600200061006400650071007500610064006f00730020007000610072006100200061002000760069007300750061006c0069007a006100e700e3006f002000650020006100200069006d0070007200650073007300e3006f00200063006f006e0066006900e1007600650069007300200064006500200064006f00630075006d0065006e0074006f007300200063006f006d0065007200630069006100690073002e0020004f007300200064006f00630075006d0065006e0074006f00730020005000440046002000630072006900610064006f007300200070006f00640065006d0020007300650072002000610062006500720074006f007300200063006f006d0020006f0020004100630072006f006200610074002000650020006f002000410064006f00620065002000520065006100640065007200200035002e0030002000650020007600650072007300f50065007300200070006f00730074006500720069006f007200650073002e> /SUO <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> /SVE <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> /ENU (Use these settings to create PDFs that match the "Required" settings for PDF Specification 4.0) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice
Yunyan Zhou, Lixi Wan, Jun Li Institute of Microelectronics, Chinese Academy of Sciences, Beijing, 100029, China
Email: [email protected]
Abstract Power integrity (PI) simulation for system-in-package
(SiP) is a bottleneck in SiP design flow. This paper presents a novel numerical algorithm for PI simulation in packaging structures. This algorithm is based on 2D Generalized Transmission Line Equation (GTLE), Finite Difference Frequency Domain (FDFD) and mesh division technique. The power distribution network is simulated using mesh division technique where the model of power distribution network is obtained by regarding each cell as a 2D transmission line. 2D GTLE is a group partial equation about voltage and current density distribution on a power/ground plane pair. After reduction, the voltage equation for 2D GTLE is obtained, which is a Helmholtz equation. One method to solve the Helmholtz equation is by the finite-difference scheme. The 2D Laplace operator can be approximated to solve the voltage equation. In this paper, the fringe effect is modeled by the addition of cells around edges which is efficient and easy to implement. Finally, the methodology described in prior sections has been implemented in a CAD tool. The results from our method were compared to those from a full-wave simulator to show efficiency in power integrity simulation.
Introduction The density of transistors dramatically increases with the
down-sizing in semiconductor technology. High-level integration with more functionality has been achieved through 3D packaging technique i.e. system-on-chip (SOC) and system-in-package (SiP). Novel electrical modeling technologies are highly demanded to tackle the challenges posed by the complexity of nano-scale integrated circuits(IC) as well as its package integration.
Usually, the whole package system can be divided into two networks: signal distribution network (SDN) and power distribution network (PDN), where the PDN is often designed as power-ground planes structure to reduce the groundâs impedance. The global coupling effects such as the simultaneous switching noise (SSN) demand a system-level modeling methodology and co-simulation of signal and power integrities. Such a system level packaging EMC simulation is a great challenge to all available electromagnetic simulators [1], [2].
Based on the special features of the package structure, we propose to simulate the PDN by Generalized Transmission Line Equations (GTLE), Finite Difference Time Domain (FDTD) and Finite Difference Frequency Domain (FDFD) [3]. For the power/ground planes, the numerical methods, mesh division technique and finite difference method are used to solve these transmission lines equations and get their equivalent RLCG parameters.
The transmission line equation technique is well known for its capability in treating a wide range of electromagnetic
problems with a great flexibility in terms of geometrical irregularity and material parameters. The equivalence between Maxwell's equation and circuit network allows this technique to solve complex problems in both time- and frequency- domains. It is known that the derivation of conventional transmission line equation (CTLE) is based on such an assumption of an infinite-length transmission line. Unfortunately, practical transmission lines are finite-length. When the CTLE are used in a finite-length unmatched uniform transmission line or arbitrary length nonuniform transmission line, the description of the CTLE for such line discontinuities needs further scrutiny [4], [5].
The reason is that when the nonuniform transmission line is generally treated as a cascading of many short uniform transmission lines, the discontinuities between any two neighboring segments are not only generate reflections, but also produce radiations. Furthermore, the equation is a one- dimensional approximation for a pair of conductor lines. This canât satisfy the simulation for power integrity (PI) in Sip. So it is necessary for extending the one-dimensional equation to 2- or 3-dimensions [6].
In this paper, based on the finite-length line concept and vector partial differential equation, we derive generalized transmission line equation (GTLE) by using circuit theory. However, the coefficients of the GTLE need to be determined by numerical methods, such as differential algebraic equations (DAE). With this equation, the power integrity in PCBs and SiP can be simulated easily and quickly. The GTLE can be solved in time domain or frequency domain. In this paper, a frequency domain solution is discussed with the Finite Difference Frequency Domain (FDFD) technique. Comparing with the methods based on Maxwellâs equation, an obvious advantage of using GTLE is reduction of memory usage and saving processing time since the voltage and current density is only computed on the conductor and not in the entire volume space [7].
