**3. Reconfigurablity with dielectric liquids**

Many different guiding structures can be used for microwave component designs. In most cases, these structures are used and modeled as transmission lines whose electrical characteristics are given by their characteristic impedance, *Zo*, and effective dielectric constant, *εr*eff. These parameters result from the mode shape propagated by the line and determine the propagation constant *β* and wave speed *ν* by:

**Figure 2.**

*Microstrip transmission line structures. (a) Conventional; (b) fluidic channel below; (c) fluidic channel above.*

$$\begin{cases} \beta = \sqrt{\varepsilon\_{\rm reff}} k\_o \\ v = \frac{c}{\sqrt{\varepsilon\_{\rm reff}}} \end{cases} \tag{3}$$

Therefore, altering the propagated mode shape using liquid dielectrics will change the electrical characteristics, thereby enabling reconfigurability. To illustrate this, consider one of the most commonly used guiding structures in microwave circuits: the microstrip line. **Figure 2a** shows the conventional microstrip line. **Figure 2b** and **c** show modified microstrip line structures with a fluidic channel included in the substrate (b) and a fluidic channel on top of the microstrip substrate (c).

Assuming a Duroid dielectric substrate having ε<sup>r</sup> = 2.33 and a height of 4.8 mm with a strip width of 3 mm, the propagation characteristics for these three structures can be computed for different fluidic fillings in **Figure 2b** and **c**. **Table 3** summarizes the obtained results at 1 GHz for selected dielectric liquids and illustrates how fluidics allows for reconfiguring the transmission line's characteristics. For a given physical length, *l*, of the reconfigurable structures, the electrical length, *βl*, and, consequently, the propagation delay will vary along with *Z*o. This principle has been employed in many applications, such as [6, 7].



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

**Table 3.** *Reconfigurable propagation characteristics of a microstrip line.*
