**Appendices**

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

*E Kv* ð Þ *<sup>=</sup>cm <sup>ε</sup><sup>r</sup>* tan *<sup>δ</sup>* **\*10**�**<sup>4</sup>** *f GHz* ð Þ **S21 dB** 1867 7.2 3.55 �0.25 1168 18.5 3. 59 �0.28 741 26 3.62 �0.39

> **Ferro+ Copper [Proposed]**

*<sup>n</sup>* <sup>¼</sup> *<sup>ε</sup>r*ð Þ� <sup>0</sup> *<sup>ε</sup>r*ð Þ *<sup>E</sup>*

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].

**Table 5**, demonstrates the comparison between the four proposed structures

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

So, this structure will provide a tunability up to 47% for E = 30 kV/cm.

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.

*<sup>ε</sup>r*ð Þ <sup>0</sup> (12)

**Ferro+ HTS 77 k [Proposed]**

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.

to a lower value of 741 at a high bias field.

*A comparative study of the different ZOR structures.*

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

*Multifunctional Ferroelectric Materials*

**Property MIM HTS 77 k**

**[Proposed]**

Performance S11 �10 �34 �18 �32

Tunability No No Yes Yes Q factor 1762 43411 9957 68714 Fabrication Simple Difficult Simple Difficult

S21 �3.55 �0.09 �0.54 �0.023

stated as:

**Table 4.**

**Table 5.**

**8. Conclusions**

**120**

```
Ferroelectric Characterization:
clear all
close all
clc
ck=8.7e+4; % Curie constant
e0=8.85e-12;
dn=2;
es=0.018;theta=175;a1=2.45e-4;t0=42;a2=4e-3; % Constants
e00=ck/t0;
En=(2*dn)/((e0)*(3*e00)^(3/2));
t=[77] %operating temperature
for j=1:1:length(t)
eta=((theta/t0)*sqrt((1/16)+(((t(j))/(theta))^2))-1) %eta(T)
  E=0:1e5:30e5 %operating electric field
for i=1:1:length(E)
   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));
   phi(i)=((x(i))^(2/3))+((y(i))^(2/3))-(eta);%phi(T,E)
   er(i,j)=(e00)/(phi(i)) %permittivity
   epsi(i)=((x(i))^(1/3))-((y(i))^(1/3)); %epsi(T,E)
   delta2(i)=((a2)*(epsi(i))^2)/(phi(i)); % tan delta2
   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
   n=er/er(i)
```
end

*Multifunctional Ferroelectric Materials*

plot(E,er)

end figure plot(E,delta)
