Symmetry Implications of a 60 GHz Inverted Microstrip Line Phase Shifter with Nematic Liquid Crystals in Diverse Packaging Boundary Conditions

Abstract

This work demystifies the role that packaging boundary conditions (both physically and electromagnetically) can play in a nematic liquid crystal (NLC)-based inverted microstrip (IMS) phase shifter device operating at the 60 GHz band (from 54 GHz to 66 GHz). Most notably, the air box radiating boundary and perfect electric conductor (PEC) enclosing boundary are numerically examined and compared statistically for convergence, scattering parameters, and phase-shift-to-insertion-loss ratio, i.e., figure-of-merit (FoM). Notably, the simulated phase tunability of the radiating air box boundary structure is 8.26°/cm higher than that of the encased (enclosed) PEC boundary structure at 60 GHz. However, the maximum insertion loss of the encased PEC structure is 0.47 dB smaller compared to that of the radiant air box boundary structure. This results in an FoM increase of 29.26°/dB at the enclosed PEC limit (relative to the less-than-optimal airbox radiation limit). Arguably, the NLC-filled IMS phase shifter device packaging with metals fully enclosed (in addition to the default ground plane) enhances the symmetry of the structure, both in the geometry and the materials system. In electromagnetic parlance, it contributes to a more homogenously distributed electric field and a more stable monomodal transmission environment with mitigated radiation and noise. Practically, the addition of the enclosure to the well-established NLC-IMS planar fabrication techniques provides a feasible manufacturing (assembling) solution to acquire the reasonably comparable performance advantage exhibited by non-planar structures, e.g., a fully enclosed strip line and rectangular coaxial line, which are technically demanding to manufacture with NLC.

1. Introduction

Nematic liquid crystal (NLC) tunable devices, technologies, and real-world applications have evolved considerably over time, dating back to the first liquid crystal display (LCD) in 1964 [1], and their portfolios have expanded to radio frequency in the last three decades [2,3,4,5]. The research initiatives incorporating NLC into phase-reconfigurable microwave (MW) components have been typified by phase shifters [6,7,8] and delay lines [9,10,11], as well as modulators [5] in terahertz (THz) photonics. These smart passive devices rely on how the anisotropic shape [8] of the NLC dielectrics changes their molecular directors (colloquially referred to orientations) and hence the polarizabilities (i.e., macroscopically leading to dielectric constant variations) when subjected to external stimuli (e.g., low-frequency voltage as an electrical biasing field). The microscopic foundations, i.e., the anisotropic-shaped rod-like molecules and hence the tunable dipolar moments which underpin the macroscopic dielectric anisotropy, have been documented in [8,12].

Fundamentally, the mathematical modelling approaches of NLC are summarized in Figure 1. Based on the vector model, NLC device designs have been established and experimental prototypes have been building sound understanding of diverse device geometries for various frequencies, including but not limited to the inverted microstrip (IMS) geometry [13] for 10 GHz, the coplanar waveguide (CPW) geometry [14] for 79 GHz and its enclosed variations, i.e., ECPW [8] for 60 GHz, as shown in Figure 2, as well as the coaxial geometries with circular symmetry reported at 60 GHz [15] and 0.3 THz [16], respectively. The authors of [2,4] offer concise yet rich insights into the challenges and opportunities in NLC-based reconfigurable devices with regard to the radio frequency landscape beyond the classical display scenarios, e.g., targeting reconfigurable intelligent surfaces [10,17] for 5G/6G applications, radio astronomy [18], and satellite communications [19].

Due to the fluid-like flow nature of NLC materials, a suitable enclosing structure (comprising either conductors or insulators) needs to be in place. The power consumption varies, depending on the number of conductors embedded in the NLC accommodating topology that affects the driving approach. For the single-conductor wave guiding system (e.g., waveguides), power-hungry magnets are uniquely required, with a bias voltage in excess of 100 V reported [2]. Contrarily, low-power electronic driving (e.g., up to 20 V [13,15]) can be achieved with ease using multi-conductor transmission lines, with the theoretical basis well documented in our past works concerning a host of NLC-based phase shifters realized in inverted microstrip lines [13,20] (with radiation loss concerns due to the air boundary), enclosed coplanar waveguides [8] and their potential optimizations by introducing artificial magnetic conductors [21], and, more recently, coaxial lines [15,16] driven electronically without spin-coating alignment layers (at the cost of a limited phase tuning range).

