Figure of Merit and Limiting Characteristics of Tunable Ferroelectric Microwave Devices

Microwave application of ferroelectrics is very promising for electrically tunable microwave devices based on the electric field dependence of the dielectric permittivity. Tunable filters and controllable phase shifters are successfully designed as integrated circuits based on multilayer structures containing thin epitaxial ferroelectric (FE) film. As a rule lumped ferroelectric capacitors are used as the tunable components. Quality of the capacitor can be evaluated using Commutation Quality Factor (CQF). There is a unique connection between the Figure of Merit of a tunable microwave device and the CQF of the FE capacitors used. The Figure of Merit gives the upper limit of the quality of a tunable device based on the FE components. Introduction Tunable devices are widely used in modern telecommunication systems. Phase shifters, tunable resonators and filters are of the most importance among them. Practical realization of the devices depends mostly on a tunable component used for the device control. Tunable ferroelectric (FE) capacitors are considered as the most suitable choice, when high speed of tuning, simple manufacturing process and low cost are of higher priority [1]. For the tunable capacitor, it is convenient to use the Commutation Quality Factor (CQF) as the main characteristic. There are some different definitions of the CQF, which are based on two main parameters: tunability of the capacitor and the loss factor of the FE material [2]. We suggested the CQF, which is invariant to the parameters of any lossless two-port network connected with the tunable capacitor [3]. This form of the CQF allows estimation of a tunable device quality [4], [5]. The tunable device is described by a set of the most important parameters: pass band width, tuning frequency range, insertion loss for the tunable resonator and filter; phase shift and insertion loss for the phase shifter. The Figure of Merit (FM) as a unified parameter can be used for a comparison of different tunable devices. The FM of a tunable device depends on the CQF of the tunable components and on the quality factor of non-tunable device components. The most significant advantage of the CQF definition used in this work is the possibility to evaluate the upper limit of the FM for a tunable device. Commutation Quality Factor of a Ferroelectric Capacitor Equivalent diagram of a ferroelectric capacitor consists of a capacitance and a resistance connected in series. Both the capacitance and the resistance depend on biasing voltage applied to electrodes of the capacitor. A correct model was derived for a description of the dielectric permittivity and loss tangent of a ferroelectric film as a function of a biasing electric field [6], [7]. The capacitor as a tunable component is presented by the two-state equivalent diagram (Fig. 1) with Z1 = R1 + iX1 corresponding to zero biasing voltage and Z2 = R2 + iX2 obtained under the control voltage Vb. The generalized definition of the CQF for a tunable component [4], [5] is determined by real and imaginary parts of the impedance of the two-state equivalent model: K = (X2 −X1) R1 · R2 + R2 R1 + R1 R2 (1) In the case of FE capacitor, the imaginary part of the component impedance is much higher than the real part. This leads to more simple form of the CQF for the tunable FE capacitor [3], [4]: K = (n− 1) n · tan δ1 · tan δ2 (2) 328 Progress In Electromagnetics Research Symposium 2005, Hangzhou, China, August 22-26