Multifractal behavior of the power dissipation of CMOS circuits

Power dissipations of complementary metal-oxide-semiconductor (CMOS) circuits under randomly generated input vector streams are found to characterize the multifractality. The multifractal behaviors have been demonstrated by box-counting method on ISCAS-85 benchmark circuits with various scales and under different average power dissipations. The range of the scaling invariance spans nearly four decades. The self-affine generalized fractal dimensions and the multifractal spectra are presented. The generalized fractal dimensions decrease with the increasing moment orders. The multifractal spectra are concave downward with maximums at the moment order of zero. The average power dissipations and the scales of the circuits are related to the range of singularity by power laws.