EFFICIENT MODELING OF POWER AND SIGNAL INTEGRITY FOR SEMICONDUCTORS AND ADVANCED ELECTRONIC PACKAGE SYSTEMS ZAW ZAW OO (B.E.(Electronic),YTU; M.Eng.(ECE),NUS) A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING NATIONAL UNIVERSITY OF SINGAPORE 2008 Acknowledgements I would like to take this opportunity to convey my deepest and sincere gratitude to people without whom I would not have completed this thesis successfully. First and foremost, I would like to express my deepest gratitude to my supervisors, Professor Li Le-Wei and Dr. Li Er-Ping, for their invaluable contributions and insightful guidance throughout the entire course of the research project. Special thanks to my immediate project supervisor, Dr. Li Er-Ping, for his patience, unselfish and enthusiastic guidance, and reviewing for all manuscripts of the published/submitted technical papers. I would also like to acknowledge the support and friendship I received from my colleagues in Advanced Electronics and Electromagnetics Group at Institute of High Performance Computing, A*STAR, especially Dr. Wei Xingchang, Dr. Liu En-Xiao and Dr. Zhang Yaojiang for their valuable advice and discussions. The sponsorship awarded for my PhD degree candidature by Institute of High Performance Computing (IHPC), A*STAR is gratefully acknowledged. Finally for all the support, love and understanding they have given me throughout the years, I wish to thank my wife, my parents and other family members. i Contents Acknowledgements i Contents ii Summary vii List of Figures ix List of Tables xvii List of Acronyms xviii Chapters Introduction 1.1 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 ii Contents iii 1.5 Original Contributions and Innovations . . . . . . . . . . . . . . . . . 14 Modeling of Interconnects, Transmission Lines, and Power-Ground Planes 15 2.1 Model of Multilayered Package . . . . . . . . . . . . . . . . . . . . . . 16 2.2 Inductance Extraction for the Interconnects in Chip and Package . . 17 2.2.1 Inductance and Reluctance Matrices . . . . . . . . . . . . . . 18 2.2.2 Stability Analysis for Reluctance K-Method . . . . . . . . . . 20 2.2.3 Efficient Inductance Extraction Method . . . . . . . . . . . . 22 2.3 Modeling of Signal Traces as Multiconductor Transmission Lines . . . 26 2.3.1 Quasi-static Matrix Parameters for Multiconductor Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3.2 Capacitance and Conductance Matrix Parameters . . . . . . . 27 2.3.3 Inductance and Resistance Matrix Parameters . . . . . . . . . 28 2.3.4 Examples for RLGC Parameters Extraction . . . . . . . . . . 29 2.4 Cavity-mode Resonator Model for Analysis of Parallel-Plate PowerGround Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Electrical Performance Modeling of Power-Ground Layers with Multiple Vias 41 3.1 Problem Statement for Modeling of Multiple Vias . . . . . . . . . . . 42 3.2 Modal Expansion of Fields in a Parallel-Plate Waveguide . . . . . . . 43 Contents iv 3.3 Multiple Scattering Coefficients among Cylindrical PEC and PMC Vias 46 3.4 Excitation Source and Network Parameter Extraction . . . . . . . . . 53 3.5 Implementation of Effective Matrix-Vector Multiplication in Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.6 Numerical Examples for Single-layer Power-Ground Planes . . . . . . 63 3.6.1 Validation of the SMM Algorithm . . . . . . . . . . . . . . . . 63 3.6.2 Co-simulation Example . . . . . . . . . . . . . . . . . . . . . . 66 3.6.3 Simulation for Power-Ground Planes Decoupling . . . . . . . . 69 3.7 Novel Boundary Modeling Method for Simulation of Finite-Domain Power-Ground Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.7.1 Perfect Magnetic Conductor (PMC) Boundary . . . . . . . . . 71 3.7.2 Frequency-Dependent Cylinder Layer (FDCL) . . . . . . . . . 72 3.8 Numerical Simulations of the Extended SMM Algorithm for Finite Power-Ground Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.8.1 Validations of the Frequency-Dependent Cylinder Layer . . . . 76 3.8.2 Experimental Validations of the Extended SMM Algorithm . . 79 3.8.3 Irregular-shaped Power-Ground Planes and Cut-out Structure 87 3.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Modeling for Multilayered Power-Ground Planes in Power Distribution Network 92 4.1 Modal Expansions and Boundary Conditions . . . . . . . . . . . . . . 93 4.2 Mode Matching in Parallel-plate Waveguides (PPWGs) . . . . . . . . 98 Contents v 4.3 Generalized T Matrix for Two-layer Problem . . . . . . . . . . . . . . 106 4.4 Formulas Summary for Two-layer Problem . . . . . . . . . . . . . . . 