Timing Optimization Through Clock Skew Scheduling

Specifically, this book deals in depth with the following issues: • A methodology for simultaneous non-zero clock skew scheduling and design of the topology of the clock distribution network. This methodology is based on the pioneering works of Friedman [1] and Fishburn [2], and builds on Linear Programming (LP) solution techniques. The non-zero clock skew scheduling of circuits with level-sensitive latches and for multi-phase clock signals is formulated as a LP problem. The simultaneous clock scheduling and clock tree topology synthesis problem is formulated as a mixed-integer linear programming problem that can be solved efficiently. The proposed algorithms have been evaluated on a variety of benchmark and industrial circuits and synchronous performance improvements of well above 60% have been demonstrated. • For those cases where reliable circuit operation and production yield are the highest level priorities, an alternative problem formulation is developed. This formulation is based on a quadratic (hence the QP—quadratic programming) measure, or cost function, of the tolerance of a clock schedule to parameter variations. A mathematical framework is presented for solving the constrained and bounded QP problem. A constrained version of the problem is iteratively solved using the Lagrange multipliers method. As these research issues are topics of great practical importance for input/output (I/O) interfacing and Intellectual Property (IP) blocks, explicit clock delay and skew requirements are fully integrated into the mathematical model described here. The theoretical derivation of the limits on the improvements on the clock period available through clock skew scheduling. The theoretical derivation is performed by identifying the limits for three local data path topologies. A methodology to mitigate the limitation of clock skew scheduling for a reconvergent path system is presented. The methodology involves delay insertion on some data paths of the reconvergent system and is formulated as an LP problem for an automated application. • A practical (and necessary) implementation of clock skew scheduling for an emerging clock generation and distribution technology in resonant rotary clocking technology. Preliminary efforts in modeling and implementation are demonstrated. Details are included on the integration of clock skew scheduling into a complete physical design flow for the automated design of rotary clock synchronized synchronous circuits. synthesis problem is formulated as a mixed-integer linear programming problem that can be solved efficiently. The proposed algorithms have been evaluated on a variety of benchmark and industrial circuits and synchronous performance improvements of well above 60% have been demonstrated. • For those cases where reliable circuit operation and production yield are the highest level priorities, an alternative problem formulation is developed. This formulation is based on a quadratic (hence the QP—quadratic programming) measure, or cost function, of the tolerance of a clock schedule to parameter variations. A mathematical framework is presented for solving the constrained and bounded QP problem. A constrained version of the problem is iteratively solved using the Lagrange multipliers method. As these research issues are topics of great practical importance for input/output (I/O) interfacing and Intellectual Property (IP) blocks, explicit clock delay and skew requirements are fully integrated into the mathematical model described here. The theoretical derivation of the limits on the improvements on the clock period available through clock skew scheduling. The theoretical derivation is performed by identifying the limits for three local data path topologies. A methodology to mitigate the limitation of clock skew scheduling for a reconvergent path system is presented. The methodology involves delay insertion on some data paths of the reconvergent system and is formulated as an LP problem for an automated application. • A practical (and necessary) implementation of clock skew scheduling for an emerging clock generation and distribution technology in resonant rotary clocking technology. Preliminary efforts in modeling and implementation are demonstrated. Details are included on the integration of clock skew scheduling into a complete physical design flow for the automated design of rotary clock synchronized synchronous circuits.