An equivalent network analysis for an arrangement that combines a microstrip line and coaxial conductor for the purpose of measuring permeability is discussed in this paper. The measurement circuit used consists of a coaxial conductor with a sample housed inside and a short microstrip line connected to both sides. The coaxial conductor is composed of an electrically grounded coaxial metal pipe with open ends and a center conductor. Equivalent networks for this arrangement are investigated to determine the complex permeability from the impedance of the measurement circuit. We have employed a π network composed of a resistor and an inductor connected in series, and shunt capacitors as the equivalent circuit for the measurement portion. It has been found that the measurement error ratio of less than a few percent can be obtained for most frequency ranges of 10 MHz to 500 MHz.

Power distribution in multilayered periodic waveguides is first analyzed by longitudinal modal transmission-line theory (L-MTLT). Novel effective characteristic impedances of the equivalent network for TE and TM modes are then derived, and a symmetrical grating guide with three layers is rigorously evaluated to clarify the validity of our approach. Excellent agreement between our results and the results due to other methods indicates that our approach is able to not only reveal all the physical meaning embedded in the multilayered and multi-sectional periodic waveguides, but also predict various possible Bragg regimes rigorously and simply.

A rigorous modal approach based on the transmission-line description has developed to explore effectively the filtering characteristics of planar optical DFB guiding structures. Using the modal transmission-line theory, the leakage and filtering characteristics of metal-strip gratings and dielectric gratings with gain or loss are first evaluated in details at the first- and third-order Bragg regimes. It can thus serve as a powerful template for computational algorithms to determine systematically and rigorously the optical effects of multilayered periodic guiding structures, which are not readily obtained by other methods.

In this paper, we discuss an abstraction method for Petri nets based on an equivalence of firing sequences of a specified subnet or a specified subset of transitions. Specifically, a method is presented to generate an equivalent net which preserves firing sequences of a specified subnet or a specified subset of transitions. The abstraction can be applied to an efficient behavioral analysis of concurrent systems constructed by composition of modules such as communication networks and Flexible Manufacturing Systems (FMS).