Fluidics for Reconfigurable Microwave Components

Abstract

Dielectric and conducting liquids with varying electromagnetic properties can offer novel alternatives for building tunable microwave passive components as well as antennas. Injecting these fluidics in or around microwave substrates alters their overall electrical characteristics, enabling circuit reconfigurability. Alternatively, changing the shapes and dimensions of conductors by using liquid metals can achieve similar reconfigurability. An overview of different liquids and their electromagnetic properties is first given. The principles behind the reconfigurability of the electrical characteristics of typical guiding structures based on mode shape variation in the presence of fluids are discussed. The realization of an N-bit programmable impedance tuner in 3D LTCC technology based on these principles is presented.

1. Introduction

The increasing importance of microwave components and antenna reconfigurability stems from the fact that such functionality can significantly improve the performance of various radio systems while promoting sustainability. Indeed, it allows maximizing hardware re-use, thereby reducing the size and component count while avoiding crosstalk and noise issues that arise in multi-band/wideband systems. While a considerable effort has been dedicated to MEMS- and semiconductor-based reconfigurability, fluidics have emerged as a viable alternative for the same purpose owing to their relative abundance, suitability for flexible electronics, and power handling capabilities. However, they may not be as performing in terms of speed and high-frequency coverage.

2. Properties of dielectric and conducting liquids

2.1 Dielectric liquids

Thousands of liquid dielectrics, either organic or synthetic, are available and can be considered for microwave component reconfigurability. Their relative abundance and characteristics, such as toxicity, viscosity, electrical, and thermal properties, depending on their chemical composition. They have been widely used in different fields, including electrical, digital, and microwave circuits [1]. For microwave component reconfigurability, the key parameter of interest is the relative permittivity, which is generally complex as well as frequency and temperature-dependent. However, these liquids are typically identified by their static permittivity (ε_s = ε_oε_rs). Table 1 summarizes the static relative permittivity of the most commonly used dielectric liquids under ambient temperature, i.e., 20°C [2, 3].

Liquid	Static relative permittivity (ℇrs)
DI water	80.29
Acetone	21.13
Methanol	33.64
Butanol	18.19
Ethanol	25.16
Propanol	21.15
Ethanediol	41.89
Benzene	2.3
Chloroform	4.8
Silicone fluid	2.3

Table 1.

Static permittivity of most common liquid dielectrics at 20°C.

For polar liquids with single Debye relaxation behavior, the frequency-dependent complex permittivity can be calculated using the Debye relaxation formula [3]:

$$\epsilon ={\epsilon }_{\infty }+\frac{\left({\epsilon }_s-{\epsilon }_{\infty }\right)}{1+\mathit{j\omega \tau }}={\epsilon }^{\prime }+j{\epsilon }^{"}$$E1

where ℇ_∞ is the high-frequency permittivity limit, τ is the relaxation time, and the loss tangent δ is given by ${\epsilon }^{"}{\epsilon }^{\prime }$ . For instance, for DI (DeIonized) water at 20°C, the frequency dependency of the permittivity can be given in terms of its dielectric constant and loss tangent explicitly by [4]:

$$\left\{\begin{array}{l}{\epsilon }_r=6.28+\frac{73.91}{1+0.26\times {10}^{-20}{f}^2}\\ \delta =\frac{4.48\times {10}^{-9}f}{80.19+2.26\times {10}^{-20}{f}^2}\end{array}\right.$$E2

Figure 1 shows the significant variation of these parameters versus frequency up to 20 GHz and illustrates how this liquid becomes increasingly lossy, which may limit its usability at very high frequencies. It should also be noted that ℇ_∞, ℇ_s, and τ are temperature dependent [4].

Figure 1.

DI water dielectric constant and loss tangent versus frequency at 20°C.

2.2 Liquid metals

Metals are abundant materials on earth. Most of them are present in a solid state at room temperature. Only a few metals are liquids under ambient temperature. Francium (Fr), cesium (Cs), rubidium (Rb), mercury (Hg), and gallium (Ga)-based metals are the known liquid metals [5]. The radioactivity of the Francium and the reactivity of cesium and rubidium are the main reasons these liquid metals are avoided in microwave component reconfigurability applications. On the other hand, mercury is considered a toxic fluid that cannot be manipulated safely and should be avoided or used under extremely well-controlled conditions. Gallium is a risk-free metal that melts at 29.7°C, which is slightly higher than room temperature. However, the melting points of Gallium-based alloys such as Eutectic Gallium Indium (EGaIn), Eutectic Gallium Tin (EGaSn), and Eutectic Gallium Indium Tin (known as Galinstan) are lower, and they are around 15, 21, and −19°C, respectively [5]. Table 2 summarizes the key physical properties of the most suitable liquid metals for use in microwaves.

Liquid metal	Melting point (°C)	Electrical conductivity (S/m)	Thermal conductivity (W/m/K)	Viscosity (kg/m/s)
Gallium	29.76	6.73 × 10^6	29.3	1.37 × 10^−3
EGaIn	15.5	3.4 × 10^6	26.6	1.99 × 10^−3
Galinstan	−19	3.46 × 10^6	16.5	2.4 × 10^−3
Mercury	−38.8	1.04 × 10^6	8.5	1.526 × 10^−3

Table 2.

Key physical properties of most commonly used liquid metals.

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, Z_o, and effective dielectric constant, ${\epsilon }_{r\mathrm{eff}}$. These parameters result from the mode shape propagated by the line and determine the propagation constant β and wave speed ν by:

$$\left\{\begin{array}{c}\beta =\sqrt{{\epsilon }_{\text{reff}}}{k}_{\mathrm{o}}\\ v=\frac{c}{\sqrt{{\epsilon }_{\text{reff}}}}\end{array}\right.$$E3

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).

