**7. Conclusion**

300 Dielectric Material

(*xE*); *Eb,r* < *Eb,p*

near one gigahertz

**Figure 15.** Electrostriction in the high- materials under the bias field looks like piezoelectric effect

"piezoelectric effect" appears that is shown in a new scale: *x* ' - *E*'.

time of relaxors can be estimated by the dielectric spectroscopy method.

Electric bias field *Еb* produces some constant internal strain *x*0 at the parabolic dependency strain *x* on field *E*. Besides of steady and relatively big bias field *Eb*, a smaller alternating electric field *E'* is applied to given dielectric material. As a result, pseudo-linear

Piezoelectric effect appears instantly after the bias field is applied, and it disappears immediately after the bias field is switched off. Electrically induced piezoelectricity is large owing to giant electrostriction. Relaxor actuators can be used as precision positioner, including microwave tunable devices. Very important for device application the response

**Figure 16.** Dielectric spectrum of PMN at microwaves, fast dispersion of dielectric permittivity started

It is obvious that response quickness is determined by the frequency dispersion of relaxor's dielectric permittivity: (). That is why dielectric dispersion in the relaxors is studied with a To achieve electromechanical control by using piezoelectric or electrostrictive actuators the dielectric air discontinuity should create significant perturbation of the electromagnetic field. It requires a certain location of the discontinuity relatively to electromagnetic field distribution. It was demonstrated that for maximal reconfiguration of electromagnetic field by the dielectric parts displacement the border between air slot and dielectric should be perpendicular to the electric filed. In this case the displacement of dielectric parts leads to a considerable rearrangement of the electromagnetic field, and as a result to device characteristics alteration.

Effective permittivity approach not only simplifies computation but provides information about controllability of microwave structures by alteration of air slot thickness *d* as well. The controllability depends on frequency and dielectric thickness *h*. Maximal range of effective permittivity alteration increases while either frequency or thickness *h* reduces. At the same time, the reducing of either frequency or thickness *h* leads to increase of the controllability effectiveness due to decrease of required displacement of device components. Utmost controllability of effective permittivity was obtained on the assumption that either frequency or thickness of dielectric *h* tends to zero. Calculated dependences reflect asymptotic control over effective permittivity by alteration of air slot thickness *d*. Analysis of the dependences shows that the effective permittivity may be controlled in the range from permittivity of dielectric to one. Such high controllability cannot be achieved by other methods including ferroelectric permittivity control by electrical bias.

For given working frequency effectiveness of controllability increases if thickness of dielectric layer is decreased. Criterion for maximal thickness of dielectric was estimated. It is necessary to note that decrease in dielectric thickness reduces characteristic impedance of structure. That is why adding of matching sections should be considered in actual device design.

Presented method of control not only preserves high quality factor of microwave devices in the case of application low loss dielectrics but demonstrates reducing of dielectric loss during the control as well.

Effective permittivity approach significantly simplifies simulation of microwave devices. However, this approach has limitations related with high order modes excitation. That is

#### 302 Dielectric Material

why this technique should be carefully verified by the rigorous solution, boundary element method for instance.
