**6. Piezoelectric and electrostrictive materials for actuators**

298 Dielectric Material

 0

<sup>0</sup> *eff* and <sup>0</sup>

**Figure 12.** Effective permittivity in near 50 microstrip line with micromechanical control (*w*/*h* = 2).

**Figure 13.** Effective loss in near 50 coplanar line with micromechanical control (*b*/*a* = 0.72).

tan *eff* are effective permittivity and loss tangent at *d/h* = 0

<sup>0</sup> *eff* and

tan *eff* are effective permittivity and loss tangent at zero *d/h* = 0

Application of usual piezoelectric ceramics for the microwave device tuning was described previously [1, 2]. However, in a strong controlling field piezoelectric ceramics show electromechanical hysteresis that produces some inconveniences. Much more prospective are relaxor ferroelectrics that have better transforming properties and practically no hysteresis.

Ferroelectrics with partially disordered structure exhibit diffused phase transition properties. Relaxor ferroelectrics near this transition show an extraordinary softening in their dielectric and elastic properties over a wide range of temperatures. Correspondingly, dielectric permittivity of the relaxor shows large and broad temperature maximum where giant electrostriction is observed (because the strain *x* is strongly dependent on the dielectric permittivity: *x* ~ 2).

Relaxors are characterized by the large ~ (2 – 6)104 and, consequently, by very big induced polarization *Pi* . A comparison of *Pi* in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 = PMN and *Pi* of paraelectric material Ba(Ti0.6,Sr0.4)O3 = BST (that also has rather big ~ 4000) is shown in Figure 14, *a*.

**Figure 14.** *a* – electrically induced polarization *Pi* in the relaxor of PMN and in the paraelectric BST; *b* – dielectric permittivity of PMN without () and under bias field *Eb*=10 kV/cm (*b*); *Pi* is the induced polarization in the relaxor PMN, obtained by pyroelectric measurements

Induced polarization in PMN many times exceeds one of BST. Moreover, in relaxor, the *Pi* depends on the temperature (like *PS* of ferroelectrics), as it can be seen in Figure 14, *b*. An example is electrically induced piezoelectric effect that is explained in Figure 15.

Electromechanical Control over Effective Permittivity Used for Microwave Devices 301

point of view of relaxor material applications in the fast-acting electronic devices. By the microwave dielectric spectroscopy method conducted in a broad temperature interval, the family of \* ,*T Ti T* , , curves are obtained, and one example is shown in

Response time of relaxor devices is determined by the mechanisms of dielectric dispersion. Electro-mechanical contribution to relaxor might be dominating factor so in relaxor based electronic devices the speed of response is defined by the sound speed in the relaxor, so the

To achieve electromechanical control by using piezoelectric or electrostrictive actuators the

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

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

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

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

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

air discontinuity should create significant perturbation of the electromagnetic

operating speed is dependent on the size of used relaxor element.

methods including ferroelectric permittivity control by electrical bias.

Figure 16.

**7. Conclusion** 

characteristics alteration.

dielectric-

design.

during the control as well.

**Figure 15.** Electrostriction in the high- materials under the bias field looks like piezoelectric effect (*xE*); *Eb,r* < *Eb,p*

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 that is shown in a new scale: *x* ' - *E*'.

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

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

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 point of view of relaxor material applications in the fast-acting electronic devices. By the microwave dielectric spectroscopy method conducted in a broad temperature interval, the family of \* ,*T Ti T* , , curves are obtained, and one example is shown in Figure 16.

Response time of relaxor devices is determined by the mechanisms of dielectric dispersion. Electro-mechanical contribution to relaxor might be dominating factor so in relaxor based electronic devices the speed of response is defined by the sound speed in the relaxor, so the operating speed is dependent on the size of used relaxor element.