Figure 2.

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

Assuming a Duroid dielectric substrate having ε_r = 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].

Table 3.

Reconfigurable propagation characteristics of a microstrip line.

4. Reconfigurability with liquid metals

There are two ways liquid metals can be used for microwave circuit reconfigurability: contacting and contactless [8]. These refer to whether or not the liquid metal enters in contact with conductors in the microwave circuit, the contacting approach, or is brought in close proximity to these conductors without touching them, the contactless method. This latter method is similar in principle to using dielectric fluids, whereby the liquid metal can behave as a capacitive load on top of or below the transmission line’s conductors, thereby altering the propagation characteristics. This requires thin dielectric layers between the liquid metal’s hosting cavities and the rest of the circuit’s conductors to avoid contact resulting in undesirable reactions, e.g., corrosion. This approach can be highly effective, particularly when the liquid metal is placed near the maximum electrical field value resulting in a good tuning range [9, 10]. In the contacting approach, liquid metals are used to short connections between conductors, i.e., like contact switches [11, 12, 13] in a microwave circuit or extend a single conductor with a custom shape determined by the encapsulating cavity [14, 15]. This allows altering signal paths in a circuit, thereby enabling the reconfiguration of their electrical length and propagation delays, which reconfigures the overall component.

While liquid metals can offer significant advantages for reconfigurable microwave components and deformable printed electronics, they are relatively complex to handle and suffer from fast-oxidation when exposed to oxygen. Therefore, they require specific packaging and manipulation guidelines to overcome these limitations [16, 17].

5. Example: LTCC-based fluidic microwave impedance tuners

The implementation of fluidic reconfigurable components is inherently three-dimensional 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_c = Z₁, E_L = E_L1) when the cell is in state 1, whereas when it is under state 2, it is characterized by (Z_c = Z₂, E_L = 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.

Figure 3.

Two-state cell: (a) illustrative view, (b) impedance distribution.

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 ith cell, C_i, has a characteristic impedance Z_ci and an electric length E_Li. When the cell is in state 1, its characteristics are (Z_ci = Z₁, E_Li = E_L1) whereas when it is under state 2 it is characterized by (Z_ci = Z₂, E_Li = E_L2). Here, we are interested in the scenario where the tuner is loaded with a 50 Ω impedance, and Z₁ 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, for a given combination of cell states, the resulting Z_in‘s impedance consists of successive movements on the circles centered on Z₁ and Z₂ 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^N 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:

Figure 4.

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

$$R=\frac{Z_1}{Z_2}$$E4

$${\mathit{EL}}_t=N.E_{l_1}$$E5

To synthesize impedances with high reflection coefficients, i.e., close to the Smith chart edge, Z₂ should be minimized, and losses should be reduced. Therefore, for a Z₁ 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 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.

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 L_c (Figure 5), the equivalent impedance and the electrical length of the complete fluidic cell can be toggled between the two states (Z₁, E_L1) and (Z₂, 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_c and the propagation constant β3 of the central section. To quantify this change, we introduce the impedance ratio r_z and the propagation ratio r_β as follow:

$$r_z=\frac{Z_{\mathrm{c}}\left({\epsilon }_{\mathrm{c}}=1\right)}{Z_{\mathrm{c}}\left({\epsilon }_{\mathrm{c}}={{\epsilon }_r}_{\text{liquid}}\right)}$$E6

$$r_{\beta }=\frac{{\beta }_{\mathrm{c}}\left({\epsilon }_{\mathrm{c}}={{\epsilon }_r}_{\text{liquid}}\right)}{{\beta }_{\mathrm{c}}\left({\epsilon }_{\mathrm{c}}=1\right)}$$E7

where we require that Z_C (ε_c = 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.

f (GHz)	Empty		DI Water		rz	rβ
	Z03 (Ω)	β3 (rad/m)	Z03 (Ω)	β3 (rad/m)
0.9	50	39.5	16.5	122	3.03	3.08
2.4	50	105	16.6	322	3.01	3.06

Table 4.

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

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

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.

Figure 6.

Fabricated RF fluidic cell.

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).

Figure 7.

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

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 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 Z₂, 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.

Figure 9.

Liquid dielectric tuner simulated reflection coefficient at different frequencies.

$${\Gamma }_{\text{in}}=\frac{{\Gamma }_{\mathrm{s}}-S_{11}}{{\Gamma }_{\mathrm{s}}{S}_{11}-1}$$E8

where Γ_in is the reflection coefficient at the required matching level, Γ_s is the reflection coefficient at a particular point in the Smith chart, and S₁₁ is the reflection coefficient at a point from the tuner constellation.

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.

Figure 10.

Fabricated fluidic tuner.

Figure 11.

Liquid dielectric tuner simulated and measured impedance coverage at different frequencies.

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.

Figure 12.

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

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 13.

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

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 14.

Liquid metal impedance tuner: 3D view.

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 frequency-dependent impedance and electrical length of the unit cell.

Figure 15.

Liquid metal-based tuner simulated and measured impedance coverage at different frequencies.

6. Conclusion

Conductive and dielectric liquids offer viable options for achieving microwave circuits’ reconfigurability. Both types of fluids can alter the wave propagation characteristics in guiding structures by injecting and removing the fluids from cavities in the close vicinity of conventional conductors. Conducting fluids offer the additional capability of reconfiguring the path of a guided wave by changing the shape of the conductors. The principles behind these reconfiguration techniques were presented and discussed. The design and realization of reconfigurable microwave impedance tuners using dielectric and conductive fluidics in LTCC technology were used to detail possible applications of the introduced reconfiguration. The results presented in this chapter, and those reported by others in the open literature, are promising and will support further research into this area.