The rest of this paper is organized as follows: 1) A description of the GTLE for modeling 2-dimensionla plane is provided. 2) Discretization and numerical methods for GTLE are briefly described. 3) Modeling techniques for fringe effect and excitation is considered. 4) Results from our method are provided, and finally, conclusions are presents.
Generalized transmission line equation In frequency domain, for an infinite-length nonuniform
( )
( )
( ) ( )
( ) ( )
Ï
Ï
(1)
where, V and I are the voltage and current for the infinitely short transmission line; R and L are the per-unit-length series
425
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
resistor and inductance, respectively; C and G are per-unit- length shunt capacitance and conductance, respectively; Ï is angular frequency.
Extending (1) to the GTLE:
( ) ( )
( )
Ï
Ï
(2)
where, Cuc, Guc, Luc, Ruc are the parameters of capacitance, conductance, inductance and resistance per-unit-area for 2- dimensional problem or per-unit-volume for 3-dimensional problem. For a non-isotropic material in the structure, the Luc and Ruc are tensors. Unlike CTLE, V and J in GTLEs are voltage and current density vector flowing through the domain. Vâ and Jââ are the grads and divergence for voltage and current density vector, respectively. Equation (2) can also be deduced from electromagnetic field analysis, Maxwell equation. Same as CTLE, the GTLE describe the voltage and current density on a conductor with reference to a âgroundâ conductor. Therefore, the study will focus on the conductor instead of a pair of conductors.
By applying divergence to both sides of the first equation in equation (2), and replace Jââ by the second equation, a new equation can be written as the following:
2 2
0 ( )( )uc uc uc uc
â + =
ui,j
ui,j-1
Figure 1 Mesh division of a PCB or substrate and
discretization of voltage Obviously, Equation (3) is a Helmholtz equation. In PI
analysis, the2 is the transverse Laplace operator parallel to the planar structures. One method to solve the Helmholtz equation is by applying the finite-difference scheme. Using mesh division technique, the PCB or substrate in SiP is divided into many cells as shown in Figure 1. The 2- dimensional Laplace can be approximated as
( )2 2 1, , 1 1, , 1 ,4 /i j i j i j i j i jV u u u u u hâ â + +â = + + + â (4)
where, h is the mesh length and uij is the voltage at node (i, j) for the cell-centered discretization as shown in Figure 1. Equation (4) is completed by assigning homogenous voltage and current density in one cell.
The discretization results in a well-known bedspring model for plane consisting of per-unit-cell resistance (Ruc) and
inductance (Luc) between neighboring nodes, capacitance (Cuc) and conductance (Guc) from each node to ground. For a parallel-plate transmission line of equal length and width (h), the resistance, inductance, capacitance and conductance per- unit-cell can be obtained as
12
2
2 /
(5)
where, Ï is the resistivity of the conductor, Δr, ÎŒr and tgα are the relative dielectric constant, relative permittivity and loss tangent of the material inside power plane and ground respectively, dC is the distance between two planes, c is the light velocity in the material, dR is the thickness of power plane, and f is the work frequency. The factor of â2â in resistance equation is because there are two conductor planes in this problem. The geometry and electrical model of a unit cell for a single plane pair is shown in figure 2.
Figure 2 Geometry (a) and electrical model (b) of a unit cell for a single plane pair
The unit cell model shown in Figure 2(b) uses a common
ground node. In a multilayered structure consisting of more than two planes, we use the nearest ground plane from the power plane as the reference common ground node.
Easily, boundary condition and connection condition between cells in GTLE can be confirmed by Kirchhoff laws. The boundary condition is current behavior on the boundary. The connection condition is that a voltage should keep in same at the connection region if two or more conductors connected together.
Fringe effect model The model and solution discussed in the previous sections
assumes that each unit cell plane-pairs of infinite extent along the lateral directions. However, fringing fields occur at edge discontinuities. This implies that both the per-unit-length inductance and capacitance will be different from that obtained from parallel plate formulae. This problem has been considered in [8], which proposes building a library that maps various geometries to model elements, and interpolating between these values. However, this technique requires the development of a large database that accounts for variations in dielectric height and permittivity, trace width and metal height, and can suffer from interpolation errors. The technique proposed in [9] modified the fringe fields by adding additional elements to edges, which is easy to implement.
(a) (b)
426
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
. . .
. . .
. . .
. . .
Figure 3 Sketch map of additional cells
( ) ( )
( )
J G j C V z I
Ï
Ï
( )
V k V hI
k j L R j C G h j L R
Ï Ï Ï
(7)
The same as above, equation (7) can also be approximated by Laplace operator.
Results The methodology described in prior sections has been
implemented in a CAD tool. Simulations were performed to compare the methodology against full-wave simulations. Full- wave simulations were performed with finite-element-method based solver, HFSS. The above equations were applied to three test cases to illustrate the application of the GTLE method.
