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Ferroelectrics are well known tunable dielectric materials. Permittivity of these materials can be controlled by an applied electrical bias field. Controllable permittivity leads to alteration of characteristics of tunable microwave components such as propagation constants, resonant frequency etc. However, dielectric losses in the ferroelectric-type tunable components are comparatively high and show substantial increase approaching to the millimetre waves due to fundamental physical reason.

Alternative way to achieve controllability of characteristics in tunable microwave devices is mechanical reconfiguration. In this case the alteration of microwave characteristics can be attained by displacement of dielectric or metallic parts of devices. Mechanical tuning is very promising to produce low insertion loss combined with good tunability in microwave subsystems. In the case of ferroelectric technique of tuning, microwaves interact with the ferroelectric material which is a part of microwave line. That is why transmitted energy is partially absorbed by this material. On the contrary, mechanical system of control is located out of microwave propagation route so it does not contribute to the microwave loss. Moreover, it will be shown that dielectric losses have a trend to reduce in such devices. Mechanical control is valid at any frequency range, including millimetre wave range.

Transformation of microwave characteristics could be described in terms of medium's effective dielectric permittivity (*eff*). Effective dielectric permittivity of inhomogeneous medium can be defined as dielectric permittivity of homogeneous medium, which brings numerically the same macro parameters to the system of the same geometrical configuration. Effective permittivity is convenient parameter to describe devices with TEM wave propagating, where propagation constant is proportional to *eff* , however it can be used to describe other devices as well.

© 2012 Prokopenko et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Application of piezoelectric or electrostrictive actuators opens an opportunity for electromechanical control over effective dielectric permittivity in microwave devices [1]. However for such applications a tuning system should be highly sensitive to rather small displacement of device components. The key idea how to achieve such a high sensitivity of system characteristics to small displacement of device's parts is to provide a strong perturbation of the electromagnetic field in the domain influenced directly by the mechanical control. For that, a tunable dielectric discontinuity (the air gap) should be created perpendicularly to the pathway of the electric field lines. This air gap is placed between the dielectric parts or the dielectric plate and an electrode. An alteration of the air gap dimension leads to essential transformation in the electromagnetic field, and revising of components' characteristics such as resonant frequency, propagated wave phase, and so on.

Electromechanical Control over Effective Permittivity Used for Microwave Devices 283

is the wavenumber in free space, is the circular frequency, *c* is the light

Using equations (1) calculations of the transverse wavenumbers are carried out in a wide range of the permittivities and thicknesses of dielectrics in domains 1 and 2. It is found that the transverse wavenumbers as the solutions of equations (1) depend on frequency, permittivities of dielectrics and sizes of domains 1 and 2. Computed results are shown in Figure 2. This figure illustrates a dependence of normalized transverse wavenumber of domain 1 for fundamental LM mode versus the normalized air gap while permittivity of

**Figure 2.** Normalized transverse wavenumber of fundamental LM mode versus normalized air gap size: (*a*) for certain normalized wavenumbers *kh* while 1 = 80; (*b*) for various permittivities of dielectric

(a) (b)

As it is seen, transverse wavenumber of LM mode is very sensitive to variation of air gap between dielectric and metal plate. The change in only tenth or even hundredth part of percent from size of dielectric in domain 1 is sufficient for considerable alteration of transverse wavenumber. Required absolute change of air gap for significant alteration is not more than tens or hundreds micrometres depending on wavelength band and permittivity

In contrast to LM mode distribution of electromagnetic field of LE mode is significantly less

cot cot 0;

*h d*

*m m y y*

normalized air gap thickness. As it is seen, for the LE mode required change of air gap is

.

1 12 2 2 2 <sup>2</sup> 1 2 1 2

*m mm m y yy y*

*k*

*m <sup>y</sup>* and <sup>2</sup> *m*

*m*

*<sup>y</sup>* of the LE mode are

(2)

*<sup>y</sup>* of the basic LE mode on

in domain 1 while normalized wavenumber is *kh* = 2.

sensitive to variation of air gap. Transverse wavenumbers <sup>1</sup>

Figure 3 illustrates a dependence of transverse wavenumber <sup>1</sup>

of dielectric in domain 1.

solutions of the dispersion equations:

respectively, *<sup>k</sup> <sup>c</sup>*

velocity in vacuum.

domains 2 is <sup>2</sup> 1 .

The goal of this chapter is to describe electromagnetic field phenomena in structures suitable for electromechanical control of effective dielectric permittivity.
