Abstract-Based on the cavity-mode model, we have developed a fast algorithm for calculating power bus impedance in multilayer printed circuit boards. The fast algorithm is based on a closed-form expression for the impedance matrix of a rectangular power bus structure; this expression was obtained by reducing the original double infinite series into a single infinite series under an approximation. The convergence of the single series is further accelerated analytically. The accelerated single summation enables much faster computation, since use of only a few terms is enough to obtain good accuracy. In addition, we propose two ways to compensate for the error due to the approximation involved in the process of reducing the double series to the single series, and have demonstrated that these two techniques are almost equivalent.Index Terms-Cavity-mode model, closed-form expression for fast calculation, power bus impedance, power bus resonance.

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The effect of Mg loading on the high-frequency tunable properties and dielectric loss of Ba 0.8 Sr 0.2 Ti 1%x Mg x O 3 (BSTM) ceramics was investigated. Variation in the lattice parameters and the 90°domain configuration with Mg loading indicated a decrease in the tetragonal distortion. Additionally, the 90°domain size decreased slightly with a low Mg loading, up to 0.1 mol %, resulting in a higher domain-wall density compared with the nondoped specimen. The 0.075 mol % Mg-loaded BSTM ceramic exhibited the highest tunability; this was attributed to the domain-size effect. The loss tangent (tan δ) roughly decreased with Mg loading, due to loaded oxygen vacancies. The maximum figure of merit value (FOM = tunability/tan δ) at 10 MHz was achieved for the 0.075 mol % Mg specimen, twice that of the non-doped specimen, due to an increase in the tunability and a decrease in the loss tangent with Mg loading.

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