By way of illustration, a snapshot of our inverted microstrip (IMS) phase shifter realized in NLC technology is given in Figure 3 for the 0 V bias state and the saturated bias state, corresponding to the diverse dielectric constant (Dk) and effective permittivity (ε) due to the change in the NLC dielectric polarizability (dipole moments’ variation with the NLC molecular reorientation as shown). More specifically, the 0 V bias state is linked to ${\mathrm{D}\mathrm{k}}_{\perp }$ and ${\mathsf{\epsilon }}_{\perp }$ (wherein the shortest dipole moment is in line with the microwave polarization), and the saturated bias state gives ${\mathrm{D}\mathrm{k}}_{\parallel }$ and ${\mathsf{\epsilon }}_{\parallel }$ (wherein the longest dipole moment is parallel with the microwave polarization). Two things are worth noting here. First, the ${\mathrm{D}\mathrm{k}}_{\perp }$ is achieved by mechanically rubbing the spin-coated polyimide (PI) layer in a direction as denoted (i.e., in line with the metal core line or the microwave signal propagation direction, as depicted in Figure 3). This alignment direction is experimentally verified [8,13] as the optimum setup (as compared with other directions of mechanical rubbing).

We wish to obey a similar setup as we did for the NLC-IMS phase shifter rethinking framework from [20]. Furthermore, we specify the practically achievable NLC layer thickness that responds quickly to external stimuli (e.g., bias voltage applied versus removed). Compared to experimental research, computational simplifications are widely adopted in numerical models nowadays for academic research and proof-of-concept device prototype development. Exemplary assumptions include dispersion-free dielectric properties across the frequency spectrum of analysis [16] and roughness-free conductor surfaces [15]. Among a host of variables and settings adapted from mainstream microstrip transmission lines [22,23,24], identifying key factors that simulations have yet to take into account is instrumental in understanding the prediction accuracy or bandwidth limitations of current models, and hence is beneficial to informing directions of device development beyond merely parameterization-based brute-force simulations that are patchy, time-consuming, memory-hungry, and susceptible to overestimations (or underestimations).

Unlike the uniform signal propagation in fully balanced and symmetric structures (e.g., our recently proposed coaxial phase shifter with NLC [15,16]), the mainstream NLC MW phase shifters are formulated in an inverted microstrip (IMS) topology, which exhibits unbalanced dielectrics, i.e., NLC, printed circuit board (PCB) substrate, and air. The core line and the grounding reference metal plane also produce another dimension of asymmetry in terms of geometry. Due to a convergence of these, the electric field peaking phenomenon enhances at the edges of the core conductor of closer proximity to the ground (as we studied in [8]). This redistribution effect of the electric field consequently leads to a surge in the insertion loss that may impede the commercial success of the ascendant NLC reconfigurable MW industry, which is a gap in the current knowledge. More specifically, the state-of-the-art technologies [20] in NLC-filled IMS phase shifter studies primarily decompose each loss element (e.g., metal loss, dielectric loss) based on the existing geometry aspect ratios and NLC thicknesses, but ignoring the packaging boundary effects. Motivated in this context, any research or engineering efforts that can mitigate the insertion loss (either incrementally or dramatically) in an unconventional approach (e.g., including the packaging boundary condition in the design and analysis, as proposed in this work) are highly valuable.

Inspired by our NLC-based ECPW demo (Figure 2) that is semi-encapsulated by a metal enclosure, this work copes with the NLC-filled IMS’s boundary condition and, more physically, examines the need for the metal enclosure (or not) for the NLC-based IMS phase shifter. Reinforced by the packaging solutions physically, the electromagnetic boundary conditions of no defined air box are electromagnetically equivalent to a PEC (perfect electric conductor) as an enclosure that confines the radiation. The performance degradation or upgrading due to the added metal enclosure (PEC boundary) has yet to be quantified for the mainstream NLC-filled IMS phase shifters, which motivates this work to bridge this knowledge gap. Furthermore, compared with our past NLC-ECPW [8] and NLC-coaxial [15] phase shifters at 60 GHz, the NLC-IMS topology in this work adds a new dimension of optimization insights concerning the effect of boundary conditions (packaging) on the device performance, the implications of which are beyond the existing optimization scope of diverse dielectric tuning states dependent on impedance matching, as we proposed in [15].