Test case 1: bared power/ground plane pair At first, a bare power/ground plane pair of 1Ă1cm2 square
conductor pair with a dielectric of 20 Όm thickness is tested. The dielectric was FR4 with Δr=4.4. The current excitation and testing port are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm), respectively. There is no component on the plane pair.
The insertion loss (S21) of the plane is shown in figure 4. In all cases, it can be seen that the accuracy of GTLE is comparable with HFSS. The reason of deviation between GTLE and HFSS is mainly about the modal difference between exciting and testing port. In HFSS, the excitation
port is one via resulting parasitic capacitance and inductance. Otherwise, in GTLE, the excitation is processed under equation (7).
This example was discretized using a cell size of 0.2 mm, resulting in about 2700 nodes, and required 34s of computation time for 100 frequencies simulated. But HFSS requires about 16 minutes of CPU time for 100 frequencies, resulting in a speed up of 28Ă.
0 2 4 6 8 10
x 109
Figure 4 S21 for bared power/ground plane pair
Test case 2: low-pass filter A novel low-pass filter of 1Ă1cm2 square is shown in
Figure 5(a). The thickness between power and ground was only 14um with high DK=16. The âwideâ and âgapâ are equal to 0.5mm as shown in Fig. 5(a). âaâ, âbâ, âcâ figure 5(a) are equal to 9, 3.75, 4.75 respectively. The port 1 and 2 are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm). The insertion loss (S21) of this low-pass filter is shown in Figure 5(b). In all cases, it can also be seen that the accuracy of GTLE is comparable with HFSS. And it is also resulting in a speed up of about 28Ă.
b
c
wide
a
gap
(a)
427
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
2009 International Conference on Electronic Packaging Technology & High Density Packaging (ICEPT-HDP)
0 2 4 6 8 10
x 109
Frequency (Hz)
S2 1
(d B)
GTLE HFSS
Figure 5 Simulation of the low-pass filter: (a) the top view of structure; (b) insertion loss (S21).
Test case 3: multilayered structure consisting of four
planes At last, a multilayered structure consisting of four planes
is simulated, that is two power/ground pairs. The up two planes is 1Ă1 cm2, and the down two planes is 2Ă2cm2. In up power/ground pair, the dielectric is FR4 with Δr=4.4 and 130 ÎŒm thickness. In down power/ground pair, the dielectric is Δr=3.2 and 90 ÎŒm thickness. The distance between two power/ground pairs is 150 ÎŒm. The current excitation and testing port are at (3.5, 5.7) (mm) and (6.5, 6.2) (mm) in up power planes, respectively. The power and ground point connecting are at (2, 3) mm and (1, 6) mm.
The insertion loss (S21) of the plane is shown in Figure 6. From Figure 6, it can be seen the deviation of GTLE from HFSS. The reason of error is mainly about the stacking strategy to model a multilayered plane by short-circuit the cells between power and ground planes. In the future work, we will improve the GTLE in multilayered structure adapting the transmission line modal.
0 2 4 6 8 10
x 109
power/ground pairs
Conclusions Generalized Transmission Line Equation (GTLE) method
was developed for simulation of power integrity in Sip structure. The fringe effect and excitation model are presented. Also the discretization and numerical methods for GTLE is presented in order to solve the problem efficiently. The methodology has been compared with full-wave simulators. The simulation results for three test cases matched well. Under similar condition, the GTLE was much faster than HFSS.
Acknowledgments This work was supported by Hi-tech Research and
Development Program of China (863 Program) No. 2006AA01Z236, 2007AA01Z200.
References [1] S. W. Leung, et al. âA mathematical model for ground
voltage fluctuation in PCBsâ, Asia-Pacific of Conference on Environmental Electromagnetic, IEEE, vol.1, 100-104, 2000.
[2] S. W. Leung, et al. âModeling of the ground bounce effect on PCBs for high speed digital circuitsâ, IEEE International Symposium on Electromagnetic Compatibility, on Vol. 1, 110â115, 2005.
[3] Wei-Da Guo, et al, âAn Integrated Signal and Power Integrity Analysis for Signal Traces Through the Parallel Planes Using Hybrid Finite-Element and Finite-Difference Time-Domain Techniquesâ, IEEE Transactions on Advanced Packaging, Vol. 30, Issue 3, pp.558-565, 2007.
[4] Lixi Wan, et al. âDesign, simulation and measurement of embedded ecoupling capacitors for multi-GHz packages/PCBsâ, ICEPT2005 Proccedings, 108-112, 2005.
[5] Er-Ping Li, et al, âAdvanced parallel algorithm for system-level EMC modeling of high-speed electronic packageâ, EMC 2008, pp.1-5.
