The development of a closed-form expression for the input impedance of power-return plane structures

In multilayer printed circuit boards, the noise on the power bus is influenced by the impedance between the power and ground planes. Power-bus noise estimates require an accurate estimate of the power-bus input impedance. This paper develops a closed-form estimate of the input impedance for circular power-return plane structures. When the structure is lossy (e.g., boards employing embedded capacitance or densely populated boards), the energy reflected from the board edge does not significantly affect the input impedance. In general, the expressions developed here for circular structures can be used to estimate the impedance of lossy powerreturn plane structures of any shape.