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Package-Chip Co-Design Prof. Lei He Electrical Engineering Department, UCLA LHE@ee. ucla. edu http: //eda. Package-Chip Co-Design Prof. Lei He Electrical Engineering Department, UCLA LHE@ee. ucla. edu http: //eda. ee. ucla. edu ASPDAC 06 Lei HE, UCLA 1

Outline • Overview of Chip Package Co-design • IO planning and placement • Power Outline • Overview of Chip Package Co-design • IO planning and placement • Power integrity in package • Reading: package tutorial at ee 201 c wiki ASPDAC 06 Lei HE, UCLA 2

Wire-bond vs Flip-chip • Wire bonding – Cheap Implementation – Difficult to design – Wire-bond vs Flip-chip • Wire bonding – Cheap Implementation – Difficult to design – IO signals are at boundary – High inductance (~1 n. H) – More worry on core and IO power distribution during design and analysis ASPDAC 06 Lei HE, UCLA 3

Wire-bond vs Flip-chip • Flip-chip – IO cells can be over entire of chip Wire-bond vs Flip-chip • Flip-chip – IO cells can be over entire of chip area – Low inductance (~0. 1 n. H) – High pin count, high cost – Less worry on power delivery ASPDAC 06 Lei HE, UCLA 4

Silicon Package Board (Cadence) ASPDAC 06 Lei HE, UCLA 5 Silicon Package Board (Cadence) ASPDAC 06 Lei HE, UCLA 5

Connection from die to board • Die (IO cells -> RTL routing -> bumps) Connection from die to board • Die (IO cells -> RTL routing -> bumps) • -> package (bumps -> escape routing -> package routing -> balls) • -> board ASPDAC 06 Lei HE, UCLA 6

VLSI-Centric Design (Problematic) • IC and package tools very separated: IC Physical Design Package VLSI-Centric Design (Problematic) • IC and package tools very separated: IC Physical Design Package Physical Design I/O Locations IBIS Models Package Modeling/Simulation IC Modeling/Simulation (From P. Franzon) ASPDAC 06 Lei HE, UCLA 7

On-Chip Design Concerns n Physical Concerns Ø Die Netlist Connectivity (logic cells to IO On-Chip Design Concerns n Physical Concerns Ø Die Netlist Connectivity (logic cells to IO cells) Ø System Connectivity (IO cells to package) Ø Power Network (power planes to power IO cells to logic cells) n Electrical Concerns Ø Ø Core Timing Constraints System Timing Constraints Power Budget Signal Integrity and Reliability Constraints Ø Supply voltage scaling imposes very tight noise margins on chip and package designs Ø Significant noise contribution from core switching Ø But greater on-chip exposure to package-side (i. e. , IO) SSN ASPDAC 06 Lei HE, UCLA 8

Package Design Concerns • Physical Concerns Ø Reduce stack-up layers and package cost Ø Package Design Concerns • Physical Concerns Ø Reduce stack-up layers and package cost Ø Place IO cells and decoupling capacitance Ø Complete escaping and package routing • Electrical Concerns Ø Reduce SSN noise Ø Lower impedance of power distribution Ø Meet timing constraints, especially for bus and differential pairs ASPDAC 06 Lei HE, UCLA 9

Typical Package Design Cycle Pad/package Iteration: P&R of IO/Pad cells, Pins; Pwr/gnd and inter-cell Typical Package Design Cycle Pad/package Iteration: P&R of IO/Pad cells, Pins; Pwr/gnd and inter-cell connections; PCB pin locations (x, y); Floorplanning of IO/Pad/Pins; Define Netlist hierarchy/manipulations Manufacturing and NRE Costs; Die, Substrate, Package/Pad/IO Rule checking (PRC): SI, timing, clocks, IO voltages, assembly rules, special regions Verify user specified requirements and rules; PCB pins, Power grid, # VSS/VDD, decoupling caps, EMI, ESD, Vias Defining Interfaces, Signals, PLL, Power, Clock, # pins, # IOs Package/Substrate Architecture Exploration (start ~4/5 months before Tapeout) ASPDAC 06 Finalize IOs/Pads/Pins; Package Tapeout Lei HE, UCLA 10