In the remainder of this paper, Section 2 starts with 50 Ω geometry derivation of key geometry dimensions of the NLC-IMS models under the air box radiating boundary as well as the PEC enclosed boundary, respectively. The computational resources required and the convergence statistics are recorded. Section 3 presents the key simulation results of the phase shifter performance in a comparative study of the air box radiating boundary condition against the PEC enclosed boundary, featuring a constitutive loss element decomposition analysis to identify and quantify the dissipative loss difference due to the radiating boundary against the metal enclosure. Section 4 conducts a quantitative comparison of the comprehensive performance metric (phase shift to insertion loss ratio, i.e., figure-of-merit) among diverse NLC-enabled geometry models to further the understanding of the impact of the packaging boundary conditions, followed by another discussion on the future optimization opportunities leveraging the insights of symmetry and asymmetry both nanoscopically and macroscopically.

2. Materials and Methods

2.1. NLC-IMS Line Model with an Air Box as a Radiating Boundary

Figure 4a depicts the cross-sectional geometry and boundary of our NLC-IMS phase shifter model with an air box defined as the radiating boundary. The three-dimensional (3D) model as depicted in Figure 4b has a length of 1 mm (along the z-axis), i.e., following the widely adopted per-unit-length framework to facilitate iterative design and optimization (theoretically or computationally) without incurring a heavy computational burden (complexity and cost). The modelling and simulation procedures are illustrated in Figure 4c. The finite-element method (FEM) finds a spectrum of applications in addressing computational electromagnetic problems and beyond [25,26,27]. To be more specific,

Table 1. Dimensions and materials of NLC-IMS phase shifter device models.

Geometry Items (Materials)	Width (x-Axis)	Thickness (y-Axis)	Length (z-Axis)
Grounding Conductor (Cu)	Wground = 5 Wcore	Tground = 0.05 mm	1 mm
Filled NLC Dielectric (GT3-24002)	5 Wcore	TLC = 0.1 mm	1 mm
Core Conductor (Cu)	Wcore	Tcore = 0.018 mm	1 mm
PCB Substrate (RT 5880)	WPCB = 5 Wcore	TPCB = 0.787 mm	1 mm

documents the geometry size of the NLC-IMS model in this work established with the FEM solver, i.e., the Ansys high-frequency structure simulator (HFSS) in version 2022 R1, based on the workstation with an 11th Generation Intel Core i5-1155G7 processor operating at 2.50 GHz and random access memory of 16 GB.

The same material grade of NLC (i.e., GT3-24002) employed in our previous iterations of NLC-based phase shifter designs was used in this work for benchmarking purposes. The NLC employed in this study exhibits the following variable dielectric constant (Dk) and dissipation factor (DF) at 60 GHz for diverse tuning states (taking the two extreme states as examples), i.e., Dk = 3.3, DF = 0.0032 in the saturated bias state and Dk = 2.5, DF = 0.0123 in the 0 V bias state [8].

The 50 Ω impedance matching of the NLC-IMS line was conducted by searching W_core (the width of the core line) based on a fixed NLC layer thickness of T_LC = 0.1 mm (for decent tuning speed) and an NLC tuning state of Dk = 3.3, DF = 0.0032 (i.e., in the saturated bias state). The 60 GHz solution statistics (convergence data) of the FEM solver for the NLC-IMS phase shifter model are depicted in Figure 5a. The maximum delta S (converged) and the correspondingly solved tetrahedrally meshed elements at convergence were parameterized with the width of the core line (W_core) in a step of 0.01 µm. The results were based on the IMS geometry impedance-matched under the NLC’s saturated bias state (Dk = 3.3, DF = 0.0032).