111 4.5 Formulas Summary for Multi-layer Problem . . . . . . . . . . . . . . 115 4.6 Numerical Simulations for Multilayered Power-ground Planes with Multiple Vias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Hybrid Modeling of Signal Traces in Power Distribution Network by Using Modal Decomposition 130 5.1 Methodology for Hybridization of SMM and Modal Decomposition . . 131 5.2 Modeling of Power-Ground Planes with Multiple Vias . . . . . . . . . 134 5.3 Modeling of Multiconductor Signal Traces . . . . . . . . . . . . . . . 135 5.3.1 Properties of the Per-Unit-Length Parameters . . . . . . . . . 138 5.3.2 Mode Decoupling of the Parameters in Frequency Domain . . 139 5.3.3 Impedance Matrix of the MTLs with Same Length l . . . . . . 144 5.4 Modeling of Entire Signal Traces in Power Distribution Network . . . 147 5.4.1 Modeling of Striplines between Power-Ground Planes . . . . . 148 5.4.2 Equivalent Circuit Model of Through-Hole Signal Vias . . . . 153 5.4.3 Combination of Equivalent Networks for Modeling of Entire Signal Trace . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 5.5 Numerical Simulations of Hybrid Modeling Algorithm for Signal Traces in PDN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Contents Conclusions and Suggestions for Future Work vi 168 6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 6.2 Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . 170 Bibliography 172 Appendixes 185 A Translational Addition Theorem in Cylindrical Coordinates 185 B Generalized Cascade ABCD Matrix for Entire System 188 List of Publications 193 Summary An accurate electromagnetic modeling of power distribution network (PDN) in an advanced electronic package together with efficient simulation of large-scale powerground vias in multilayered structures has become of vital importance for optimizing the electrical performance of high-speed digital circuits. This thesis focuses on developing accurate and efficient modeling and simulation methods for analyzing the power distribution network for high-speed digital circuits and performing the system-level analysis of advanced electronic packages. Specifically, a systematic approach of efficient system-level simulation for an electronic package is illustrated. The electronic package is separated into two domains: the top/bottom domain and the inner domain. The inner domain is the portion of the package confined by the top and bottom power-ground planes. The former comprises signal traces (microstrip type), microstrip to via transitions, solder balls (for flip-chip packages) etc. The latter mainly consists of parallel-plate power-ground planes and vias. Those two domains are self-contained multiport networks, and they are connected at the outmost anti-pad regions of the plate-through vias. Then, an accurate hybrid modeling approach of multiple scattering theory for coupling of power-ground (P-G) vias in the multilayered electronic package and modal decomposition of the propagating modes in the package is implemented for the power integrity (PI) and signal integrity (SI) analyzes of the signal traces in the electronic package in the presence of large number of vias. The proposed semi-analytical approach of the scattering matrix method (SMM) vii Summary viii is first developed for the analysis of multiple scattering of vias in the power distribution network. A novel boundary modeling method, that is, frequency-dependent cylinder layer (FDCL), is then proposed based on the factitious layer of PMC cylinders with frequency-dependent radii at the periphery of an electronic package to simulate the finite power-ground planes of real world packages. The formulation of the SMM algorithm with FDCL is extended to simulate multilayered structures of the P-G planes by using the modal expansions of parallel-plate waveguide and mode matching in the anti-patch region of each via. Numerical experiments are provided for validation of the developed algorithm. The results demonstrate that the proposed method is accurate and efficient to address the power integrity analysis of real world electronic package with multilayered P-G planes and large-scale P-G vias. Subsequently, an efficient modeling technique based on modal decomposition of the electromagnetic fields is proposed for system-level analysis of the power distribution network in the package including the signal traces and the multilayered power-ground planes with multiple vias. An analytical model is also introduced for modeling of the discontinuities of the signal traces at the through-hole via. Then, a novel hybrid modeling algorithm is developed to calculate the equivalent network parameters for the entire power distribution. Numerical simulations of the developed hybrid algorithm are presented and validated with full-wave numerical method. The hybrid modeling algorithm developed in this research work provides the accurate and computationally efficient results. List of Figures 1.1 Power distribution noises coupling in system-on-package (SOP). (Courtesy: M. Swaminathan et al ) . . . . . . . . . . . . . . . . . . . . . . 