Ridge Gap Waveguide Based Liquid Crystal Phase Shifter

In this paper, the gap waveguide technology is examined for packaging liquid crystal (LC) in tunable microwave devices. For this purpose, a line based passive phase shifter is designed and implemented in a ridge gap waveguide (RGW) topology and filled with LC serving as functional material. The inherent direct current (DC) decoupling property of gap waveguides is used to utilize the waveguide surroundings as biasing electrodes for tuning the LC. The bed of nails structure of the RGW exhibits an E-field suppression of 76 dB in simulation, forming a completely shielded device. The phase shifter shows a maximum figure of merit (FoM) of 70 °/dB from 20 GHz to 30 GHz with a differential phase shift of 387° at 25 GHz. The insertion loss ranges from 3.5 dB to 5.5 dB depending on the applied biasing voltage of 0 V to 60 V.


I. INTRODUCTION
Nowadays, the development in communication is already driven by mobility/portability and data rate, which will be emphasized even more by future applications such as IoT, industrial digitization, 5G or autonomous driving. For concepts like cognitive radio or high data rate wireless communication, flexible filtering in the frequency or spatial domain is required. This poses additional challenges for the radio frequency (RF) frontend design. Here, varactors and phase shifters are a key component to realize tunable filters and beamsteering antennas.
This work focuses on a line-based passive phase shifter, utilizing a functional material. These kind of phase shifters are appealing due to their ease of design: They consist only The associate editor coordinating the review of this manuscript and approving it for publication was Weiren Zhu . of a transmission line section combined with the functional material. They do not require additional power like active or ferrite based phase shifters [1], [2], nor complicated varactor designs like loaded line or reflection type phase shifters [3]. Other advantages are their compactness and robustness compared to electromechanical approaches [4]. Further, a continuous tuning of the phase shift is possible.
The choice for the functional material fell on LC since it provides low losses especially for frequencies above 20 GHz up to the THz range [5], which makes it a promising functional material for future communication systems operating in the millimeter wave range and above. The working principle of LC is summarized in Fig. 1c. LC, being a mesophase material at room temperature, exhibits properties of a liquid and a crystal at the same time, including birefringence. The molecules of the used nematic mixture can be considered rod shaped, whereas they exhibit no long-range spatial order but a VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ certain directional order, which is macroscopically described by the director vector n, see Fig. 1c. Associated with the director, the birefringent property can be described by a Fresnel ellipsoid with a permittivity ε parallel to the director and a permittivity ε ⊥ perpendicular to it. A transversal electromagnetic wave interacting with this kind of material will experience any permittivity on the Fresnel ellipsoid, i.e. between ε ⊥ and ε , depending on the tilt angle α between the electric field vector E and the director n. The LC molecules' orientation can be controlled in three different ways: Mechanically, utilizing surface anchoring forces, magnetically and electrically [6], where the LC will orient its molecules parallel to the field lines in order to minimize its free energy. In practical applications, usually electric tuning is used, often in combination with a mechanical pre-orientation by surface anchoring. Magnetic tuning is mostly used for material characterization and in test setups only due to its bulkiness and power consumption. To compare the performance of different phase shifters, a figure of merit (FoM) was previously introduced [7], which relates the maximum differential phase shift achieved to the maximum insertion loss over the tuning states, described by the tuning voltage V bias .
The best performance so far (FoM = 200 • /dB at f op = 30 GHz, [8]) is achieved with a magnetically biased hollow waveguide topology. However, for the electric tuning of liquid crystals, a biasing circuitry, i.e. electrodes are necessary to generate the quasi-static E-fields. In the case of rectangular waveguides, such electrodes need to be placed inside the waveguide, so that the DC fields can interact with the LC, see in Fig. 1. The addition of these electrodes leads to mode coupling of the TE 10 mode into the biasing electrodes, where different kind of Stripline modes can be excited. Hence, the insertion loss is increased and the performance decreases (from FoM = 200 • /dB to FoM = 150 • /dB, [8]). To mitigate this effect, certain care has to be taken in the electrode design. For example, stepped impedance filters can be integrated into the electrodes to avoid mode coupling [9]. However, a complete suppression of these unwanted modes, especially at higher frequencies, is difficult in practice, mainly due to the small feature size close to or even beyond manufacturing tolerances.
