Basic numbers for a power distribution network: the target impedance for a supply, the capacitance of a power and ground plane pair, the frequency where that capacitance alone meets the target, the first plane resonance and the self-resonance of a decoupling capacitor.
Target impedance. Ztarget = V·ripple/ΔI: the impedance the network must stay below so that the current step causes no more than the allowed ripple.
Plane capacitance. Parallel plates: C = ε0·εr·A/d. Its reactance meets the target at f = 1/(2π·Ztarget·C); above that frequency (and below the plane resonances) the planes alone keep the impedance low.
Plane resonance. The first cavity mode of a rectangular plane pair is at f = c/(2·a·√εr), with a the longest side.
Decoupling capacitor. Self-resonant frequency f = 1/(2π√(L·C)), where L is the mounted inductance: the capacitor's ESL plus its pads, vias and the path to the planes. Above this frequency the capacitor behaves as an inductor with impedance 2πfL.
At high frequency a capacitor's impedance is set by its loop inductance. Short, wide connections and vias close to the pads lower it more than a larger capacitance value would.
Thinner dielectrics give more capacitance and lower spreading inductance. 0.1 mm or less between adjacent power and ground planes is common in high-speed boards.
Inductance of a square, hexagonal, octagonal or circular spiral drawn in copper on a PCB.
Width a trace needs for a current, or the current a trace can carry, with IPC-2152 and IPC-2221.
Impedance of an outer-layer trace over a plane, with solder mask or embedded, and width for a target impedance.
Impedance of an inner-layer trace between two planes, symmetric or offset, and width for a target.
Differential, odd, even and common-mode impedance of edge-coupled microstrip and stripline pairs.
Impedance of a coplanar waveguide, with or without a ground plane underneath (grounded CPW).