VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig 1 EECS 527 Paper Presentation Topological Design of Clock Distribution Networks Based on Non-Zero Clock Skew Specifications - by Jose Luis Neves and Eby G. Friedman Presented by Shaobo Liu Department Electrical Engineering and Computer Science University of Michigan, Ann Arbor 04/2013

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig EECS 527 Paper Presentation  Outlines  Introduction  Determination of Clock Path Delay Theoretical background Clock Path Delay Algorithm  Topology of Clock Distribution Network Construction of the Clock Tree Structure Calculation of Branch Delay Reorganization of the Clock Tree  Results  Summary  Q & A 2

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Introduction 3  Several techniques  Repeater Insertion Convert highly resistive-capacitive networks into effectively capacitive networks  H-tree structures Symmetric distribution networks Ensure minimal clock skew  Zero skew clock routing algorithms Automatically layout these high speed networks in cell-based designs

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Introduction 4  Two fundamental properties of clock distribution networks  Clock skew is only meaningful between sequentially adjacent register  Clock skew can be used to improve circuit performance by evening out the delay between slow and fast path

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Introduction 5  Clock Skew Description  Negative If the clock delay to the initial register is less than the clock delay to the final register  Positive If the clock delay to the initial register is greater than the clock delay to the final register

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 6  Theoretical Background  Definition 1  Given two sequentially adjacent registers, Ri and Rj  The clock skew between these two registers is defined as  T CDi : Clock delays from the clock source to the register Ri  T CDj : Clock delays from the clock source to the register Rj

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 7  Theoretical Background  More Definition  Local data path The path between two sequentially adjacent registers  Global data path Consist of one or more local data path

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 8  Theoretical Background  Theorem 1  For any given global data path, clock skew is conserved The clock skew between any two registers which are not necessary adjacent Sum of the clock clock skew between each pair of registers along the global data path between those two same registers  Extends Definition 1 Any non-sequentially adjacent registers belong to the same global data path Clock skew between two registers not belong to the same global data path has no physical meaning

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 9  Theoretical Background  Circuits may contain sequential feedback paths  The relation between feedback and forward path is formalized

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 10  Theoretical Background  Theorem 2  For any given global data path containing feedback paths  Clock skew in feedback path between any two registers, Rl and Rj  Relate to the clock skew of the forward path by the following relationship

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 11  Clock path delay algorithm  Circuits for this paper

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 12  Clock path delay algorithm  Optimal delay assignment for the data path example

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 13  Clock path delay algorithm  Algorithm Path Delay

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Determination of Clock Path Delay 14  Clock path delay algorithm  Clock distribution network

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Topology of Clock Distribution Network 15  Construction of the clock tree structure  Hierarchical representation of the data path example

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Topology of Clock Distribution Network 16  Calculation of branch delay  Two characteristics of the hierarchical representation  The clock skew between sequentially adjacent registers may not depend on the delay of the internal branches  The clock skew specifications may be satisfied if the delay of some of the internal branches is known

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Topology of Clock Distribution Network 17  Calculation of branch delay  Three steps to determine the individual branch delays  Delay of External Branches  Delay of Internal Branches  Delay Shifting

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Topology of Clock Distribution Network 18  Calculation of branch delay  Delay assignment for each branch of the example

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Topology of Clock Distribution Network 19  Reorganization of the clock tree  Delay assignment for non-hierarchically defined clock distribution network

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Results 20  Minimum clock delay and total number of delay units for several example circuits

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig Summary 21  Determination of Clock Path Delay  Theoretical Background  Clock Path Delay Algorithm  Topology of Clock Distribution Network  Construction of the Clock Tree Network  Calculation of Branch Delay  Reorganization of the Clock Tree  Future Research  Determine the Optimal Non-zero Clocking Characteristics  Design of Circuits Structure to Emulate Delay values of the Network Branches

VLSI Physical Design: From Graph Partitioning to Timing Closure Paper Presentation © KLMH Lienig EECS 527 Paper Presentation Thanks! Q & A 22