Needs of Chip-Package Co-Design • High system frequency – – 400 MHz buses becoming Needs of Chip-Package Co-Design • High system frequency – – 400 MHz buses becoming common On-chip exposure to package noise • Simultaneous switching noise • Package resonance • High density packaging and high pin count • Difficult to layout and escape-route • Again, more SSN for on-die circuit • Tight time to market – ASPDAC 06 Convergence of package and IO becomes a bottleneck if chip and package handled by separated flows Lei HE, UCLA 11

Keys Problems to Solve • Chip and package co-extraction and co-simulation – Difficult to Keys Problems to Solve • Chip and package co-extraction and co-simulation – Difficult to obtain accuracy for sign-off – More difficult to achieve efficiency with accuracy or fidelity for planning and design – Challenging to handle mutual inductance and large number of ports • Co-design focuses on important links between chip and package – Chip side: IO buffer design, noise isolation circuitry, P/G network, IO pad macro-placement, RDL estimation, – Package side: Package stack-up, P/G plane design, macroplacement of balls and pins, and estimation of escape routing – key issues: • IO planning and placement, power delivery system ASPDAC 06 Lei HE, UCLA 12

Outline • Overview of Chip Package Co-design • IO planning and placement – Design Outline • Overview of Chip Package Co-design • IO planning and placement – Design constraints – Multi-stage solutions • Power integrity in package ASPDAC 06 Lei HE, UCLA 13

Design Constraints for IO Planning and Placement • • Power integrity Timing I/O standards Design Constraints for IO Planning and Placement • • Power integrity Timing I/O standards Core and board floorplanning ASPDAC 06 Lei HE, UCLA 14

Power Integrity Constraints • Power domain constraint – I/O cell voltage specification – Cells Power Integrity Constraints • Power domain constraint – I/O cell voltage specification – Cells from same domain prefer physically closer • Minimize power plane cut lines in the package – Provide proper power reference plane for traces – Depend on physical locations of I/O cells • Proper signal-power-ground (SPG) ratio – Primary and secondary P/G driver cells – Minimize voltage drop and Ldi/dt noise ASPDAC 06 Lei HE, UCLA 15

Timing Constraints • Substrate routes in package varies significantly – Length spans from 1 Timing Constraints • Substrate routes in package varies significantly – Length spans from 1 mm to 21 mm – Timing varies more than 70 ps for SSTL_2 • I/O cells with critical timing constraints shall take this into account – Differential pairs and bus prefer to escape in parallel and in same layer ASPDAC 06 Lei HE, UCLA 16

I/O Standard Related Constraints • High-speed design high-speed I/O • I/O standard requirements – I/O Standard Related Constraints • High-speed design high-speed I/O • I/O standard requirements – Relative timing requirements on signals – Likely to be connected to the same interface at other chips, so prefer to keep relative order to ease routing • Closeness constraint – Less process variation • Bump assignment feasibility constraint ASPDAC 06 Lei HE, UCLA 17

Floorplan Induced Region Constraints • Top-down design flow – PCB floorplan • Bottom-up design Floorplan Induced Region Constraints • Top-down design flow – PCB floorplan • Bottom-up design – Chip floorplan • I/O cells have region preference – Which side? – What location? ASPDAC 06 Lei HE, UCLA 18

Connection from die to board • Die (IO cells -> RTL routing -> bumps) Connection from die to board • Die (IO cells -> RTL routing -> bumps) • -> package (bumps -> escape routing -> package routing -> balls) • -> board ASPDAC 06 Lei HE, UCLA 19

Flow of IO planning and placement • Global I/O and Core coplacement • Bump Flow of IO planning and placement • Global I/O and Core coplacement • Bump array Placement • I/O site definition • Constraint driven detailed I/O placement ASPDAC 06 Lei HE, UCLA 20

Global I/O and Core Co-placement • Minimize both wire length and power domain slicing Global I/O and Core Co-placement • Minimize both wire length and power domain slicing • Power domain plans I/O cells location, and becomes region constraints for I/O cells for the following steps ASPDAC 06 Lei HE, UCLA 21

Bump and Site Definition • Regular bump pattern is preferred – Escapability analysis • Bump and Site Definition • Regular bump pattern is preferred – Escapability analysis • Regular I/O site is preferred – I/O proximity – RDL planar routability analysis • I/O sites more than I/O cells – SPG ratio consideration – Flexibility for later bump assignment • I/O super site: a cluster of I/O sites ASPDAC 06 Lei HE, UCLA 22