1.2 Chip, package and power distribution network. (Courtesy: M. Swaminathan et al ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Schematic diagram of a multilayered advanced electronic package. . . 10 1.4 Illustration of the system-level modeling approach for advanced electronic packages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 A schematic of multilayered microprocessor package. . . . . . . . . . 16 2.2 A schematic of top-level metal for signal interconnects has an underlying orthogonal interconnect array. . . . . . . . . . . . . . . . . . . . 23 2.3 Crosstalk noise on the center bus of signal-lines system in Fig. 2.2. . 25 2.4 Signal delay on the center bus of signal-lines system in Fig. 2.2. . . 25 2.5 Sketch of coupled microstrips. All dimensions are in mm. . . . . . . . 30 2.6 Sketch of multiconductor transmission lines on a multilayered board. All dimensions are in mm. . . . . . . . . . . . . . . . . . . . . . . . . 30 2.7 Geometric structure of a rectangular power-ground planes. . . . . . . 32 ix Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 25 Figure 2.3: Crosstalk noise on the center bus of signal-lines system in Fig. 2.2. Figure 2.4: Signal delay on the center bus of signal-lines system in Fig. 2.2. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 2.3 26 Modeling of Signal Traces as Multiconductor Transmission Lines The signal traces in the electronic packages broadly consist of the straight transmission lines, via discontinuities and through-hole vias. The straight signal traces in the signal layers of the packages can be modeled by multiconductor transmission lines. The via discontinuities and through-hole vias are modeled as the equivalent circuits using the analytical formula. In this section, the modeling method for the uniform transmission lines is presented. By considering the uniform transmission lines as two-dimensional problem, the integral equation solved by the method of moments (MoM) is applied to extract the RLCG (resistance, inductance, capacitance, and conductance) parameters. 2.3.1 Quasi-static Matrix Parameters for Multiconductor Transmission Lines Assume that the multiconductor transmission line system to have N signal conductors and one (or two) reference (“ground”) conductor(s), that it is uniform along its length, and that its dielectric is piecewise homogeneous. The primary quasistatic parameters of the system are the matrix of inductances per unit length [L], the matrix of capacitances per unit length [C], the matrix of resistances per unit length [R], and the matrix of conductances per unit length [G]. In a quasi-static analysis, assuming the skin-effect to be fully stated, the matrices [C] and [G] are evaluated from the solution to one electrostatic problem, while the matrices [L] and [R] are evaluated from the solution to another electrostatic problem. The first electrostatic problem is the analysis of a two-dimensional system which coincides with the analyzed multiconductor transmission line. The dielectric losses are evaluated by taking the dielectric permittivity to be complex, and the analysis results in a complex matrix of electrostatic induction coefficients from which the required real Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 27 matrices [C] and [G] are obtained. If the dielectrics are nonmagnetic, the second electrostatic problem consists of only the transmission line conductors while the dielectrics are removed and replaced by a vacuum. The solution of this problem results in the matrix [C0], and [L] = √ (1/c20 )[C0 ]−1, where c0 = 1/ ε0µ0 , µ0 is the permeability of free space, and is the permittivity of free space. Using the perturbation approach, the matrix [C] can be evaluated from the solution. In the case where the material is magnetic, but linear, the evaluation of the matrix [L] can be reduced to an analysis of an equivalent electrostatic system where the relative dielectric permittivity is taken to be εr = 1/µr , as explained in [81]. Once the capacitance, conductance, inductance, and resistance matrices of the multiconductor transmission line system are known, the complete behavior of the system can be determined, to the transmission line approximation, by the multiconductor transmission line theory [82]. 