To disambiguate the curves, the maximum delta S was plotted in blue as per the vertical axis on the left, while the solved elements (denoted in red) aligned with the right axis, as shown. The characteristic impedances were quantified through three approaches, i.e., power–current, voltage–current, and power–voltage, represented by Z_PI, Z_VI, Z_PV, respectively, as presented in Figure 5b. As per the Z_PI approach, the derived W_core was 0.1616 mm at T_LC = 0.1 mm and L = 10 mm.

As evidenced in Figure 5b, the impedance deviations between the three approaches are not negligible for the air box radiating boundary case. By way of quantitative illustration in Figure 6 (i.e., Z_PI–Z_PV, Z_PI–Z_VI and Z_VI–Z_PV), these differences range from 0.4634 Ω to 2.8365 Ω, the levels of which are larger than those of the fully symmetric coaxial structure [15] (with a single dielectric fully enclosed by conductors and no radiating boundary required) at 60 GHz (using the same grade of NLC). The escalated deviation is due to the multi-dielectric geometry of the IMS, with both the tunable dielectric (NLC) and the non-tunable dielectrics (RT 5880 and air) arranged in a semi-open air-radiation boundary. This asymmetry arguably increases the chance of the results’ deviations among diverse calculation methodologies. Interestingly, the nearly symmetric distribution of the Z_PI and Z_PV curves with respect to the relatively stable Z_VI curve in Figure 5b results in nearly identical results of Z_PI–Z_VI and Z_VI–Z_PV, as evidenced in Figure 6.

2.2. Air Box Radiating Boundary vs. PEC Enclosed Boundary

As depicted in Figure 7, the computational model without defining the air box boundary arguably leads to a metal (PEC) packaging design, i.e., actioning towards a strip line-like symmetry geometrically and electromagnetically. This enhanced symmetry is due mainly to the added PEC on the top (mirroring the ground plane at the bottom). To implement the benchmark model, the same line dimensions of the 50 Ω NLC-IMS (with the air box radiating boundary) are maintained (i.e., T_LC = 0.1 mm, W_core = 0.1616 mm, L = 10 mm), whereas the air box is removed.

Based on the two models established (i.e., one with an air box radiating boundary in Figure 4, and the other with PEC enclosed boundary in Figure 7), the solution statistics for the two extreme biasing states of NLC (i.e., 0 V bias with Dk = 2.5 and saturated bias with Dk = 3.3) are detailed in Figure 8. Accordingly, the memory usage and convergence time of the diverse boundary scenarios and diverse tuning states are recorded in

Table 2. Computational memory and time for NLC-IMS phase shifter models with an air box radiating boundary vs. no air box (i.e., PEC enclosed boundary) at 60 GHz (8 processes and 8 cores in total).

Boundary Designs and Tuning States	Maximum Memory/Process	Average Memory/Process	Elapsed Time
Air box radiating boundary, NLC Dk = 3.3	260 MB	259 MB	00:04:54
Air box radiating boundary, NLC Dk = 2.5	271 MB	271 MB	00:04:49
PEC enclosed boundary, NLC Dk = 3.3	243 MB	243 MB	00:06:04
PEC enclosed boundary, NLC Dk = 2.5	187 MB	186 MB	00:06:05

.

Figure 9 details the number of solved elements (Figure 9a) as well as the minimum edge length in each meshed component (Figure 9b). From Figure 9a, the number of solved elements in metals, i.e., the meshed elements on the surfaces of the core line and the ground, is significantly lower than that of those meshed in the dielectric volumes, i.e., the tunable NLC, the non-tunable PCB substrate, and the air box (for the radiating boundary condition). Notably, the highest number of meshed elements (4010) occurs in the saturated bias state of the NLC (Dk = 3.3) under the PEC enclosed boundary, which is 1.36 times higher than in the 0 V bias state (NLC Dk = 2.5) with the same PEC enclosed boundary. Contrarily, the dielectric tuning states of the NLC have less impact on the air box radiating boundary, as evidenced by the 3204 elements (NLC Dk = 3.3 state) versus the 3187 elements (NLC Dk = 2.5 state). Similar meshing behaviors happen for the PCB substrate (non-tunable Dk), except for the difference regarding the air box radiating boundary, wherein the tuning states of the NLC have a more pronounced deviation.

