**5. Example: LTCC-based fluidic microwave impedance tuners**

The implementation of fluidic reconfigurable components is inherently threedimensional in nature, while the circuits are mostly planar. This has led to the use of various 3D printed PDMS structures that are assembled onto microwave circuits [18]. Low-Temperature Cofired Ceramics (LTCC) technology is three-dimensional circuit fabrication technology that is well suited for fluidic applications. This section uses this technology to illustrate the microwave reconfigurability of impedance tuners using dielectric fluids and liquid metal.

#### **5.1 Design approach**

#### *5.1.1 Two-state cell*

As discussed in Sections 3 and 4, if we alter the materials surrounding a signal conductor in a microwave circuit by injecting a dielectric fluid or a liquid metal in a nearby cavity, we can generate a two-state cell (**Figure 3a**): one state for the empty cavity and the other for when the cavity is filled. The characteristic impedance and the electric length are (*Z*<sup>c</sup> = *Z*1, *E*<sup>L</sup> = *E*L1) when the cell is in state 1, whereas when it is under state 2, it is characterized by (*Z*<sup>c</sup> = *Z*2, *E*<sup>L</sup> = *E*L2). Therefore, considering a 50 Ω load, we generate two different input impedances, as illustrated by the blue and the red dots in **Figure 3b** for the two states.

### *5.1.2* N*-state tuner*

Reconfigurable impedance tuners present a promising alternative to fixed ones in the design of reconfigurable circuits as they can offer multiple impedances at different frequency bands. Here, we consider distributed impedance tuners where N identical uniformly distributed two-state RF cells, C1-CN, cascaded, as shown in **Figure 4a** [18]. The *i*th cell, *Ci*, has a characteristic impedance *Z*ci and an electric length *E*Li. When the cell is in state 1, its characteristics are (*Z*ci = *Z*1, *E*Li = *E*L1) whereas when it is under state 2 it is characterized by (*Z*ci = *Z*2, *E*Li = *E*L2). Here, we are interested in the scenario where the tuner is loaded with a 50 Ω impedance, and *Z*<sup>1</sup> is set to 50 Ω in a 50 Ω system such that when all cells are in state 1, we have a 50 Ω line. Consequently,

#### **Figure 3.** *Two-state cell: (a) illustrative view, (b) impedance distribution.*

for a given combination of cell states, the resulting *Z*in's impedance consists of successive movements on the circles centered on *Z*<sup>1</sup> and *Z*<sup>2</sup> by an electrical length *E*L1 and *E*L2, respectively, starting from the Smith chart center, as shown in **Figure 4b**. A wide coverage at a particular frequency corresponds to one where the 2<sup>N</sup> synthesized impedances are distributed uniformly throughout the Smith chart. We define, therefore, the impedance ratio R and the tuner's total electric length *E*Lt by:

$$R = \frac{Z\_1}{Z\_2} \tag{4}$$

$$EL\_t = N.E\_{l\_1} \tag{5}$$

To synthesize impedances with high reflection coefficients, i.e., close to the Smith chart edge, *Z*<sup>2</sup> should be minimized, and losses should be reduced. Therefore, for a *Z*<sup>1</sup> set to 50 Ω, we seek to increase *R*. We also note that the generated impedances *Z*in are located within a region of the Smith chart limited by *E*Lt, as shown in **Figure 4b**. For an *E*Lt close to a multiple of half-wavelength (*λ*/2), a large coverage with well-distributed impedances is expected. However, this condition may be satisfied only for some frequencies. Apart from its impact on *E*Lt, the cell number *N* also controls the coverage resolution, i.e., a low value leads to scattered impedances points while a high one leads to a crowded coverage with a larger size and an increased complexity. Therefore, the tuner's coverage depends on the cells' electrical parameters and their number.

In the next sub-sections, we propose two types of RF fluidic impedance tuners based on the distributed architecture of **Figure 4a**, where reconfigurability is enabled through liquid dielectrics or metals. Here, the proposed tuners are built in LTCC substrate. Therefore, they leverage the LTCC's inherent 3D nature and its ability to realize buried transmission lines and cavities inside a multilayer substrate to form fluidic channels of varying shapes, sizes, and positions in a few standard fabrication steps.

### **5.2 LTCC dielectric fluidic impedance tuner**

This section proposes the design of a new RF fluidic impedance tuner in a 3D LTCC substrate for RF frequency applications [19]. To do so, the design of a single

**Figure 4.** *Impedance tuner illustrative. (a) Scheme, (b) smith chart coverage.*

fluid cell is detailed. Then, we introduce an eight-cell LTCC fluidic impedance tuner covering the 0.9–2.4 GHz frequency range. Its coverage is characterized based on EM simulations.

### *5.2.1 Two-state cell*

A 3D view of the proposed two-state RF fluidic cell is shown in **Figure 5**. It is implemented in a multilayer LTCC substrate. It consists of a grounded coplanar waveguide (CPWG) transmission line buried in an LTCC multilayer substrate with an empty cavity, i.e., a channel, above a part of the line. An inlet and an outlet to inject/ extract the desired gas or liquid, along with two tapered transitions, for on-wafer probe measurement, are also integrated into the cell design.