Assign I/O Cells to Super I/O Sites • A set of region constraints (Ri, Assign I/O Cells to Super I/O Sites • A set of region constraints (Ri, Ci. R) – A rectangular restricted area Ri for I/O cells Ci. R – E. g. , floorplan, power domain definition, wire length minimization • A set of clustering constraints (Li, Ci. L) – The spread of I/O cells should be less than a bound – E. g. , I/O standard const. , floorplan, timing • A set of differential pair constraints – Different pairs should be connected to bumps with similar characteristics – E. g. , timing • Solve by ILP or LP followed by netflow-based legalization – Paper 2 C-4, Wednesday afternoon at this conference ASPDAC 06 Lei HE, UCLA 23

Experiment Setting • Real industrial designs • Constraints not include the ones that are Experiment Setting • Real industrial designs • Constraints not include the ones that are generated internally ASPDAC 06 Lei HE, UCLA 24

Experiment Result • Obtain 100% CSR (constraint satisfaction ratio) in short runtime ASPDAC 06 Experiment Result • Obtain 100% CSR (constraint satisfaction ratio) in short runtime ASPDAC 06 Lei HE, UCLA 25

Power Plane Cuts Core Domain Plane Cut Island IO Domain ASPDAC 06 Lei HE, Power Plane Cuts Core Domain Plane Cut Island IO Domain ASPDAC 06 Lei HE, UCLA 26

Power Domain Routing ASPDAC 06 Lei HE, UCLA 27 Power Domain Routing ASPDAC 06 Lei HE, UCLA 27

Outline • Chip Package Co-design Flow • IO planning and placement • Power integrity Outline • Chip Package Co-design Flow • IO planning and placement • Power integrity in package – Overview and modeling – Decap insertion • Impedance based • Noise-based ASPDAC 06 Lei HE, UCLA 28

Power Integrity • Time domain • Frequency power and domain analysis signal integrity of Power Integrity • Time domain • Frequency power and domain analysis signal integrity of Power Planes • Signal Noise Analysis Impedance • Return Path Modelling for EMI and SSN analysis • EMI Analysis • Package Plane Resonance ASPDAC 06 coupled with power plane models • Superposition of Power Noise on Signal Noise • IBIS, SPICE and PEEC models are employed Lei HE, UCLA 29

PDS: Power Distribution System Detailed Network Modeling is needed for accurate analysis of Core PDS: Power Distribution System Detailed Network Modeling is needed for accurate analysis of Core and IO Power ASPDAC 06 Lei HE, UCLA 30

Ideal Package Power Planes Early Package Design Exploration ØPlanes have no holes or perforations Ideal Package Power Planes Early Package Design Exploration ØPlanes have no holes or perforations ØPerfect Microstrip or Stripline Patterns ØImpedance is well conditioned ASPDAC 06 Lei HE, UCLA 31

Non-ideal Package Power Planes Detailed Plane Modeling ØPlanes are split for different voltage domains Non-ideal Package Power Planes Detailed Plane Modeling ØPlanes are split for different voltage domains ØPlanes could have any number of holes / perforations ØMicrostrip or Stripline Patterns: imperfect ASPDAC 06 Lei HE, UCLA 32

PDS Modelling • Wire capacitance can be extraction using 2. 5 D model [He-et PDS Modelling • Wire capacitance can be extraction using 2. 5 D model [He-et al, DAC’ 97] – With extension to arbitrary routing angle • Plane capacitance needs to consider impact of wires in between • Inductance is must and can be formula based – Bonding wires have well controlled shapes • Susceptance (L-1) makes sparsification easier • But sign-off often needs 3 D field solver ASPDAC 06 Lei HE, UCLA 33

PDS Design • Assign power planes in package stackup • Assign power domains: V PDS Design • Assign power planes in package stackup • Assign power domains: V 18, V 25, Vanalog, … • Decide via stapling • Improve power delivery • Reduce current loop and eliminate noise • Assign P/G balls ASPDAC 06 Lei HE, UCLA 34

PDS Concerns • DC Concerns Ø On-Chip IR Drop Ø Not a big concern PDS Concerns • DC Concerns Ø On-Chip IR Drop Ø Not a big concern in Flip-chip Designs Ø In-Package IR Drop Ø Important but still very small Ø In-PCB IR Drop Ø Can be ignored • AC Concerns Ø Low impedance Network across a broad frequency spectrum Ø Reduce inductive effective to reduce SSN Ø Control Chip/Package resonance ASPDAC 06 Lei HE, UCLA 35

