An interconnecting apparatus employing a lossy power distribution network to reduce power plane resonances. In one embodiment, a printed circuit board includes a lossy power distribution network formed by a pair of parallel planar conductors separated by a dielectric layer. The pair of parallel planar conductors includes a first power supply plane suitable for use, for example, as a ground plane and a second power supply plane suitable for use, for example, as a power plane (e.g., VCC). The dielectric layer has a loss tangent value of at least 0.2, and preferably of at least 0.3. In one embodiment, the dielectric material between the power planes could have a frequency dependent loss tangent, such that a loss tangent value of 0.3 is achieved at and above the lowest resonance frequency of the planes. Due to the relatively large loss tangent characteristic of the dielectric layer separating the power supply planes, the electrical impedance characteristics associated with the power planes may be stabilized, and power plane resonances may be reduced. The printed circuit board may also include one or more signal layers separated from the power planes by respective dielectric layers. The dielectric layers separating the signal layers from the power planes or other signal layers may be associated with much lower loss tangent values, such as in the range of 0-0.05. In this manner, high frequency losses associated with the signal traces may be kept relatively low. In another embodiment, power plane resonances are suppressed by decreasing the thickness of the dielectric material between the power supply planes to less than 0.5 mils. For example, in one embodiment, the plane separation is preferably reduced to less than 0.2 mils such as, for example, 0.1 mils. In embodiments where the plane separation approaches 0.1 mils or less, plane resonances may be substantially suppressed.