*Fluidics for Reconfigurable Microwave Components DOI: http://dx.doi.org/10.5772/intechopen.104857*

**Figure 5.** *Two-state RF dielectric liquid cell 3D view.*

Reconfigurability of the proposed RF fluidic cell is accomplished by changing the fluidic content of the cavity, thereby varying the dielectric constant of the central section, i.e., the transmission line section where the cavity is added. This results in changing the propagation constant. Therefore, based on the fluid filling the cavity and its length Lc (**Figure 5**), the equivalent impedance and the electrical length of the complete fluidic cell can be toggled between the two states (*Z*1, *E*L1) and (*Z*2, *E*L2).

For wide reconfigurability, we should increase *R*, as demonstrated in Section 5.1.2. Considering the fixed physical parameters of the different CPWG sections, this can be achieved through a wide change in the cavity dielectric constant, generating the highest change in the characteristic impedance *Z*<sup>c</sup> and the propagation constant β3 of the central section. To quantify this change, we introduce the impedance ratio *r*<sup>z</sup> and the propagation ratio *r*<sup>β</sup> as follow:

$$\sigma\_{\mathfrak{x}} = \frac{Z\_{\mathfrak{c}}(\mathfrak{e}\_{\mathfrak{c}} = \mathfrak{1})}{Z\_{\mathfrak{c}}(\mathfrak{e}\_{\mathfrak{c}} = \mathfrak{e}\_{\text{liquid}})} \tag{6}$$

$$r\_{\beta} = \frac{\beta\_{\text{c}} \left(\varepsilon\_{\text{c}} = \varepsilon\_{\text{liquid}}\right)}{\beta\_{\text{c}} (\varepsilon\_{\text{c}} = 1)}\tag{7}$$

where we require that *ZC* (*ε<sup>c</sup>* = 1) = 50 Ω. In this manner, the fluidic cell presents a 50 Ω impedance if the cavity is empty. Here, different sections of the cells are therefore dimensioned using multiple layers of DuPont 951 to provide 50 Ω under the empty state. For maximum ratios, high values of *ɛ*rliquid must be chosen. Here, DI-water is chosen as the filling fluid given its high relative permittivity, as stated in Section 1.1. Consequently, based on the central section physical parameters and DI-water permittivity, we obtain a change in the electrical characteristics, as shown in **Table 4**.

To complete the design of the fluidic cell, several (cavity length: *Lc*; cell length *Ls*) combinations were considered and simulated. We aim to minimize DI-water-related loss while maintaining considerable change in the reflection coefficient; we selected an *Lc* of 1.5 mm and an *Ls* of 3 mm.


#### **Table 4.**

*Characteristics for the central section when empty and filled with DI water.*

The designed cell depicted in **Figure 5** was fabricated using Lacime in-house LTCC process flow [20]. Multiple tapes of DuPont 951 were employed. Particularly, silver paste is used to print the outer and inner conductors and fill the vias. Rectangular and circular shapes are laser drilled on the required tapes to form the necessary fluidic channels, inlets, and outlets. To maintain the structural integrity during the stacking and laminating steps, fugitive carbon tapes are used to fill the inner and outer cavities, respectively. They sublimate at 600°C during the sintering step leaving behind empty channels. **Figure 6** shows the fabricated fluidic circuit.

The designed fluidic cell was simulated and measured between 0.9 and 2.4 GHz for filled and empty cavity cases. As can be seen, the measured and simulated insertion loss and input impedances track very well (**Figure 7**). For instance, an input impedance of 50 Ω is obtained for the empty cell, whereas when DI-water is injected into the cavity, the cell impedance and its electrical length change and show variation with frequency. Consequently, a part of the signal is reflected, resulting in an insertion loss increase (**Figure 7a**) and a change in the reflection magnitude and phase (**Figure 7b**).

### *5.2.2 Eight-cell tuner*

Eight fluidic cells were cascaded to form the tuner, as shown in **Figure 8**. Two 50 Ω vertical CPW transitions to upper CPWG lines were added at the input and output to measure the fabricated device easily. The overall tuner size, including the vertical transitions, is 26 mm 10 mm 1.5 mm.

**Figure 6.** *Fabricated RF fluidic cell.*

*Fluidics for Reconfigurable Microwave Components DOI: http://dx.doi.org/10.5772/intechopen.104857*

**Figure 7.** *Liquid dielectric cell measured and simulated: (a) insertion loss; (b) reflection coefficient.*

**Figure 8.** *Fabricated fluidic tuner.*

The operation of this tuner was characterized through ADS/HFSS simulations. The obtained input impedances when a 50 Ω load terminates its output port as shown with the red points in **Figure 9**. As can be seen, the tuner offers reasonable coverage of the Smith chart, particularly at higher frequencies. However, the coverage tends to be concentrated away from the edge of the Smith chart. This is attributed to the value of the fluidic cell's impedance *Z*2, which depends basically on the fluid parameters. Still, despite the retracted coverage, the impedance matching capability of the proposed tuner is quite good, even at such low frequencies. In fact, based on (8) as introduced in [21], each point in the Smith chart, representing ideal matching with a given tuner state, would become a circle if lower matching levels are permitted. For example, an impedance coverage area larger than the 256 individual points is reached at a 10 dB matching level at the considered frequencies, as shown in **Figure 9**.

$$
\Gamma\_{\rm in} = \frac{\Gamma\_{\rm s} - \mathcal{S}\_{\rm 11}}{\Gamma\_{\rm s} \mathcal{S}\_{\rm 11} - \mathbf{1}} \tag{8}
$$

where Γin is the reflection coefficient at the required matching level, Γ<sup>s</sup> is the reflection coefficient at a particular point in the Smith chart, and *S*<sup>11</sup> is the reflection coefficient at a point from the tuner constellation.

**Figure 9.** *Liquid dielectric tuner simulated reflection coefficient at different frequencies.*

The fluidic tuner was also fabricated using the Lacime LTCC process (**Figure 10**). To measure the entire eight-cell impedance tuner, we measure a single cell in both states and cascade 8 measurement results in various combinations in ADS. The tuner's impedance coverages based on cascaded measurements and HFSS simulation are depicted in **Figure 11** for six frequency points in the range of [0.9–2.4 GHz]. The measurement results show a contracted coverage compared to HFSS simulations, particularly at low frequencies. This is attributed to the non-conformity of the fabricated and designed circuits due to the LTCC fabrication errors, as layer misalignment. Still, the tuner offers good impedance coverage and can provide reconfigurability at low RF frequencies.

*Fluidics for Reconfigurable Microwave Components DOI: http://dx.doi.org/10.5772/intechopen.104857*

**Figure 10.** *Fabricated fluidic tuner.*

#### **5.3 LTCC liquid metal imoedance tuner**

A dielectric fluidic-based RF tuner with good Smith chart coverage up to 2.4 GHz has been introduced in Section 5.1. However, as explained in Section 2, DI-water is a lossy material at higher frequencies. Therefore, this tuner is not recommended to be used at upper microwave frequencies. Most dielectric liquids have either low dielectric constants and/or high losses [2]. Therefore, they are not suitable to be used in impedance tuning. Liquid metals with good electrical conductivity and deformable capability, as shown in Section 2, have gained attention in the RF field and seem to be good candidates as a filling liquid for our LTCC tuner. In this section, we will prove how liquid metals may enable reconfigurability based on the dielectric fluid two-state cell tuner [22].

#### *5.3.1 Two-state cell*

In the two-state liquid dielectric design of **Figure 12**, the cavity content is in direct contact with the signal line as no barrier between the two is used. If the same cavity were to be used with liquid metal, a short circuit would occur between the signal line in silver, and the liquid metal, Galinstan. In this case, there will be a risk of chemical reactions between the two that may lead to corrosion of the signal lines. Therefore, the cavity design has been altered to include a thin dielectric insulating layer, as shown in green in **Figure 12**, to prevent any contact.

The cell's reconfigurability is achieved by changing its corresponding capacitance: empty and liquid metal-filled states corresponding to low and high capacitance, respectively. A big ratio between these two capacitances results in a higher R ratio and, thereby, a wider Smith chart coverage of an n-state impedance tuner. Here we kept the same physical parameters of the liquid dielectric cell (**Figure 5**), and we added a 2-mil thin LTCC layer. **Figure 13** shows the insertion loss and the complex reflection coefficient of the designed and fabricated cell and demonstrates a good agreement between HFSS simulation and measurements for both states in the frequency band [1–10 GHz]. For instance, as expected, the empty cell is perfectly matched to 50 Ω, and Ga filled cavity cell shows an insertion loss and a variation in the reflection coefficient.

**Figure 12.** *Two-state RF liquid metal cell: a) 3D view; b) side view.*

*Fluidics for Reconfigurable Microwave Components DOI: http://dx.doi.org/10.5772/intechopen.104857*

**Figure 13.** *Liquid metal cell measured and simulated: (a) insertion loss; (b) reflection coefficient.*

**Figure 14.** *Liquid metal impedance tuner: 3D view.*

#### *5.3.2 Eight-cell tuner*

Similar to the dielectric-fluidic tuner, eight liquid-metal cells were cascaded, as shown in **Figure 14**. Two 50 Ω vertical CPW transitions to upper CPWG lines were added at the input and output for interconnection and measurement purposes. The final tuner has the same dimension as the liquid dielectric one, i.e.,

26 mm 10 mm 1.5 mm. **Figure 14** shows the designed and fabricated tuner. **Figure 15** shows the simulated and measured Smith chart coverage when a 50 Ω load terminates the output port. Good impedance distributions are obtained at different frequency points in the frequency range [1 GHz, 10 GHz], particularly at higher frequencies. Like the fluidic tuner discussed previously, a well-distributed and uniform coverage cannot be obtained for all the frequencies because of the frequencydependent impedance and electrical length of the unit cell.
