Frequency Sensitivity of Lossless Planar Devices by FEM

In this paper numerical calculation of frequency sensitivity of a planar device using flnite element is presented. The flnite element method has been shown to be an e-cient and ∞exible way of computing the equivalent circuit parameters of N-port planar devices (microstrip, stripline, rectangular waveguide, etc.). In addition it can provide at little extra cost the sensitivity of admittance parameters to change in operating frequency. This way, frequency sensitivity of the equivalent circuit parameters can be found by two dimensional flnite element method. This approach has been implemented by triangular flnite elements and the sensitivity was computed for microstrip bend: the agreement with previously published result was excellent. 1. INTRODUCTION In this paper we describe how Foster reaction theorem and flnite element can be used to calculate Y parameter frequency sensitivity of a planar device using data of a single simulation and at a little extra computational cost A planar device can be deflned as one in which electromagnetic flelds do not vary signiflcantly in one dimension (1,2) so that the simulation can be carried out in a plane. Rectangular waveguide at dominant mode is an example of perfect planar device. After introduction of magnetic wave guide model for analysis of microstrip structures (3) these classes of microwave structures were added in planar devices by using equivalent relative permittivity, width and magnetic walls at two side ends (3,4). Determining frequency sensitivity can be help full in determining broadband calculation of circuit parameters since in each simulation beside the circuit parameters their sensitivity relative to frequency gets calculated. In resonant structures calculating frequency sensitivity due to change in structure parameter can be very useful for tuning bandwidth. 2. THEORY Because our goal is to calculate the frequency sensitivity of planar device we flrst begin by deflning equivalent circuit parameters and planar device. We assume ei and hi are tangential electric and magnetic fleld at port i due to the dominant mode wave incident on port i, when this wave carries unit real power to the port. In general tangential electric and magnetic fleld on ports are