[6] Yuanqing Wang, et al. âAnalysis of nonuniform coupled transmission lines using generalized transmission line equationsâ, proceeding of APMC, IEEE, vol.3, 2005.
[7] Lixi Wan, et al. âSimulation of switching noise in multi- layer structures using generalized transmission line equation methodâ, IEEE International Symposium on Electromagnetic Compatibility, Vol.2, 1026â1031, 2002.
[8] Ching-Chao Huang, et al, âAccurate Analysis of Multi- Layered Signal and Power Distributions Using the Fringe RLGC Models â, IEEE 13th Topical Meeting on Electrical Performance of Electronic Packaging, 103-106, 2004.
[9] Krishna Bharath, et al, âEfficient Simulation of Power/Ground Planes for SiP Applicationsâ, ECTC '07, 1199-1205.
(b)
428
Authorized licensed use limited to: NANJING UNIVERSITY OF SCIENCE AND TECHNOLOGY. Downloaded on December 16, 2009 at 22:29 from IEEE Xplore. Restrictions apply.
http://www.edatop.com
(www.edatop.com)
ADS
ADS
ADS
http://www.edatop.com/peixun/ads/13.html
HFSS
HFSSHFSS
HFSS
CST
CST
3 âŠ
HFSS
HFSS âŠ
13.56MHz
13.56MHz
13.56MHz
<< /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Warning /CompatibilityLevel 1.6 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize false /OPM 0 /ParseDSCComments false /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo false /PreserveFlatness true /PreserveHalftoneInfo true /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts false /TransferFunctionInfo /Remove /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true /Arial-Black /Arial-BoldItalicMT /Arial-BoldMT /Arial-ItalicMT /ArialMT /ArialNarrow /ArialNarrow-Bold /ArialNarrow-BoldItalic /ArialNarrow-Italic /ArialUnicodeMS /BookAntiqua /BookAntiqua-Bold /BookAntiqua-BoldItalic /BookAntiqua-Italic /BookmanOldStyle /BookmanOldStyle-Bold /BookmanOldStyle-BoldItalic /BookmanOldStyle-Italic /BookshelfSymbolSeven /Century /CenturyGothic /CenturyGothic-Bold /CenturyGothic-BoldItalic /CenturyGothic-Italic /CenturySchoolbook /CenturySchoolbook-Bold /CenturySchoolbook-BoldItalic /CenturySchoolbook-Italic /ComicSansMS /ComicSansMS-Bold /CourierNewPS-BoldItalicMT /CourierNewPS-BoldMT /CourierNewPS-ItalicMT /CourierNewPSMT /EstrangeloEdessa /FranklinGothic-Medium /FranklinGothic-MediumItalic /Garamond /Garamond-Bold /Garamond-Italic /Gautami /Georgia /Georgia-Bold /Georgia-BoldItalic /Georgia-Italic /Haettenschweiler /Impact /Kartika /Latha /LetterGothicMT /LetterGothicMT-Bold /LetterGothicMT-BoldOblique /LetterGothicMT-Oblique /LucidaConsole /LucidaSans /LucidaSans-Demi /LucidaSans-DemiItalic /LucidaSans-Italic /LucidaSansUnicode /Mangal-Regular /MicrosoftSansSerif /MonotypeCorsiva /MSReferenceSansSerif /MSReferenceSpecialty /MVBoli /PalatinoLinotype-Bold /PalatinoLinotype-BoldItalic /PalatinoLinotype-Italic /PalatinoLinotype-Roman /Raavi /Shruti /Sylfaen /SymbolMT /Tahoma /Tahoma-Bold /TimesNewRomanMT-ExtraBold /TimesNewRomanPS-BoldItalicMT /TimesNewRomanPS-BoldMT /TimesNewRomanPS-ItalicMT /TimesNewRomanPSMT /Trebuchet-BoldItalic /TrebuchetMS /TrebuchetMS-Bold /TrebuchetMS-Italic /Tunga-Regular /Verdana /Verdana-Bold /Verdana-BoldItalic /Verdana-Italic /Vrinda /Webdings /Wingdings2 /Wingdings3 /Wingdings-Regular /ZWAdobeF ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages false /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /ColorImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /GrayImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e55464e1a65876863768467e5770b548c62535370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002> /CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc666e901a554652d965874ef6768467e5770b548c52175370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002> /DAN <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> /DEU <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> /ESP <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> /FRA <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> /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN <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> /KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020be44c988b2c8c2a40020bb38c11cb97c0020c548c815c801c73cb85c0020bcf4ace00020c778c1c4d558b2940020b3700020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e> /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR <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> /PTB <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> /SUO <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> /SVE <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> /ENU (Use these settings to create PDFs that match the "Required" settings for PDF Specification 4.0) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice
