**6. Tunable composite right/left-handed transmission lines using ferroelectric thin films**

Ferroelectric/superconductor thin films (*YBa*2*Cu*3*O*7�*<sup>δ</sup>=Ba*0*:*0*Sr*0*:*9*TiO*3) are used to realize an electrically tunable, low-loss composite right/left-handed transmission line. A resistive line is deployed as both the DC bias path and RF choke. The whole device maintains a simple all-planar configuration. The composite right/left-handed transmission lines that are well-matched shows a wide passband [28].

Various tuning elements, such as surface-mounted discrete varactors or ferroelectric parallel plate varactors, have been used [29]. Through the series capacitors, tuning is accomplished, although tuning the capacitance and shunt inductance [30] simultaneously would be advantageous in maintaining the impedance match for critical requirements. Cables, the introduction of RF capacitive bases, decoupled capacitors [31], or more complicated networks trace the DC bias of the reported structures.

In this study, the tunable low-loss device is realized by planar ferroelectric/ superconductor thin films. Tunable elements based on ferroelectric materials avoid surface mounting components compared to discrete diode varactors, so neither contact losses nor parasitics are present in the configuration. Furthermore, it is possible to continuously vary capacitance values.

The electrical tuning is based on ferroelectric permittivity's electric-field dependency. As the fundamental tuning element for its ability, between planar structures, to establish a relatively high electric field between its two electrodes, an interdigital capacitor (IDC) is used. Between the circuit layer (HTS) and the substrate, the ferroelectric thin film is sandwiched. Using a bias tee, the DC bias can either be excited through the RF ports or through an independent bias network with an RF choke. In that it introduces less interference to the main circuit and is often easy to fit into measurement systems, the previous approach is beneficial. However, due to the high-pass nature of a CRLH-TL, it is not straightforward to apply DC voltage through the RF ports.

In this case, we propose a resistive line approach as shown in **Figure 4** for a three unit cascaded CRLH-TL. The resistive line prevent the RF trnamission from flowing into the DC path if its resistance is sufficiently high.With line dimensions of 10*μm* wide, the simulated responses for different surface resistances are given in **Figure 5**. The attenuation losses are estimated 0.6 dB for 20*Ω* surface resistance, 0.3 dB for 0*Ω*, and 0.2 dB for 90*Ω*, corresponding to a line resistance of over 2, and 9 *KΩ* per unit-cell.

The substrate is 0.5 *mm* thick *MgO*. The ferroelectric material (*Ba*0*:*0*Sr*0*:*9*TiO*3Þ is deposited on the upper side of the substrate. On top of *BST*, the *YBa*2*Cu*3*O*<sup>7</sup>�*<sup>δ</sup>* (*YBCO*) is deposited and represents the superconducting circuit layer. Silver is used for the contact pads to reinforce the electrical connection with the on-wafer probes and bonding wires. The resistive line is made of titanium material that has surface resistance . The *BST* film has a measured permittivity of 400–500 with a loss tangent of 0.02–0.03.

The CRLH-TL single-unit shown in **Figure 6** was simulated and manufactured by

[28]. It shows only the simulations, and the measurements are given in **Figure 7**. Within the bias range of 0-70 V, the return loss is better than �1 dB from 4 to 14GH. Calculations show that 0.1 dB would have contributed to the ferroelectric loss (tan δ = 0.03). If the bias increases from 0 to 70 V (indicated by the effect of surface

resistance variation), the phase shifts by 3.60 at 10 GHz in **Figure 8**.

*Simulated responses of a 3-unit CRLH-TL with different surface resistances of the bias line.*

*Layout of a 3-unit CRLH-TL with resistive bias line, IDC, and meander line inductor [28].*

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials*

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

**Figure 4.**

**Figure 5.**

**113**

#### **Figure 4.**

*<sup>n</sup>* <sup>¼</sup> *<sup>ε</sup>*ð Þ **<sup>0</sup>**

and the relative tunability *nr* defined as the relative change of the permittivity between zero bias and an electric field *E* with respect to its permittivity at zero bias

*<sup>ε</sup>*ð Þ **<sup>0</sup>** <sup>¼</sup> **<sup>1</sup>** � **<sup>1</sup>**

Ferroelectric/superconductor thin films (*YBa*2*Cu*3*O*7�*<sup>δ</sup>=Ba*0*:*0*Sr*0*:*9*TiO*3) are used to realize an electrically tunable, low-loss composite right/left-handed transmission line. A resistive line is deployed as both the DC bias path and RF choke. The whole device maintains a simple all-planar configuration. The composite right/left-handed