Power Plane Noise (AC vs DC) ASPDAC 06 Lei HE, UCLA 36 Power Plane Noise (AC vs DC) ASPDAC 06 Lei HE, UCLA 36

PDS Design • PDS Impedance • Smaller Zo larger current • PDS Bandwidth • PDS Design • PDS Impedance • Smaller Zo larger current • PDS Bandwidth • Maintain Zo from 0 to fmax • Decide on Decap Allocation • High speed drivers draw current from nearby decoupling capacitors • Decoupling capacitors reduce the size of the current loop ASPDAC 06 Lei HE, UCLA 37

Chip-Package Plane Resonances are produced due to inductance and capacitance Z e tiv ci Chip-Package Plane Resonances are produced due to inductance and capacitance Z e tiv ci pa Ca e iv ct u nd I Capacitor becomes inductive beyond its self resonant frequency, f(SR) frequency Resonant frequency is Need a set of capacitors to cover small, medium, and high frequency ranges ASPDAC 06 Lei HE, UCLA 38

Decoupling capacitors optimization • Needs for power integrity – Reduce resonance. – Reduce effective Decoupling capacitors optimization • Needs for power integrity – Reduce resonance. – Reduce effective inductance and resistance. • Different levels of decoupling capacitors – Board, package, chip – Different effective frequency range. • Decoupling capacitors is not perfect capacitor – ESL – ESR – Lower ESL and ESR, higher cost • Designing of decoupling capacitors needs to determine – Values – Location – Decoupling capacitor type ASPDAC 06 Lei HE, UCLA 39

Impact of decoupling capacitors ASPDAC 06 Lei HE, UCLA 40 Impact of decoupling capacitors ASPDAC 06 Lei HE, UCLA 40

Existing Solutions • Manual trial-and-error approaches – [Chen et al. , ECTC ’ 96] Existing Solutions • Manual trial-and-error approaches – [Chen et al. , ECTC ’ 96] – [Yang et al. , EPEP 2002] • Automatic optimization – [Kamo et al. , EPEP 2000], [Hattori et al. , EPEP 2002] • Ignore ESL and ESR. – [Zheng et al. , CICC 2003] • Use impedance as noise metric – [Chen et al. , ISPD 2006] • Noise driven decap insertion ASPDAC 06 Lei HE, UCLA 41

Limit of Impedance Metric • Can not capture noise accurately • Will Lead to Limit of Impedance Metric • Can not capture noise accurately • Will Lead to large over-design ASPDAC 06 Lei HE, UCLA 42

Incremental impedance computation • When adding one decoupling capacitor Zd at port k – Incremental impedance computation • When adding one decoupling capacitor Zd at port k – the new impedance from port j to port i is • When removing one decoupling capacitor Zd at port k – the new impedance from port j to port i is ASPDAC 06 Lei HE, UCLA 43

Time complexity • With one or a few decoupling capacitors inserted – O(np 2): Time complexity • With one or a few decoupling capacitors inserted – O(np 2): np is the number of ports – Existing work: O(np 3) • Especially suitable for trial-and-error or iterative methods – Only a few decoupling capacitors changed in each iteration – Able to compute only impedance or I/O ports before updating rest ports ASPDAC 06 Lei HE, UCLA 44

Noise Calculation • FFT methods – Frequency components of noise from port j to Noise Calculation • FFT methods – Frequency components of noise from port j to port i • Worst case noise from all ports – Superposition ASPDAC 06 Lei HE, UCLA 45

Algorithm • Simulated annealing with objective function • pi: Penalty function for noise violation Algorithm • Simulated annealing with objective function • pi: Penalty function for noise violation • ci: cost of decoupling capacitor • α, β: weights ASPDAC 06 Lei HE, UCLA 46

Example • 4 types of decoupling capacitors • 3 I/O ports – Each connected Example • 4 types of decoupling capacitors • 3 I/O ports – Each connected to 10 I/O cells • 90 possible location for decoupling capacitors • Total 93 ports • Worst case noise bound: 0. 35 V Type 1 2 3 4 ESC(n F) 50 100 ESR( Ω) 0. 06 0. 03 ESL(p H) 100 40 40 1 2 2 Power planes 4 Price ASPDAC 06 Lei HE, UCLA 47