To rule out the disturbance due to impedance mismatch and hence to amplify the boundary condition (packaging) implications in this study, the key results of the scattering parameters are post-processed without renormalization first, followed by a 50 Ω renormalized result benchmark for a full picture of the overall behavior approximating the connector-encompassed real-world applications.

3. Full-wave Numerical Results Benchmark and Verification

3.1. Simulated Phase Shifting Performance

From Figure 10a, it can be seen the results on characteristic impedance agree well with the theory that the air box dielectric-enclosing scenario exhibits higher impedances than the PEC enclosing boundary case, and this applies to both the saturated NLC bias state and the 0 V bias state. As evidenced in the saturated bias state of NLC (Dk = 3.3), the characteristic impedance of the air box radiating boundary design (black line) is 49.87 Ω, which is 1.68 Ω higher than that of the PEC enclosing boundary design (blue line). For the 0 V bias state of NLC (Dk = 2.5), the characteristic impedance of the air box radiating boundary design (red line) is 55.97 Ω, which is 1.75 Ω higher than that of the PEC enclosing boundary design (green line). Interestingly, the deviation for the 0 V bias state (NLC Dk = 2.5) is slightly higher than that for the saturated bias state (NLC Dk = 3.3). This is due mainly to the dielectric constant ratio of the tunable NLC dielectric to the non-tunable dielectrics (PCB and air box). For the 0 V bias state (NLC Dk = 2.5), this ratio is lower (than that of the NLC Dk = 3.3 case), hence indicating that a more significant role is played by the non-tunable parts (PCB substrate and air box) in the multi-dielectric asymmetric transmission line system, thus leading to a higher deviation with an air box radiating boundary versus without an air box (i.e., PEC enclosed boundary).

The effective permittivity of interest (which closely links to the achievable tuning range of the differential phase shift) is quantified in Figure 11 and compared among the two packing solutions (boundary conditions enforced). Interestingly, with the diverse boundary conditions compared at 60 GHz, the deviation in effective permittivity is 0.01414 in the saturated bias state of NLC (wherein the air box radiating boundary design obtains higher effective permittivity) and 0.01048 in the 0 V bias state of NLC (wherein the PEC enclosed boundary design obtains higher effective permittivity).

The differential phase shift presented in Figure 12b is derived based on the cumulative phase (Figure 12a) deviation between the filled NLC in diverse tuning states, i.e., 0 V bias against the saturated bias. The phase tuning capability of the air box radiating boundary design is 8.26°/cm higher than that of the PEC enclosed boundary design at 60 GHz. However, the maximum insertion loss results (from Figure 13a) indicate that at 60 GHz, the PEC enclosed design exhibits 0.47 dB lower loss than that of the air box radiating boundary design. Using the PEC enclosed boundary (compared to the presence of the air box radiating boundary), a boost in the figure-of-merit (FoM) by 29.26°/dB at 60 GHz is evidenced in Figure 13b.

3.2. Loss Element Decomposed Analysis and Benchmark

Dissipative loss analysis of each constitutive material component of the NLC-IMS phase shifter is conducted by integrating the volumetric loss density over the dielectric volume (for the dielectric loss) and integrating the surface loss density over the conductor surface (for the conductor loss), focusing on two extreme tuning states (0 V bias of NLC versus saturated bias of NLC) and two boundary conditions (PEC enclosed boundary versus air box radiating boundary). The non-renormalized results are presented in Figure 14, while the 50 Ω-renormalized results are shown in Figure 15. For the PEC enclosed boundary design, no energy can escape the fully enclosed model, resulting in a mitigated radiation loss of 8.06% (0 V bias in Figure 14a) and 7.72% (saturated bias in Figure 14b) for the non-renormalized treatment and a decline by 8.03% (0 V bias in Figure 15a) and 7.72% (saturated bias in Figure 15b) for the 50 Ω-renormalized treatment.