In order to avoid these difficulties in electrode design and integration, the basic idea of this work is to utilize the waveguide surroundings itself as electrodes as depicted in Fig. 1b. For this, the waveguide is cut in half in its H-plane. In between this cut, a component has to be introduced, which serves as a short for the RF wave and as a block for the applied DC voltage. One type of waveguide, which exhibits exactly these desired properties, called gap waveguide, has been studied intensively in the last few years [10]- [14]. It consists of two parallel metal plates, where one of the plates is patterned to form a metamaterial surface, called bed of nails in this case, which prevents wave propagation in its stop band, see Fig. 2. With the help of the metamaterial pattern, an electromagnetic wave can be guided similar to a hollow waveguide but without the necessity of an electrical contact between the waveguide's side walls.
The aim of this work is to validate the applicability of the gap waveguide for a LC based phase shifter to ease the electrode integration and to improve isolation. For this, a LC filled RGW was designed and fabricated, which will be described in more detail in the next section. To ease the coupling design and to prevent tolerance issues during fabrication, this demonstrator was chosen to operate around 26 GHz

II. DESIGN AND IMPLEMENTATION
The bed of nails structure used in this work consists of periodic electric pins surrounding the desired waveguide. This structure is patterned on one of the metallic plates, acting as the bottom and side walls of the waveguide. The other plate is unpatterned, forming the top wall of the waveguide. A gap is left between the top of the nails and the top plate, so that they are DC-decoupled. Thus, the lower plate and the upper plate can act as electrodes for aligning the LC vertically. Horizontal alignment is achieved in this design by utilizing surface anchoring forces at the top and bottom plate.
The bed of nails structure realizes a high impedance surface, which limits the electromagnetic wave propagation for frequencies between 14 GHz and 37 GHz, forming an electronic band gap. For this, the designed bed of nails has to comply the following conditions [10]: • Nail height d, corresponds to the quarter-wavelength at 22 GHz, roughly at the center of the stop-band region.  • Space between upper and lower plate h + d, corresponds to the half-wavelength at 40 GHz, determining the upper end of the stop-band region.
To ensure sufficient wave guidance and shielding, three rows of nails are placed around the waveguide in a first design. However, later simulations (see Fig. 8) showed that two rows of nails are still sufficient for wave guidance and shielding, which was adapted to the final implementation in favor of fabrication simplicity and compactness.
Since the alignment speed of LC depends on field-strength and layer thickness, a ridge was introduced in the gap waveguide, reducing the distance between the lower and the upper plate to 0.2 mm for the LC section. The so designed RGW allows for the propagation of a quasi-TEM mode.
A LC container made of Rexolite is used to prevent LCleakage. This container extends from the input to the output port as shown in Fig. 2. The length of the phase shifter part, i.e. the LC-cavity was chosen to enable a full 360 • differential phase shift with the LC mixture GT3 23001 from Merck KGaA (see Table 1). This LC is filled through two holes on the upper plate, which are close to the end of the LC cavity.
Female SMA thread-in connectors are used in the top plate to connect the phase shifter to the measurement equipment. To match the impedance of the LC region (14 ) to the 50 connectors, a linear taper reduces the ridge height. The ridge extends by λ/4 after the coax connector, where it is shorted by the first pin of the bed of nails. Moreover, the inductive nature of the connector-ridge interface is compensated by introducing a disk capacitor in Rogers RT/duroid 6010 substrate between the connector pin and the ridge (see Fig. 2). Additionally, this capacitor serves as DC block between bottom plate and SMA connector pin.
The upper plate and the lower plate are fabricated separately by milling using Brass. The Rexolite container is pressed between top and bottom plate and additionally sealed using glue. PVC alignment rings are placed around the waveguide to ensure alignment between both plates, which are then held together by Nylon screws. All separate parts except the top plate are shown in Fig. 3a. The assembled phase shifter including the top plate is depicted in Fig. 3b.

III. SIMULATIONS AND MEASUREMENTS
The phase shifter is designed and simulated using CST Studio Suite and the fabricated prototype is measured using a vector network analyzer calibrated for a frequency range of 20 GHz to 30 GHz.
For modelling the LC material inside CST Studio Suite, use is made of the tensor formula material model, which is fed by the permittivity and loss tangent tensor of the used GT3 23001 material (see Table 1). For a z-oriented LC director, the permittivity tensor is described bȳ VOLUME 8, 2020 Arbitrary orientation of the LC director is accounted by a coordinate transformation of the microwave field components into this LC director coordinate system and back. Since wave propagation along the y-direction and LC director alignment in the xz-plane is assumed (see Fig. 2), this coordinate transformation can be carried out by rotation around the y-axis where α is the tilt angle of the LC director with respect to the z-axis (see Fig. 1c). Hence, the final permittivity tensor formulation for the CST Studio Suite model is given by equation (6), as shown at the bottom of this page. The loss tangent tensor formulation is derived analogously.
