Uniform Repeater Insertion in Trees

Repeater insertion can be used to overcome the quadratic increase in the time required for a signal to propagate through an interconnect. A new timing model, based on short-channel equations, has been developed to characterize the signal delay through a resistive line. These analytical expressions provide the foundation for algorithms used to insert uniform repeaters into tree structures. Both local and global optimization algorithms for repeater insertion are presented. While the local optimization algorithm provides a computationally fast solution to the repeater insertion problem, the resulting circuit implementation is less power, area, and speed efficient than applying global optimization techniques. The global optimization algorithm for repeater insertion is achieved through the downhill simplex method. The circuit equations, algorithms, and software implementation of this repeater insertion system are presented in this paper. Results from these insertion methodologies improve delay from 25% to 60% versus typical cascaded buffer methodologies. Global repeater insertion further decreases delay times by up to 22% over the local repeater insertion method. The accuracy of the timing model characterizing the repeater insertion process as compared to SPICE simulations is generally within 10%. Applications of these algorithms for minimizing the signal delay through an tree, such as in data paths, and targeting signal delays through an tree, such as in clock distribution networks, are also discussed.