A novel hierarchical radial tree based on constructal theory for PCB power plane

This paper proposes a hierarchical radial tree distribution network based on constructal theory for optimal direct current performance in printed circuit board power plane. The optimal radial tree dimensions of each order are obtained for optimal voltage drop and resistance. The constraints are the total areas of the plane and the high conductivity paths. The degrees of freedom are the width/length ratio H_i/L_i of the constructal block, high conductivity paths ratio D_i+1/D_i (i=1, 2, etc). According to constructal theory, the optimal performance consists of constructing the giving area in a sequence of building blocks from the smallest size toward larger sizes hierarchically. High assembly level is not necessary. The optimal order is 12 for the designed tree. Then a radial PCB power plane is developed based on the radial tree which illustrates that the designed plane has multifunctions of low voltage drop, current robustness, equidistribution, compactness and effective noise isolation while maintaining a relatively simple design of geometry.