Experiment results: noise based Type 1 2 3 4 ESC(n F) 50 100 ESR( Experiment results: noise based Type 1 2 3 4 ESC(n F) 50 100 ESR( Ω) 0. 06 0. 03 ESL(p H) 100 40 40 1 2 2 4 Price port • Cost=20 1 2 before optimization 2. 52 V after optimization ASPDAC 06 0. 344 V 0. 343 V 0. 344 V Lei HE, UCLA 2. 49 V 3 2. 48 V 48

Comparison: Impedance Based • Cost=72 – 3 X larger than noise based • Impedance Comparison: Impedance Based • Cost=72 – 3 X larger than noise based • Impedance bound is not met but noise bound has already been met. – Overdesign port 1 2 3 5. 31Ω 5. 59Ω 7. 12Ω 0. 7Ω worst-case 0. 256 noise V 0. 302 V 0. 284 V 0. 35 V Maximum Impedance ASPDAC 06 bound Lei HE, UCLA 49

Runtime Comparison 1 Noise via incremental impedance + decap 2 Noise via admittance matrix Runtime Comparison 1 Noise via incremental impedance + decap 2 Noise via admittance matrix inversion [Zhao et al, EPEP 2004] + decap 3 Impedance + decap [Zheng et al, CICC 2003] approach ports 1 2 3 93 93 20 iterations 5881 5403 1920 runtime(s) 389. 5 4156. 1 2916 0. 0662 0. 7692 1. 519 avg. runtime(s) • 10 x speedup compared to method based on admittance matrix inversion ASPDAC 06 Lei HE, UCLA 50

Conclusions • High-speed IO signaling requires package-aware design and analysis (co-design) • Package-aware chip Conclusions • High-speed IO signaling requires package-aware design and analysis (co-design) • Package-aware chip IO planning improves convergence and turnaround time • On-chip devices are increasingly exposed to package effects • Power integrity is getting harder • Efficient and accurate macro models are needed to enable chip-package co-design ASPDAC 06 Lei HE, UCLA 51

Benefit of Chip-Package Co-Design (Design from client of Rio Design Automation) ~24% reduction − Benefit of Chip-Package Co-Design (Design from client of Rio Design Automation) ~24% reduction − Package Size 27 mm x 27 mm − Substrate Layers: 3 -2 -3 − Original Die Size: 7. 2 x 7. 4 mm − New Die Size: 6. 3 x 6. 5 mm − #Voltage Domains: 7 − Two different voltages: 3. 3 V, 1. 8 V − Total IOs: 341 − Frequency: 200 Mhz − Original Bump pitch: x: 225, y: 225 − New Bump Pitch: X: 201, 225, 275 Y: 216, 225 − TSMC 0. 18 u process ASPDAC 06 Lei HE, UCLA 52

Reading Assignment • J. Xiong, Y. Wong, E. Sarto, L. He, Reading Assignment • J. Xiong, Y. Wong, E. Sarto, L. He, "Constraint Driven I/O Planning and Placement for Chip-package Co-design", IEEE/ACM Asia South Pacific Design Automation Conference, Jan. 2006. • J. Chen and L. He, “Noise driven in-package decoupling capacitor optimization for power integrity, " in International Symposium on Physical Design, 2006. ASPDAC 06 Lei HE, UCLA 53

References • Extraction and sparsification – K. Nabors and J. White, References • Extraction and sparsification – K. Nabors and J. White, "Fastcap: A multipole accelerated 3 -d capacitance extraction program, " IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, pp. 1447 -1459, Nov. 1991. – J. Cong, L. He, A. B. Kahng, D. Noice, N. Shirali and S. H. -C. Yen, "Analysis and Justification of a Simple, Practical 2 1/2 -D Capacitance Extraction Methodology", – – ACM/IEEE Design Automation Conference, June 1997, pp. 627 -632. M. Kamon, M. Tsuk, and J. White, "Fasthenry: a multipole-accelerated 3 D inductance extraction program, " IEEE Trans. on MIT, 1994. L. He, N. Chang, S. Lin, and O. S. Nakagawa, "An Efficient Inductance Modeling for On-chip Interconnects", IEEE Custom Integrated Circuits Conference, pp. 457460, May 1999. F. Grover, “Inductance Calculations: Working Formulas and Tables”, Dover Publications, New York, 1946. M. Beattie, H. Zheng, B. Krauter, A. Devgan, “Spatially Distributed 3 D Circuit Models”, IEEE/ACM Design Automation Conference, 2005 ASPDAC 06 Lei HE, UCLA 54