Contrary to the tangible improvement of the radiation-resistant (loss-mitigated) effect observed above, other loss components exhibit minor differences between the two packaging boundaries. With the introduction of the PEC enclosed boundary (compared with the air box radiating one), the NLC dielectric loss declines by 0.18% (0 V bias in Figure 14a) and 0.03% (saturated bias in Figure 14b) for the non-renormalized treatment, and displays a decline by 0.18% (0 V bias in Figure 15a) and 0.03% (saturated bias in Figure 15b) for the 50 Ω renormalized one, i.e., an infinitesimally small difference between the non-renormalized and renormalized results for the NLC dielectric loss characterization. Similar conclusions are observed in the conductor loss quantifications.

To understand the statistical significance, Figure 16 and Figure 17 provide further verifications by quantifying the deviations in the forward transmission coefficient (phase and amplitude, respectively) between renormalization and non-renormalization with different boundary (packaging) designs. From 54 GHz to 66 GHz, the differential phase shift displays up to 0.23° deviation (Figure 16b), the insertion loss in Figure 17a displays up to 0.05 dB deviation, and the FoM (Figure 17b) exhibits a maximum deviation of 4.29°/dB.

4. Discussions on Advantages and Limitations

4.1. FoM Comparison Numerically with Other Planar and Non-Planar Phase Shifters with NLC

To expedite the performance comparison process, the maximum phase shifting range to the maximum insertion loss level, the ratio of which represents the figure-of-merit (FoM) of an NLC-enabled phase shifter device, is quantified and depicted in Figure 18 at a few strategically targeted frequencies (e.g., 60 GHz, 79 GHz, and 300 GHz applications) for various geometry designs, including coaxial lines at 60 GHz [15] and 300 GHz [16], ECPW at 60 GHz [8], symmetric CPW at 79 GHz [14], and meandered ECPW at 79 GHz [28].

From Figure 18, the NLC-IMS model with a PEC enclosed boundary (i.e., metal-enclosed packaging) in this work has the chance of outperforming our previously proposed NLC-ECPW model [8] in terms of the FoM (a rise by 6.55°/dB at 60 GHz), as well as the recently raised coaxial model [15] (an increase in FoM by 13.18°/dB at 60 GHz). The same geometry of the NLC-IMS model but with the air radiating boundary (i.e., semi-open without metal-enclosure packaging) degrades the FoM by 29.26°/dB and becomes 22.71°/dB less competitive than the ECPW model (metal-enclosed design). On the other hand, the enhancement of the FoM is at the cost of the metal addition, which increases the weight of the device (a limitation for certain applications requesting lightweight systems as the priority).

Another limitation that merits attention (when conducting performance comparison with other states of the arts) is the per-unit-length framework employed in this work for obtaining the differential phase shift, insertion loss, and FoM results for the NLC-IMS models (for both the air box radiating boundary and the PEC enclosed boundary). While the capability of the differential phase shift can be accurately represented by the per-unit-length characterization approach (as the phase shift is linearly proportional to the line length), the insertion loss (and hence the FoM) may suffer from unfair comparison (and inconsistent conclusion) due to the non-linearities in the conductor loss, dielectric loss, and return loss when integrated along the line length, as we first explored in [8] for NLC-ECPW phase shifters and [20] for NLC-IMS phase shifters (without referring to PEC boundaries).

In summary, the implications of the boundary conditions of burgeoning NLC-IMS phase shifters are studied in this work by ideating two designs of diverse boundaries for comparison at the V band. The insertion loss mitigation (and thus the rise in FoM) is a testament to the radiation-free and noise-suppressed advantages comparable to strip lines or fully enclosed strip lines (rectangular coaxial lines). More importantly, the manufacturing hurdles underpinning these non-planar structures can be overcome with ease by leveraging the well-established planar treatments for the circuit board part and more specifically the NLC layer (i.e., planar alignment), with the enclosure attached to the ground plane for unified potentials and corrosion-free packaging. This offers a graceful enabling solution to the fabrication challenges of the fully enclosed structures as encountered by NLC, making a low-power-consuming (e.g., 0–10 V) electrically driven approach possible (without resorting to the power-consuming magnet-driven solution [29,30] with a surge in the required bias voltage, e.g., 177 V reported in [31]). The cost and size of the overall device and system (when integrated into a large-scale array) can hence be significantly reduced. Limitations of the current study do exist, which inspires the following optimization discussion in the symmetry (and asymmetry) parlance.

