Fast transient simulation algorithm for a 3D power distribution bus

Extensive transient simulations for on-chip power delivery networks are required to analyze power delivery fluctuations caused by dynamic IR and Ldi/dt drops. Speed and memory has become a bottleneck for simulation of power distribution networks in modern VLSI design where clock frequency is of the order of GHz. The traditional SPICE based tools are very slow and consume a lot of memory during simulation. The problem is further aggravated for huge networks like power distribution network within a stack of ICs inter-connected through TSVs. This type of 3D power distribution network may contain billions of nodes at a time. In this paper we proposed a faster transient simulation algorithm using visual C++. First we reduce 3D power distribution bus containing n nodes to a two terminal π network. Then we solve this two terminal reduced network for voltages and currents. After this, we apply back solving algorithm to the network to solve it for each of the intermediate nodes using visual C++. The proposed algorithm is quite accurate with 1-2% error when compared with Ansoft Nexxim4.1. The proposed algorithm is several times faster than Ansoft Nexxim as well as consumes significantly less memory as compared to Nexxim.