Two‐dimensional analysis of monolithic crystal filters using mode‐matching technique

Abstract

AbstractTo perform a two‐dimensional analysis of a monolithic filter (MCF), the distributed parameter analysis based on an approximate two‐dimensional model and the coupled oscillation analysis based on a variational method are used widely. However, the error in the first method is large for a conventional MCF which is designed to prevent nonharmonic higher‐order vibration. This is because approximations are introduced to the displacement distribution. In the second method, the distributed parameter characteristics of an MCF cannot be estimated because it is equivalent to that based on an approximate coupling circuit with lumped elements. This paper introduces a more rigorous distributed parameter method for MCF's based on the mode matching technique. This analysis can also be applied to an MCF with two‐dimensionally placed electrodes. First, the coupling coefficient of a two‐dimensionally placed two‐electrode pair and the filter characteristics of a one‐dimensionally placed three‐electrode pair MCF are analyzed. It is confirmed that the present method evaluates correctly the distributed parameter characteristics of an MCF with a weak energytrapping capability. The conventional methods cannot be applied to this kind of MCF. Next, as an example of MCF's with two‐dimensionally placed electrodes, we treat a four‐electrode pair MCF with an attenuation pole on the high‐frequency side. It is shown that the filter characteristic obtained by the present method can realize the distributed parameter characteristics that cannot be analyzed by the conventional methods. Thus the usefulness of this method for distributed parameter analysis of MCF's with two‐dimensionally placed electrodes is confirmed.