PCB Power Plane Impedance Calculator

The Power Plane Impedance Calculator treats a power-ground plane pair of length $l$, width $w$ and separation $d$ as a parallel-plate structure. It reports the plane capacitance, the plane inductance for current flowing along the length, the reactance of that inductance at a chosen frequency, and the plane pair's first cavity resonances, TM₁₀ and TM₀₁. The capacitance is $C = \varepsilon_0 \varepsilon_r l w / d$: 3.117 nF for the default 100 × 80 mm pair with 0.1 mm of dielectric ($\varepsilon_r = 4.4$), about 38.96 pF per cm². Halving the separation doubles it.

A plane pair also has a sheet inductance of $\mu_0 d$ per square: 1.2566 nH per mm of separation, or 125.66 pH per square at 0.1 mm. For current flowing uniformly from one edge to the opposite one, the inductance is $L = \mu_0 d \, l / w$, the sheet inductance times the $l/w$ squares along the path. It depends on the separation and on the aspect ratio, not on the area: the defaults give 0.15708 nH, whose reactance $X_L = 2\pi f L$ is 98.70 mΩ at 100 MHz. That reactance describes the planes only well below their first resonance, and it is not the impedance a device sees at one point on the plane.

The inductance and the capacitance are not a lumped LC circuit. A plane pair is a distributed structure, a two-dimensional transmission line, and it resonates when one of its sides is a whole number of half wavelengths in the dielectric. With open edges, the resonant frequencies of a rectangular plane pair are $f_{mn} = \frac{c}{2\sqrt{\varepsilon_r}}\sqrt{(m/l)^2 + (n/w)^2}$ (Swaminathan and Engin; Novak). TM₁₀ is a half wave along the length and TM₀₁ a half wave across the width: 714.6 MHz and 893.3 MHz for the defaults. The lower of the two, the half wave along the longer side, is the first resonance. The separation $d$ does not appear, so a thinner dielectric does not move the modes. Treating $L$ and $C$ as a lumped circuit gives $1/(2\pi\sqrt{LC}) = c/(2\pi l \sqrt{\varepsilon_r})$, a factor of π too low: 227.5 MHz here.

Cavity resonances matter for PDN design because the impedance between the planes peaks at each of them: an anti-resonance, where the plane pair stops behaving like a capacitor. Each mode has a standing-wave voltage pattern that is largest at the edges and corners of the plane and zero on its nodal lines, such as the line across the middle of the length for TM₁₀. A capacitor on a nodal line cannot damp that mode; capacitors near the edges and corners can. The rail's target impedance, $Z_{target} = \Delta V / \Delta I$, sets how low the impedance must stay: a 1.0 V rail allowed 5 % (50 mV) with a 2 A transient needs 25 mΩ. The planes do most of that work where mounted decoupling capacitors are limited by their mounting inductance, up to about the first cavity resonance. Above it, model the modes and the capacitors together with the PDN impedance tool.