Power Distribution Networks with On-Chip Decoupling Capacitors

Assuming d i I = s i I = d, from (15.3) the mutual inductance between the power and ground paths f the different voltage domains for a fully interdigitated power distribution grid with DSDG is
Substituting (A.1) (A.4) into (15.8), the mutual inductive coupling M loop intI between the two current distribution grid with DSDG is
Simplifying (A.5) and considering that ln ? and ln k are approximately the same for different distances between the lines, M loop intI is