Since there is no possibility in CST Studio Suite to simulate the LC directors orientation in dependence of the applied bias field, the model of the Freedericks cell was used to relate the bias voltage V bias to the tilt angle α by [15] with the threshold voltage where K 11 denotes the elastic splay constant of the LC mixture (see Table 1). During measurement, the upper plate was grounded through external bias tees (see Fig. 4), which provide also additional protection in case the inherent DC block of the phase shifter fails. The lower plate was connected to a 60 V DC power supply for biasing the LC (see Fig. 3 and Fig. 4, respectively). Fig. 5 shows the scattering parameters. It can be seen that the matching is below −10 dB for a frequency range from 21 GHz to 27 GHz, which is slightly better than predicted by the simulation. This is caused by non-covered loss mechanisms, which also impact the insertion loss by roughly 2 dB. Depending on the tuning state, the measured insertion loss ranges from around 3.5 dB to 5.5 dB. The contribution of the coaxial transitions and the linear taper to the overall insertion loss is roughly 1 dB, which was estimated using a supplementary back to back assembly, revealing 0.5 dB and 1 dB of insertion loss in simulation and measurement, respectively. Despite of the 2 dB difference, the measured insertion loss conforms well to the simulated data up to 27 GHz, where the measurement shows a large drop. This stems from the used SMA thread-in connectors and accords to their specified frequency limit of 26.5 GHz. Here, higher order modes are excited despite the fundamental mode. The result is mode mismatch and signal loss as observed. With appropriate connectors for higher frequencies (e.g. K-connectors), the presented phase shifter should also be operable above 27 GHz as depicted by the simulation, since the simulation model does not include the connectors.
From the linear phase and flat group delay depicted in Fig. 6, it can be concluded that the phase shifter exhibits no dispersion as can be expected for a purely line based phase shifter. To assess the aimed shielding property of the RGW, the E-field in the cross section of the plane centered in the LC layer was evaluated in simulation. With a perpendicular LC alignment, the worst case was assumed. The results are depicted for a frequency of f = 25 GHz in Fig. 8 for the three and two row RGW. Here, one can observe a field damping of 79 dB at a distance of 3λ 0 from the waveguides center for the RGW with three bed of nails rows. The two row RGW exhibits only a slightly less damping of 76 dB, which justifies the choice for the implementation of the phase shifter. To compare these field damping results to common waveguides, the models of the Microstrip and Stripline depicted in Fig. 7 have been simulated and evaluated analogously (see Fig. 8). For both waveguides, different scenarios were simulated: A purely theoretic scenario with air as supporting superstrate material (i.e. the material above the actual waveguide's LC substrate), since the bed of nail section of the RGW is also mainly filled with air. For a more practical scenario, a common microwave substrate (Rogers RO4003C) has been assumed as superstrate. In both cases, the superstrate thickness has been altered between d = 3.4 mm for comparison to the RGW and d = 0.5 mm for a more practical use case and the corresponding line widths were adjusted to match the 14 line impedance of the RGW phase shifter. Here, it can be observed that the implemented two row RGW suppresses the E-field at 3λ 0 by additional 43 dB compared to a similar Microstrip setup and by additional 42 dB compared to a similar Stripline setup, both on the Rogers substrate. Assuming a thinner superstrate, the damping of the Microstrip setup increases but the suppression is still 18 dB larger for the two row RGW. Contrary, the damping of the Stripline setup decreases and exhibits a 58 dB less damping compared to the RGW. Only the theoretical scenarios of air filled waveguides show the least difference to the RGW with 8 dB fewer suppression, mainly caused by the lower dielectric constant of air, leading to a field displacement towards air.
This shielding property could also be confirmed during the measurements by moving a metallic perturber alongside the bed of nails structure, which had no influence on the measurement result.
A sweep over the bias voltage (see Fig. 9 and Fig. 10) revealed a saturation of the phase variation at around V bias = 60 V, indicating complete alignment of liquid crystal with the bias electric field. The maximum differential phase shift is shown in Fig. 9 by the red and blue curves for simulation and measurement, respectively. It takes roughly 7 s to achieve the parallel state. As already mentioned, there VOLUME 8, 2020  are only two electrodes and there is no active way of realigning the LC, hence the phase shifter needs more than 10 min to return to its unbiased state. Here, simulation and measurement show close agreement and the goal of at least 360 • of differential phase shift is accomplished.
