Computation of Q-factors of dielectric-loaded cylindrical cavity resonators zyxw M. Mohammad-Taheri D. Mirshekar-Syahkal zyxwvutsrqp Indexing terms. Oscillators, Dielectric materials, Q-factors zyxwvutsrqpon Abstract: zyxwvutsrqpon Based on the one-dimensional finite element method reported in References 1 and 2, a general formulation is presented for the calcu- lation of the conductor Q-factor, Q, , associated with metallic losses of cylindrical cavity resonators loaded axisymmetrically with dielectrics. The for- mulation is employed to accurately determine Q, relating to the first few modes of the cylindrical cavity resonator loaded with a hollow cylindrical dielectric as well as to obtain Q, relating to the fundamental mode (TE,,,) of the ring resonator on a microstrip substrate. 1 Introduction In filter design employing cylindrical cavity resonators loaded with axisymmetric dielectrics, Fig. 1, the dielec- +r Fig. 1 loaded with dielectrics trics, are usually chosen to be of high permittivity. This choice offers the advantage of reduced conductor losses, because the electromagnetic field is effectively confined to the dielectric regions. For high dielectric constant materials, the Q-factor associated with dielectric losses is approximately proportional to the reciprocal of the loss- tangent irrespective of the nature of the mode in the res- onator [3] and is expressed in References 4 and zyxwvut 5. Therefore, provided that Q, , the Q-factor of the reson- ator because of conductor losses, is known for a particu- lar resonant mode, the associated unloaded Q-factor of the resonator, Qu, can be calculated by the well known expression Cross-section o f a cylindrical cavity resonator axisymmetrically Paper 7523H (E12), recaved 5th January 1990 The authors are with the Department of Electronic System Engineering, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom 312 This paper is mainly concerned with the development of a formulation for the computation of Q, . The formula- tion is based on a technique which has been introduced recently by the authors [l, 21 and forms a complement to it. In that technique an H-vector variational expression is used to obtain the resonant frequencies and the corre- sponding field components of resonators of general cross- section in Fig. I. Because of the use of one-dimensional finite element basis functions and trigonometric functions for the approximation of the field components, the tech- nique enjoys a great versatility and efficiency. Accord- ingly, the formulation of Q, presented in this paper has the virtues of simplicity and generality. In contrast to a similar formulation based on the mode matching tech- nique [3], the present formulation does not depend on the number of dielectrics in the structure. Therefore, as this parameter changes, the formula presented here will remain the same. The formulation presented in this paper is applied to several resonator structures, including those shown in Figs. 24. Of special interest in this work is the determi- nation of the conductor Q-factors of the cylindrical cavity Fig. 2 Cross-section of a drical dielectric I lr lindrical cavity loaded with a hollow cylin- loaded with a hollow dielectric, Fig. 2, and the dielectric ring on a microstrip substrate, Fig. 4. In spite of the importance of these structures in certain filter design, there is little data available in the literature on Q,s of these resonators. 2 Theory In the work reported in References 1 and 2, which is based on a variational technique, it is shown that the general configuration of the dielectric loaded cavity in IEE PROCEEDINGS, Vol. zyxwvut 137, Pt. H, No. 6. DECEMBER 1990