References • Model order reduction – A. Odabasioglu, M. Celik, and L. Pileggi, “PRIMA: References • Model order reduction – A. Odabasioglu, M. Celik, and L. Pileggi, “PRIMA: Passive reduced-order interconnect macro-modeling algorithm, " IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, pp. 645 -654, 1998. – R. W. Freund, “SPRIM: Structure-preserving reduced-order interconnect macromodeling, " in IEEE/ACM ICCAD, 2004. – H. Yu, L. He, and S. X. D. Tan, “Block Structure Preserving Model Reduction, ” IEEE International Behavioral Modeling and Simulation Conference, September 22 -23, 2005. ASPDAC 06 Lei HE, UCLA 55

References • P/G noise – M. Zhao, R. V. Panda, S. S. Sapatnekar, and References • P/G noise – M. Zhao, R. V. Panda, S. S. Sapatnekar, and D. Blaauw, ``Hierarchical analysis of power distribution networks, '' IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, no. 2, pp. 159 --168, 2002 – E. Chiprout, ``Fast flip-chip power grid analysis via locality and grid shells, '' in ICCAD, 2004. – J. M. Wang and T. V. Nguyen, Extended Krylov subspace method for reduced order analysis of linear circuits with multiple sources, " in Proc. Design Automation Conf. (DAC), 2000. – Y. Lee, Y. Cao, T. Chen, J. Wang, and C. Chen, Hi. Prime: Hierarchical and passivity preserved interconnect macro-modeling engine for RLKC power delivery, " IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 26, no. 6, pp. 797 -806, 2005. – Y. Y Shi, H. Yu, and L. He, “Generalized Second-Order Arnoldi Method for Model Order Reduction with Multiple Non-impulse Sources”, ACM International Symposium of Physical Design, 2006. ASPDAC 06 Lei HE, UCLA 56

References • IO planning and placement – W. -K. Mak, References • IO planning and placement – W. -K. Mak, "I/O placement for FPGAs with multiple I/O standards, " IEEE Trans. On Computer-Aided Design of Integrated Circuits and Systems, vol. 23, pp. 315 -320, February 2004. – J. Wang, K. Muchherla, and J. Kumar, "A clustering based area I/O planning for flip -chip technology, " in Quality Electronic Design, 5 th International Symposium on, pp. 196 -201, 2004. – A. Caldwell, A. Kahng, S. Mantik, and I. Markov, "Implications of area-array I/O for row-based placement methodology, " in IC/Package Design Integration, IEEE Symposium on, pp. 93 -98, Feb. 1998. – M. M. Ozdal and M. D. Wong, "Simultaneous escape routing and layer assignment for dense PCBs, " in Proc. Int. Conf. on Computer Aided Design, Nov. 2004. – C. Tan, D. Bouldin, and P. Dehkordi, "Design implementation of intrinsic area array ICs, " in Advanced Research in VLSI, Seventeenth Conference on, pp. 82 -93, Sept. 1997. – J. Xiong, Y. Wong, E. Sarto, L. He, "Constraint Driven I/O Planning and Placement for Chip-package Co-design", IEEE/ACM Asia South Pacific Design Automation Conference, Jan. 2006. ASPDAC 06 Lei HE, UCLA 57

References • Decoupling capacitors – L. Smith, R. Anderson, D. Forehand, T. Pelc, and References • Decoupling capacitors – L. Smith, R. Anderson, D. Forehand, T. Pelc, and T. Roy, "Power distribution system design methodology and capacitor selection for modern cmos technology, " IEEE Transactions on Advanced Packaging, vol. 22, pp. 284 -291, 1993. – H. Zheng, B. Krauter, and L. Pileggi, "On-package decoupling optimization with package macromodels, " in Custom Integrated Circuits Conference, 2003. – J. Zhao and O. P. Mandhana, "A fast evaluation of power delivery system input impedance of printed circuit boards with decoupling capacitors, " in IEEE Topical Meeting on Electrical Performance of Electronic Packaging, 2004. – J. Chen and L. He, “Noise driven in-package decoupling capacitor optimization for power integrity, " in International Symposium on Physical Design, 2006. ASPDAC 06 Lei HE, UCLA 58