**Table 2.**

*Dielectric constant and loss tangent of single-crystal SrTiO3 material at various temperatures.*


#### **Table 3.**

*Parameters values of Figure 11.*

#### **Figure 11.**

*Variation of the magnitude of the transmission coefficient with the frequency at different operating temperature T. (a) S21. (b) S11.*

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials DOI: http://dx.doi.org/10.5772/intechopen.98475*

**Temperature (***oc***)** *ε<sup>r</sup> tanδ* **\*10**�**<sup>4</sup>** �50/223 K 438 4.1 �25 /248 K 380 4.5 0/273 K 3 0 4.8 +25/298 K 320 5.2

*Dielectric constant and loss tangent of single-crystal SrTiO3 material at various temperatures.*

*T K*ð Þ *ε<sup>r</sup> f GHz* ð Þ **S21 dB** 7811 3.41 �0.25 269 3.5 3 �0.21 1867 3.56 �0.22

*Variation of the magnitude of the transmission coefficient with the frequency at different operating temperature*

**Table 2.**

**Table 3.**

**Figure 11.**

**118**

*T. (a) S21. (b) S11.*

*Parameters values of Figure 11.*

*Multifunctional Ferroelectric Materials*

The temperature dependence of *ε<sup>r</sup>* and *tan δ* for single-crystal SrTiO3 ferroelectric material has been reported by Krupka et al. [36] and is summarized in **Tables 2** and **3**.

**Figure 11** shows the variation of resonance frequency with the temperature which is very attractive at very low temperatures.

The data were conducted at 77 K in the 2.5 to 4.5 GHz frequency range. It is worth to observe that, at no bias and at 3 GHz, the insertion loss IL = 0.2 dB. These simulated data are not de-embedded, meaning that any contribution from the SMA launchers used for the measurement to the overall insertion loss has not been compensated from the data.

**Figure 12** and **Table 4** indicates the effect of E-field on the response of ZOR, the E-fields is varying from 0 to 30 Kv/cm. If the sample kept at a constant temperature

**Figure 12.** *Variation of the magnitude of the transmission coefficient with the frequency at different electric field E. (a) S21 (b) S11.*

#### *Multifunctional Ferroelectric Materials*


**Table 4.**

*Parameters values of Figure 12 at T = 77 K.*


#### **Table 5.**

*A comparative study of the different ZOR structures.*

of 77 K, the *ε<sup>r</sup>* STO is reduced from a high value of approximately 1867 at zero bias to a lower value of 741 at a high bias field.

The dynamic range of dielectric tunability with low additional microwave dielectric losses due to the insertion of ferroelectric thin films is one of the important criteria for the use of ferroelectric thin films in tunable circuits. Dielectric tunability is defined as the (*εr*ð Þ 0 at zero bias – *εr*ð Þ *E* at large bias)/ *ε<sup>r</sup>* at zero bias.

$$n = \frac{\varepsilon\_r(\mathbf{0}) - \varepsilon\_r(E)}{\varepsilon\_r(\mathbf{0})} \tag{12}$$

HTS/ferroelectric hybrid circuits may be of great interest. Tunable HTS/STO/LAO ZOR resonators have a more than 47 percent frequency tunability factor and have

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials*

*DOI: http://dx.doi.org/10.5772/intechopen.98475*

The author is deeply grateful to colleagues and professors at the Faculty of Electronic Engineering, Monofiya University, Egypt, for contributing and insightful comments and suggestions in conducting the above research. I would also like to express my gratitude to Kyushu University, Japan, and Prof. Haruichi Kanaya for his constructive revision, supervision, and financial support. Without their assistance and consultation, the research work would not come true. This work is partially supported by the Cabinet Office (CAO), Crossministerial Strategic Innovation Promotion Program (SIP), "An intelligent knowledge processing infrastructure, integrating physical and virtual domains" (NEDO), SCOPE, and KAKENHI

been demonstrated at 77 K.

**Acknowledgements**

(JP18K04146) JSPS.

**Conflict of interest**

**Appendices**

clear all close all clc

e0=8.85e-12;

e00=ck/t0;

for j=1:1:length(t)

for i=1:1:length(E)

n=er/er(i)

end

**121**

dn=2;

No conflict of interest.

Ferroelectric Characterization:

ck=8.7e+4; % Curie constant

En=(2\*dn)/((e0)\*(3\*e00)^(3/2)); t=[77] %operating temperature

es=0.018;theta=175;a1=2.45e-4;t0=42;a2=4e-3; % Constants

eta=((theta/t0)\*sqrt((1/16)+(((t(j))/(theta))^2))-1) %eta(T)

phi(i)=((x(i))^(2/3))+((y(i))^(2/3))-(eta);%phi(T,E)

delta1(i,j)=((((a1)\*(t(j)/t0)^2))/(phi(i))^(3/2)); %tan delta1 delta(i,j)=delta1(i,j)+delta2(i) % Total Tangetial loss

epsi(i)=((x(i))^(1/3))-((y(i))^(1/3)); %epsi(T,E) delta2(i)=((a2)\*(epsi(i))^2)/(phi(i)); % tan delta2

E=0:1e5:30e5 %operating electric field

e(i)=sqrt((es^2)+((E(i)/En)^2)); %e(E) x(i)=(((e(i)^2)+(eta^3))^0.5)+(e(i)); y(i)=(((e(i)^2)+(eta^3))^0.5)-(e(i));

er(i,j)=(e00)/(phi(i)) %permittivity

Dielectric tunability as high as 90% is attainable in STO thin films at moderate loss-tangent values (typical values between 0.005–0.01 at GHz frequencies) [37]. So, this structure will provide a tunability up to 47% for E = 30 kV/cm.

**Table 5**, demonstrates the comparison between the four proposed structures stated as:

Case 1: The MIM with a normal conductor (Copper).

Case 2: Adding HTS in replace of Copper to the MIM.

Case 3: Adding the ferroelectric material in case of Copper.

Case 4: Adding the ferroelectric material in case of HTS.

### **8. Conclusions**

A tunable ZOR CRLH resonator is successfully illustrated using a thin film ferroelectric material. ZOR can be applied to the ferroelectric material and this provides a different resonance frequency by altering either the electric field applied or the operating temperature. In addition, the incorporation of HTS material in place of normal conductors (e.g., gold, copper) significantly reduced conductor losses and consequently improved circuit performance. Therefore, for the development of low-loss and tunable microwave components and systems for wireless, radar and satellite communications, the design, manufacture and optimization of

HTS/ferroelectric hybrid circuits may be of great interest. Tunable HTS/STO/LAO ZOR resonators have a more than 47 percent frequency tunability factor and have been demonstrated at 77 K.
