“…Accurate estimation of substrate noise is required for circuit design to reduce the impact of substrate noise and to minimize the area overhead due to noise immunity design. There are many reports about substrate noise, such as measurements of substrate noise on the fabricated chip [1,2,3,4], extraction methods of substrate resistance [5,6], simulation methods of substrate noise [2,3,7,8], and modeling of noise source for fast substrate noise simulation [4].…”