2.3.2 Capacitance and Conductance Matrix Parameters Under the assumption of the quasi-static TEM approximation, the capacitance and conductance parameters of a transmission line can be obtained by solving an electrostatic problem. Its governing equation in free space is given by the Poisson equation: ∆φ(r) = − ρs (r ) , ε0 (2.21) where ∆ is the Laplacian operator and ρs stands for total surface charges. The 2D Green’s function for (2.21) is G(r, r ) = − ln |r − r | . 2πε0 (2.22) For the problem of multilayered multiconductor transmission lines, we solve it using free-space Green’s function with total charges on conductors and polarization charges on dielectric interfaces. The potential φ due to electric charges can be Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes written as φ(r) = 2πε j Ωj ρs (r ) ln |r − rˆ | dl , |r − r | 28 (2.23) ˆ where Ωj denotes the surface of conductors and dielectric interfaces. r, r and r represent the positions of the observation, source and image points, respectively. By enforcing the appropriate boundary conditions, we can solve for ρs by the MoM. Then, the capacitance matrix C can be obtained by Nc i = 1, · · · , Nc Cij Vj = Qj , (2.24) j=1 where Nc is the number of conductors excluding the reference ground conductor. The free charges on the conductor j is Qj = Ωj ρs (r )dl . (2.25) If the multilayered substrates are made of lossy media, then we can let ε be a complex number given by εˆ = ε − j σd ω , (2.26) where σd is the conductivity of the dielectric substrate. This will results in a complex matrix Cˆ in (2.24). Then we have the following capacitance matrix [C] and conductance matrix [G] below: ˆ [C] = Re(C) (2.27) ˆ ·ω. [G] = −Im(C) 2.3.3 Inductance and Resistance Matrix Parameters Similar to the extraction of the p.u.l. (per unit length) capacitance and conductance in the previous section, we can extract the inductance and resistance matrices of multiconductor transmission lines by solving a magnetostatic problem. Az (r) = µ0 2π j Ωj Jz (r ) ln |r − rˆ | dl , |r − r | (2.28) where Az is the z component (longitudinal direction of the multiconductor transmission lines) of the magnetic vector potential at an arbitrary point r. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 29 Comparing (2.28) to (2.23), we observed that these two equations have exactly the same expression if we exchange 1/ε with µ0 . Therefore, we can use the results obtained from (2.23) to produce the inductance and resistance matrices. In fact, we have [L] = [C0 ]−1 , c20 (2.29) where c0 is the speed of light in vacuum and [C0] is the free-space capacitance matrix of the multiconductor system. The resistance matrix R can be derived from the surface-current density by Js = c20ρs and the power loss in conductors per unit length is given by Nc Pc = j=1 Ωj s Jz dl , (2.30) and s = ωµ0 = , 2σ σδ (2.31) where σ is the conductivity of the conductors, and δ is the skin depth. The power loss expressed in (2.30) can be also formulated as Nc Nc Pc = Rmn Im In . (2.32) m=1 n=1 Thus, the resistance matrix [R] = [Rmn ] is obtained by equating (2.32) to (2.30). 2.3.4 Examples for RLGC Parameters Extraction Some numerical examples are shown here to demonstrate the extraction of RLCG parameters using the above method. Consider the pair of coupled microstrips touching a dielectric slab over a conducting plane as shown in Fig. 2.5. Table 2.4 compares the computed results with those of [83, 84]. Another example is presented to calculate the results for the multiconductor transmission line sketched in Fig. 2.6. The thickness of the conductors is taken to be finite in this case of 20 µm, they are assumed to be made of copper with conductivity σ = 56 × 106 S/m, the loss tangent of both dielectrics is assumed to be 0.001, and the operating frequency is GHz. The geometries of the structure are Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 30 Figure 2.5: Sketch of coupled microstrips. All dimensions are in mm. Table 2.4: Comparison of results for the coupled microstrips in Fig. 2.5 (Units: pF/m) Simulated results Reference [84] Reference [83] C11 91.654 90.17 92.24 C12 -8.2202 -8.059 -8.504 C21 -8.2202 -8.059 -8.504 C22 91.654 90.17 92.24 Figure 2.6: Sketch of multiconductor transmission lines on a multilayered board. All dimensions are in mm. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 31 shown in Fig. 2.6. The resulted matrices of the primary parameters are obtained and given by ⎡ [C] = ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ −19.8456 ⎤ −19.8412 155.0641 −0.3749 ⎥ ⎥ −31.5590 −0.3347 ⎥ ⎥ −2.1475 −30.7721 106.7193 −7.7258 −0.3677 −0.3289 −7.7266 97.8107 138.5509 −2.2135 ⎡ [L] = ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ [G] = pF/m , ⎤ 282.2224 46.4450 27.1491 46.4450 268.3930 80.9855 7.5104 ⎥ ⎥ 15.8952 ⎥ ⎥ 27.1491 80.9846 282.2272 47.8455 ⎥ ⎥ 7.5103 15.8950 47.8455 287.7354 ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎥ ⎦ ⎥ ⎥ nH/m , ⎦ ⎤ 837.2265 −122.2908 −1.6245 −122.2381 938.4743 −174.7545 −0.0318 ⎥ ⎥ −0.2013 ⎥ ⎥ −0.9993 −164.6412 558.5089 −14.6500 ⎥ ⎥ 0.0371 −0.1496 −14.6574 512.9538 ⎥ ⎥ ⎦ ⎡ ⎤ ⎢ 15.6558 0.0853 ⎢ ⎢ ⎢ 0.0853 16.9353 [R] = ⎢ ⎢ ⎢ ⎢ ⎣ µS/m , 0.7262 0.3329 0.1356 ⎥ ⎥ 0.1920 ⎥ ⎥ 0.7262 0.3329 11.2885 0.2512 0.1356 0.1920 0.2512 ⎥ ⎥ ⎥ ⎥ ⎦ Ω/m . 8.6857 The above computed matrices resulted in a good symmetry show that a confidence in the accuracy of the results, as compared to those in [68]. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 2.4 32 Cavity-mode Resonator Model for Analysis of Parallel-Plate Power-Ground Planes A power delivery network much less than the smallest wavelength of interest in dimension can be characterized by a 2-D Helmholtz’s equation in terms of the E-field normal to the planes, along with the open boundary conditions (perfect magnetic wall) around the periphery of the planes [13]. Then, the power delivery network can be considered as a 2-D microwave planar circuit with n external observation ports. For power and ground planes with simple shapes, such as a rectangle and an equilateral triangle, the impedance matrix can be obtained analytically [13, 48, 85]. Figure 2.7: Geometric structure of a rectangular power-ground planes. Figure 2.7 shows a typical schematic of rectangular power-ground planes as a cavity structure. The two conductor planes of length a and width b and conductivity σ are separated by the dielectric substrate, characterized with the relative permittivity εr and loss tangent tan δ. The separation distance of the two planes is d and is assumed to be much electrically small compared to the shortest operating wavelength. The square ports i and j are located at (xi , yi ) and (xj , yj ) with dimensions Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 33 (Wxi , Wyi ) and (Wxj , Wyj ), respectively. According to the cavity model, the mutual impedance between port j to port i can be calculated [13, 48, 86] as ∞ ∞ Zij (ω) = m=0 n=0 jωµdNmni Nmnj , − k2) ab (kmn (2.33) where the integers m, n are mode indices, and mπ nπ + a b tan δ + r/d √ k = ω µε − j = kmn (2.34b) ωµσ r = Nmni = cm cn cos ⎧ ⎪ ⎨ cm , cn = (2.34a) 1, √ ⎪ ⎩ 2, (2.34c) mπxi a nπyi b cos sinc mπWxi 2a sinc m, n = nπWyi (2.34d) 2b (2.34e) m, n = . Figure 2.8 presents four examples of the power-ground planes with different port locations. The following simulation results are based on these port locations to characterize the impedance properties of the power-ground planes. In Fig. 2.8(a), both Port and Port are considered locating at the center of the plane. Figure 2.9 gives the frequency-dependent impedance characteristics of the power bus plane, calculated with different number of modes. It can be seen that for a specific mode, there is only one corresponding resonant frequency at which the real part of impedance reaches to the maximum and imaginary part of impedance is approaching zero. The resonant behavior of the power-ground planes can be explained by rewriting (2.33) as follows M N Zij (ω) = m=0 n=0 Nmni Nmnj jωC0 + Gmn + jωLmn , (2.35) where Lmn = ωmn = C ωmn kmn µε (2.36a) (2.36b) Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 34 Figure 2.8: Illustration of port locations for the numerical examples of power-ground planes. C0 = abε d Gmn = C0 ωmn tan δ + (2.36c) r . d (2.36d) The Lmn , C0 and Gmn represent the inductance, capacitance and conductance, respectively. Figure 2.10 compares the real and image parts of the self-impedance of center port of the power bus plane. It can be seen that more than 200 × 200 = 40, 000 modes need to be included to obtain the accurate impedance properties of the power bus over a wide spectrum from DC to 80 GHz. Few modes can give accurate results in lower frequency band while fail at high frequency. Figure 2.11 compares the self and mutual impedances of two ports shown in Fig. 2.8(b). It can be seen that for either self-impedance or transfer impedance, the peak value occurs at the same resonant frequency pertaining to a specific resonant mode. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 35 (a) Real part (b) Imaginary part Figure 2.9: Self-impedance of the port at the center of the power-ground plane. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 36 (a) Real part (b) Imaginary part Figure 2.10: Input impedance of the port at the center of the power-ground plane. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 37 Figure 2.11: Self and mutual impedances of two ports shown in Fig. 2.8(b). Then, we consider the layout of ports shown in Fig. 2.8(c). The Port is the center of the plane while the Port is located at the one fourth point of a diagonal bisection. The corresponding results are presented in Fig. 2.12. Obviously, the asymmetric Port and Port excite different resonant mode sets and the transfer impedance (mutual noise) can be suppressed due to asymmetric configuration. Similar result is also found in Fig. 2.13 for the port configuration of Fig. 2.8(d). Figure 2.12: Self and mutual impedances of two ports shown in Fig. 2.8(c). Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 38 Figure 2.13: Self and mutual impedances of two ports shown in Fig. 2.8(d). Shorting vias or buried vias and decoupling capacitors are usually used to suppress via coupling noise. Suppose there are Ns shorting vias and Np ports in the power-ground planes. According to the cavity model of the power-ground planes, the impedance expression for total Ns + Np ports is given as follows: ⎡ ⎢ ⎣ ⎤ ⎡ ⎤⎡ ⎤ Vp ⎥ ⎢ Zpp Zps ⎥ ⎢ Ip ⎥ ⎦=⎣ ⎦⎣ ⎦. Vs Zsp Zss Is (2.37) The voltages along the shorting vias should be vanished, i.e., Vs = 0. Therefore, the voltages along ports Vp can be obtained as Vp = Zpp − Zps Z−1 ss Zsp Ip . (2.38) Figure 2.14 shows the input impedance of a 15.2 × 9.0 cm2 power-ground planes with a shorting pin. The positions of the port and shorting pin are (12.2, 6.0) and (3.0, 3.0); all in cm. The dielectric layer is 1.27 mm thick and with relative permittivity of εr = 4.3 and a loss tangent of tan δ = 0.02. The calculated result shown in Fig. 2.14, which is calculated by the cavity-mode resonator model, agrees with the measurement data in Fig. of [87]. Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 39 Figure 2.14: Magnitude of input impedance of two-layered plate with a shorting pin. 2.5 Summary In this chapter, the concept of reluctance K element is introduced and the stability issue in the reluctance K-method is discussed. Then, the direct extraction method for partial reluctance K is developed to analyze the inductance of interconnects (signal lines) in chips and electronic packages. The numerical examples for extracting the inductance matrix of the interconnects are presented to simulate the crosstalk noise and signal delay of the signal lines system. An efficient numerical technique is also presented for the evaluation of the primary matrix parameters (R, L, G, C) of multiconductor transmission lines with piecewise-homogeneous dielectric substrates. The method is based on solving two electrostatic problems, where the distribution of the free and bound charges is obtained as a solution of a system of integral equations using the Galerkin’s procedure with a pulse approximation. The resulting integrals are evaluated in closed forms. The numerical examples are presented for the RLGC parameters extraction of the coupled microstrip lines and the multiconductor transmission lines on multilayered Chapter 2. Modeling of Interconnects, Transmission Lines and P-G Planes 40 board. As compared to the point-matching method, a significant improvement in accuracy is achieved by using the present method. Power-ground plane structures are usually used in multilayered electronic packages and printed circuit boards (PCBs) for digital circuits and systems. Due to the very small thickness compared with the package or PCB dimensions, the planes behave somewhat like the resonators that signals in some points of the geometry may couple strongly to another propagation through the cavity for certain resonant frequencies. Based on the cavity model with experimental validation, the modal analysis and simulation results of the power-ground planes in the PCBs are presented in the chapter. This frequency-domain approach can acquire some impedance values directly that would be very useful in the primary board-level and package-level designs for high-speed digital circuit and systems. [...]