M.Sc Thesis

M.Sc StudentLavy Omer
SubjectMEMS Microwave Filters
DepartmentDepartment of Electrical and Computer Engineering
Supervisors PROFESSOR EMERITUS Yael Nemirovsky
PROF. Saad Avraham
Full Thesis text - in Hebrew Full thesis text - Hebrew Version


The development of tunable filters is of great commercial and military interest. MEMS technology enables fabrication of high Q high linear low loss components. This work address the challenge of design, fabrication and modeling of a band pass filter operating in the GHz range.

Our filter is based on two lumped resonant circuits which are inductively coupled to introduce two stages band pass filter centered at the resonant frequency. The common approach to design such filters is based on Darlington's theory. We use an analytic approach which can be used in the design of small degrees' (1-3) filters. This approach is based on analyzing the coupled LC circuits and examines the affect of the coupling on the zeros and poles of the transmission function. In order to have tenability, the resonance of the LC circuits must be controlled. This is done by controlling the capacitance.

MEMS tunable varactors are usually designed as electrostatic actuators, and are implemented by surface micromachining. The dynamic range of this class of varactors is governed by the pull-in instability. The theoretical limitation in tunability is ideally one-third of the initial gap between the two electrodes.

In this work we present a simple T varactor, whose pull-in stability is increased and hence its dynamic range is increased, by applying two independent voltage sources. One electrode is located under the clampad clamped beam and the other under the free end cantilever. The spring constant of the clamped clamped beam is designed to be much larger than the one of the cantilever so that after lowering it down to its pull in point we can further lower down the cantilever. Due to the ratio in the spring constants the power applied to the cantilever will not affect the already lowered clamped clamped beam so that the cantilever can now be lowered down to one-third of its initial air gap. We introduce an electro mechanic model to the proposed structure and full analytic solution to the attached pull in problem. For this we write the total co energy of the system and then seek for terms on the 1st and 2nd derivatives. These terms lead to pull in equations that describe in this case a stable surface. Among this surface we look for a point which gives best result that is a point with maximum displacement. With this approach we measured varactors with capacitance ratio of 2.47.