Substrate noise analysis has become increasingly important in recent LSI design. This is because substrate noise, which affects PLLs, causes jitter that results in timing error. Conventional analysis techniques of substrate noise are, however, impractical for large-scale designs that have hundreds of millions of transistors because the computational complexity is too huge. To solve this problem, we have developed a fast substrate noise analysis technique for large-scale designs, in which a chip is divided into multiple domains and the circuits of each domain are reduced into a macro model. Using this technique, we have designed a processor chip for use in the supercomputer (die size: 20 mm 21 mm, frequency: 3.2 GHz, transistor count: 350M). Computation time with this design is five times faster than that with a 1/3000 scale design using a conventional technique, while resulting discrepancy with measured period jitter is less than 15%.