A fast time-domain simulation technique of plane circuits via two-layer Cellular Neural Network (CNN)-based modeling, which is necessary for power/signal integrity evaluation in VLSIs, printed circuit boards, and packages, is presented. Using the new notation expressed by the two-layer CNN, 1,553 times faster simulation is achieved, compared with Berkeley SPICE (ngspice). In CNN community, CNNs are generally simulated by explicit numerical integration such as the forward Euler and Runge-Kutta methods. However, since the two-layer CNN is a stiff circuit, we cannot analyze it by using an explicit numerical integration method. Hence, to analyze the two-layer CNN and reduce the computational cost, the leapfrog method is introduced. This procedure would open an application of CNN to electronic design automation area.