4.2. Rethinking the Optimization Opportunity via Symmetry and Asymmetry

From the lens of symmetry, the PEC-based fully enclosed boundary as depicted in Figure 19 enhances the symmetry, i.e., from the traditional air box radiation boundary (with 1-line mirror symmetry) to the quasi-two-line symmetry (due to the additional conductors arranged with rotational symmetry). This enhanced symmetry arguably contributes to the spatial homogenization of the 60 GHz electric field (peaking mitigation), which resultantly leads to insertion loss suppression and a boost in the overall performance (i.e., FoM of interest). The FoM maximization may be obtained by translating the current quasi-two-line symmetry into a true two-line symmetry, the formation of which is dependent on the competition of tunable dielectrics and non-tunable dielectrics, i.e., in terms of Dk_NLC versus Dk_non-tunable and T_NLC versus T_non-tunable (materials arrangement), and coupled with the aspect ratios of W_core to T_NLC as well as W_core to T_non-tunable (geometry arrangement), as sketched in Figure 19. The enhanced symmetry de facto enhances the degree of stability both mechanically and electromagnetically (noise resistant).

Notably, asymmetry (due to multi-dielectrics) impacts a couple of deviation effects. First, this is exemplified in the characteristic impedance difference between the air box radiating boundary design and the PEC enclosed boundary design, wherein the deviation that occurs at the 0 V bias state (NLC Dk = 2.5) is higher than that of the saturated bias state (NLC Dk = 3.3). Second, there exist decent deviations in the impedance results provided by different characterization methods, as evidenced in Figure 5b and Figure 6.

5. Conclusions and Future Research Outlook

In conclusion, the packaging and symmetry implications represent noteworthy advances of significance to NLC-based mmW specialists for building best-in-class phase shifters by unlocking the full potential of NLC-IMS boundary conditions, towards informing a broader community of microwave engineers and designers with qualitative and quantitative understanding of the subject. The FoM enhancement and radiation resistance resulting from the newly introduced PEC enclosed packaging boundary (featuring enhanced symmetry) is envisaged to shape the next-generation paradigm of high-spatial-resolution beam-steering phased array antennas for 5G/6G communications, meteorological radars, remote sensing, and other phase-shifting-critical applications requiring low-insertion-loss performance. The desirable symmetry as discussed can be maximized in future work by leveraging the 60 GHz electric field distributing competition between the tunable dielectric (i.e., NLC) and the non-tunable dielectric (i.e., PCB substrate), more specifically by fine tuning their dielectric constants as well as the dielectric thicknesses. The numerically validated results and insights also target the backbone of formulating an expanding portfolio of other tunable components realized in the NLC-filled IMS structure (e.g., a variable band-stop filter development underway filled with NLC realized in IMS topology with a quarter-wave stub) for interference elimination, serving 60 GHz high-data-rate communication and high-precision imaging applications.

Besides the relatively macroscopic symmetry (and asymmetry) implications as discussed in this work concerning the 60 GHz phase shifting device geometry, another area of interest in the future is nanoscopically incorporating a variety of symmetries into the LC’s chemical structure [32,33,34] and leveraging the asymmetry in the surface anchoring (alignment) strength [35,36,37] for faster tuning rates [38]. Characterizing the asymmetric flow [39,40,41] of NLC in the encapsulated device’s cavity or channel can arguably be another challenging yet fundamental topic of future research interest.

Another knowledge advancement opportunity in the future research endeavor is seeking a more comprehensive FoM metric in response to the discussed vulnerabilities of the cross-section per-unit-length-based computation framework. A redefined line length selection criterion based on a maximally achievable phase shifting range of up to $\mathsf{\pi }$ can be unified for a fairer benchmark study among diverse geometries and diverse packaging boundary condition designs of NLC-based phase shifters.