... planes and the split stripline 15 1 5 .10 Through-hole signal via and its equivalent circuit 15 3 5 .11 PEC/PMC boundaries defined for analysis of the via region as a bounded coaxial cavity 15 4 5 .12 Overall equivalent network for the signal trace routed in the power distribution network 15 6 5 .13 The dimensions of a signal. .. an electronic package Numerical validations for the implemented SMM algorithm with the proposed Chapter 1 Introduction 12 Figure 1. 4: Illustration of the system-level modeling approach for advanced electronic packages Chapter 1 Introduction 13 frequency-dependent cylinder layer (FDCL) are presented as well The formula derivation for multilayered structure of power- ground planes in an advanced electronic. ..List of Figures x 2.8 Illustration of port locations for the numerical examples of powerground planes 34 2.9 Self-impedance of the port at the center of the power- ground plane 35 2 .10 Input impedance of the port at the center of the power- ground plane 36 2 .11 Self and mutual impedances of two ports shown in Fig 2.8(b) 37 2 .12 Self and mutual impedances of two ports... region In the latter part of the chapter, the cavity model analysis for transfer impedance of the power- ground planes in parallel-plate structure is presented 15 Chapter 2 Modeling of Interconnects, Transmission Lines and P-G Planes 2 .1 16 Model of Multilayered Package A schematic of the multilayered structure of an electronic package is shown in Fig 2 .1 Besides the power and ground metal plates in... 16 0 5 .16 Reflection and transmission characteristics of the signal trace with the decoupling capacitors shown in Fig 5 .15 16 1 5 .17 The dimensions of two coupled signal traces routed between the powerground planes (top view and side view) - Case 1 All black dots represent the P-G vias (unit: mm) 16 2 5 .18 Reflection characteristic of the two coupled signal traces... between the power- ground planes shown in Fig 5 .17 16 3 5 .19 Transmission characteristic of the two coupled signal traces routed between the power- ground planes shown in Fig 5 .17 16 4 5.20 Crosstalk characteristic of the two coupled signal traces routed between the power- ground planes shown in Fig 5 .17 16 4 5. 21 The dimensions of two coupled signal traces routed between the powerground... schematic of the cylindrical coordinates in global expression for cylinders p and q 18 6 List of Figures xvi B .1 Definition for generalized cascade matrix of 2N-port network 18 9 B.2 Total generalized matrix of cascaded networks 18 9 B.3 Cascade a 2N-port network with a two-port network 19 1 List of Tables 2 .1 Geometry details for simulation of signal. .. frequency and convergence toward mixed -signal systems, supplying clean power to the integrated circuits and managing the noise coupling in the system are very important and the power supply can be a major bottleneck for the reliable functioning of the system [16 , 17 ] Modeling of power distribution networks represents an integral part of the power delivery design process In the last 15 years, the modeling. .. 14 4 5.5 Signal trace route in the power- ground planes of power distribution network 14 7 5.6 Cross-section view of the stripline route 14 8 5.7 Transmission line representations of the stripline and its split model 14 9 5.8 Port voltages and currents defined for three equivalent networks 15 1 5.9 Combination for the equivalent Y-networks of the power- ground... articles and 12 conference papers, as illustrated at the end of the thesis Chapter 2 Modeling of Interconnects, Transmission Lines, and Power- Ground Planes The advanced electronic package is constructed with various interconnections inside the package such as multilayered power- ground planes and signal layers, powerground pins (vias), signal vias, plate-through holes (PTHs), and different kinds of transmission . vii List of Figures ix List of Tables xvii List of Acronyms xviii Chapters 1 1 Introduction 1 1 .1 BackgroundInformation 1 1.2 Overview 3 1. 3 Motivations 7 1. 4 OutlineoftheThesis 11 ii Contents iii 1. 5. EFFICIENT MODELING OF POWER AND SIGNAL INTEGRITY FOR SEMICONDUCTORS AND ADVANCED ELECTRONIC PACKAGE SYSTEMS ZAW ZAW OO (B.E. (Electronic) ,YTU; M.Eng.(ECE),NUS) A THESIS SUBMITTED FOR THE. al 4 ) 9 1. 3 Schematic diagram of a multilayered advanced electronic package. . . 10 1. 4 Illustration of the system-level modeling approach for advanced elec- tronicpackages 12 2 .1 A schematic of multilayered