Various tuning elements, such as surface-mounted discrete varactors or ferroelectric parallel plate varactors, have been used [29]. Through the series capacitors, tuning is accomplished, although tuning the capacitance and shunt inductance [30] simultaneously would be advantageous in maintaining the impedance match for critical requirements. Cables, the introduction of RF capacitive bases, decoupled capacitors [31], or more complicated networks trace the DC bias of the reported

In this study, the tunable low-loss device is realized by planar ferroelectric/ superconductor thin films. Tunable elements based on ferroelectric materials avoid surface mounting components compared to discrete diode varactors, so neither contact losses nor parasitics are present in the configuration. Furthermore, it is

The electrical tuning is based on ferroelectric permittivity's electric-field dependency. As the fundamental tuning element for its ability, between planar structures, to establish a relatively high electric field between its two electrodes, an interdigital capacitor (IDC) is used. Between the circuit layer (HTS) and the substrate, the ferroelectric thin film is sandwiched. Using a bias tee, the DC bias can either be excited through the RF ports or through an independent bias network with an RF choke. In that it introduces less interference to the main circuit and is often easy to fit into measurement systems, the previous approach is beneficial. However, due to the high-pass nature of a CRLH-TL, it is not straightforward to apply DC voltage

In this case, we propose a resistive line approach as shown in **Figure 4** for a three unit cascaded CRLH-TL. The resistive line prevent the RF trnamission from flowing into the DC path if its resistance is sufficiently high.With line dimensions of 10*μm* wide, the simulated responses for different surface resistances are given in **Figure 5**. The attenuation losses are estimated 0.6 dB for 20*Ω* surface resistance, 0.3 dB for 0*Ω*, and 0.2 dB for 90*Ω*, corresponding to a line resistance of over 2, and 9 *KΩ* per unit-cell.

The substrate is 0.5 *mm* thick *MgO*. The ferroelectric material (*Ba*0*:*0*Sr*0*:*9*TiO*3Þ is

deposited on the upper side of the substrate. On top of *BST*, the *YBa*2*Cu*3*O*<sup>7</sup>�*<sup>δ</sup>* (*YBCO*) is deposited and represents the superconducting circuit layer. Silver is used for the contact pads to reinforce the electrical connection with the on-wafer probes and bonding wires. The resistive line is made of titanium material that has surface resistance . The *BST* film has a measured permittivity of 400–500 with a loss

*n*

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

**6. Tunable composite right/left-handed transmission lines using**

transmission lines that are well-matched shows a wide passband [28].

possible to continuously vary capacitance values.

**ferroelectric thin films**

*Multifunctional Ferroelectric Materials*

structures.

through the RF ports.

tangent of 0.02–0.03.

**112**

*<sup>ε</sup>*ð Þ *<sup>E</sup>* (1)

(2)

*Layout of a 3-unit CRLH-TL with resistive bias line, IDC, and meander line inductor [28].*

**Figure 5.** *Simulated responses of a 3-unit CRLH-TL with different surface resistances of the bias line.*

The CRLH-TL single-unit shown in **Figure 6** was simulated and manufactured by [28]. It shows only the simulations, and the measurements are given in **Figure 7**. Within the bias range of 0-70 V, the return loss is better than �1 dB from 4 to 14GH.

Calculations show that 0.1 dB would have contributed to the ferroelectric loss (tan δ = 0.03). If the bias increases from 0 to 70 V (indicated by the effect of surface resistance variation), the phase shifts by 3.60 at 10 GHz in **Figure 8**.

frequencies have been the most promising ferroelectrics for integration with HTS circuits [32]. The popular ferroelectric tunable structures are based on conductor/

*Simulated phase responses and the phase shift of the one-unit CRLH-TL with two cases [28].*

The modified microstrip structure of **Figure 9** consists of a dielectric substrate (e.g., LAO or MgO, typically 254 to 500 um thick, LAO with permittivity 23.6 is selected to represent the base substrate [32], a ferroelectric thin-film layer

ferroelectric/dielectric two-layered microstrip.

*Tunable Zeroth-Order Resonator Based on Ferroelectric Materials*

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

*Layout of ZOR with ferroelectric material (a) top view (b) side view.*

**Figure 8.**

**Figure 9.**

**115**

**Figure 6.** *Picture of the one-unit CRLH-TL [28].*

**Figure 7.** *Simulated responses of a one unit CRLH-TL with different surface resistances of the bias line [28].*