The FoM for the phase shifter as defined by (1) is shown in Fig. 11. Due to the 2 dB higher insertion loss in the measurement, the measured FoM is roughly 30 • /dB lower than predicted by the simulation, exhibiting a maximum of 70 • /dB at 25 GHz.
In the presented measurement, the phase shifter has been biased by a DC electric field. Despite the current necessary to load the capacitance between the top and bottom plate of the phase shifter, no additional power is required to bias the LC. However, in a practical application, the LC will be biased with a low frequency alternating current (AC) field of around  f bias = 1 kHz to prevent degradation of the LC mixture due to electrochemical effects. In this case, the capacitance formed by the phase shifter and the corresponding equivalent series resistance will affect the biasing power consumption. To assess these losses, a low frequency simulation was performed and the capacitance of the built phase shifter was measured. For the biasing scenario, a maximum bias with V bias = 60 V (peak) was assumed. The simulated admittance is Y = 138 × 10 −21 S + j516 nS which translates to a capacitance of C = 82 pF and an equivalent series resistance of ESR = 518 n , leading to ohmic losses of P = 248 × 10 −18 W and hence being practically negligible. The measured capacitance was almost twice the simulated with C = 160 pF due to the extended top and bottom plates for the mechanical fixation. The equivalent series resistance was not measurable. Table 3 summarizes the simulated and measured results including the reactive power and current, 77838 VOLUME 8, 2020   which has to be provided to the phase shifter for full bias. For the built phase shifter a loading current of I bias = 60.3 µA and hence a reactive power of Q = 1.81 mvar needs to be provided for full phase shift.

IV. CONCLUSION
This paper examines the applicability of gap waveguides for LC-based electrically-tunable phase shifters. For this purpose, a proof of concept demonstrator was implemented operating around 26 GHz. Hereby, the gap waveguide's inherent property of DC decoupling is utilized to form the electrodes for LC biasing directly from the waveguide surroundings, eliminating the need for a specific electrode design. A ridge was introduced to further reduce the LC cavity height to 0.2 mm. The capacitive coaxial coupling of this ridge gap waveguide additionally acts as DC block for the RF feed, eliminating the need for external bias tees. To the author's best knowledge, this is the first time that such a device was implemented.
The measurement of this demonstrator revealed a differential phase shift of 387 • at 25 GHz, with an insertion loss ranging from 3.5 dB to 5.5 dB depending on the tuning state. Here, the maximum FoM achieved is 70 • /dB (see (1)), which is comparable to other similar phase shifter topologies like ridged hollow waveguide [16] or inverted Microstrip lines [17], but cannot compete with hollow waveguide [8] or sub wavelength fiber [18] topology. A more comprehensive comparison with other LC based phase shifters is given in Table 4. Fig. 12 further condenses the data from Table 4 by comparing the achieved FoM versus the electrical size of the phase shifters. Here, it is apparent that, although achieving a reasonable FoM, the realized RGW phase shifter is still quite bulky.
Apart from its size, the proof of concept here presents the promising potential of gap waveguides for packaging LC in tunable microwave components. The inherent DC decoupling eases the biasing network and electrode design. Attenuating the E-field by 76 dB, the bed of nail structure not only prevents the excitation of parallel plate modes, but also shields the RGW laterally without the need for via placing in the LC layer. Further, the top and bottom metal layer act as RF ground, shielding the device also in a multilayer setup and making integration easier.
The loading current and necessary reactive power to fully bias the presented phase shifter was assessed to I bias = 60.3 µA and Q = 1.81 mvar, respectively. This comparatively small current might sum up in the application VOLUME 8, 2020 specific biasing network (e.g. phased array) and might create additional power loss there.
The size could be addressed by implementing the gap waveguide in planar, mushroom-structure like PCB topologies [32] or by micromachining technologies [33], being especially interesting for millimeter wave frequencies. Further size reduction could be achieved, using resonant structures instead of a pure line based phase shifter, leaving scope for further investigations.  His research interests include reconfigurable smart radio frequency (RF) systems based on electronically tunable microwave components, such as phase shifters, adaptive matching networks, tunable filters, duplexer, and multiband antennas. Their integration into system components such as adaptively matched power amplifiers, reconfigurable RF frontends or fully integrated electronically beam-steering transceiver antenna arrays is in the focus of the work.