A Tunable K-Band Reflector

This letter presents a concept for a surface exhibiting tunable reflectivity that operates within the K-band using varactor diodes. Thereby, the impedance of a two-layer metasurface is controlled through lumped components at its back side and not at the front, where discrete elements would scatter the incident wave. A reflector's design, verification, and modeling through an equivalent circuit as well as full-wave simulations are presented in detail. Finally, the tunable reflection parameters of the surface as well as its reflection beam pattern under different biasing conditions are shown.


I. INTRODUCTION
U PCOMING technology trends in wireless communication require novel concepts of over-the-air (OTA) wave scattering and beam steering [1]. This is important to provide sufficient connectivity in blind spot and shaded regions, while saving valuable radiation power. Moreover, future solutions in, e.g., radar or antenna characterization are based on nonmechanical beam manipulation. Current investigation on active metamaterial reflectors potentially provides solutions to these problems and enables the needed innovation [2], [3], [4].
Tunable reflectors usually consist of two metal layers, one continuous at the back plane and one periodically structured layer facing the incident wave. The structured metal is then manipulated through active components to absorb or reflect with a certain phase shift. Lumped elements are either located directly at the front as in [5], [6], [7], [8], [9], and [10] or behind the back side, connected to the periodic layer through vias [11], [12]. Both of these design principles exhibit disadvantages in highfrequency applications. Discrete elements at the front scatter the incident wave unintendedly, becoming increasingly problematic at dense grids where the lumped component size becomes comparable to the grid periodicity. Back side via connections through the reflector show high losses at millimeter-wave frequencies, which potentially lead to a loss of the component's effects on the reflector.
In contrast to the aforementioned design conventions, this work consists of two noncontinuous layers, where the active  elements influence primarily the back grid. A controllable resonance between the surface and the lumped component is then used to lower reflection magnitude at certain frequencies or switch between phase-shift states. The front structure can be used for additional phase tapering or a broadening of the resonance.

II. SIMPLE RESONATOR
The proposed design in Fig. 1 consists of 1-D periodic grids on a t = 0.25 mm thick RO4350 substrate with a lateral permittivity of ε r = 3.4 [13]. Under TM incident waves (electric field normal to metal strips), the grids are represented as shunt capacitors in the equivalent circuit (EQC) with the dielectric substrate acting as transmission line. Neighboring metal strips at the top grid are connected with varactor diodes MAVR-000120-1411 that are modeled as series RLC circuits. By applying voltage U b to the strips, the varactor capacitance C v changes from 1.1 to 0.1 pF, which influences the resonance of the EQC, and consequently, the scattering properties of the reflector. The size of each unit cell measures D = 5 mm, resulting in ten independent columns with a total of 100 varactors and an active area of 50 × 50 mm 2 .
Although the EQC elements of the passive layer structure (C t and C b ) can be modeled in good approximation [14], [15], it is difficult to determine the behavior of the entire system. This is first, due to a lack of information about the varactor's inductance L v , which obviously affects the resonance of the reflector. Second, the flip-chip die and solder mounting is not considered in the aforementioned circuit. This causes unknown parasitics such that R = R v + R par. and L = L v + L par. .
To extract these unknown effects, focused-beam measurements [16] were performed on the reflector using thin-film capacitors instead of varactor diodes. Thereby, components with similar size and capacitance were chosen for the replacement. The Kyocera AVX capacitors from the 0201 Accu-P series with 0.1 and 0.4 pF capacitance exhibit self-resonances at 19.4 and 12.5 GHz, corresponding to series inductances of 0.673 and 0.405 nH, respectively. However, considering the device tolerances, a comparison of the measured reflection coefficients with the resonance of the EQC results in 0.41 nH for both configurations.
Assuming that the inductance of the varactor diode is similar to that of the thin-film capacitor, a top grid gap width of g t = 0.2 mm results in a tuning range from 19.6 to 30.8 GHz. The effects of the bottom grid with a width of w b = 0.5 mm are negligible in the presented design. These become present with increasing layer interactions at grid widths of around 2 mm.

III. MODELING AND VERIFICATION
The actual tuning range of the reflector was again evaluated through focused-beam measurements. Thereby, the reflector was mounted between two lenses with a diameter of 100 mm and a focal length of 60 mm, as shown in Fig. 2. These were illuminated by 20 dBi horn antennas, which were further connected to a network analyzer. Arising parallel wave fronts in the center of the build-up allowed accurate OTA S-parameter characterization of the metasurface. A general phase drift over the whole frequency range is probably caused by a slight off-center position of the sample between the lenses. During the measurements, the reflector was stuck to a supporting FR4 frame to improve the planarity and mechanical stability.
In Fig. 3, the measured reflection and transmission coefficients at different varactor bias voltages are compared to the EQC and HFSS simulations. The reflector's resonance frequency ranges from 21 to 28.6 GHz, which corresponds to circuit parameters R = 3.75 Ω, L = 0.38 nH, and C v from 1.0 to 0.149 pF. One sees that the varactor inductance is slightly lower, but close to the inductance of the thin-film capacitors. Additionally, the conformity between the EQC response and the measurements strongly depends on L v . These are two indications that the EQC characteristics represent the actual system well. The calculated absorption in Fig. 3(c) peaks at the reflection minima, showing that a considerable amount of energy is absorbed at the varactor and the solder joint. Besides the comparison to rather simplified EQCs, the reflector behavior was verified through full wave simulations in Ansys HFSS. Thereby, the varactor was modeled as series RLC boundary [red area in Fig. 4(a)] between two copper pads with a GaAs cuboid on top. A unit cell of the reflector was simulated applying Master/Slave boundaries and Floquet ports. Boundary parameters matching the measurements with similar capacitances as in the varactor data sheet are R sim = 4.1 Ω, L sim = 0.05 nH, and C sim from 1.25 to 0.105 pF. The mismatches at higher frequencies in Fig. 3(a) and (b) might arise from the simplified simulation model or capacitance variations between the parts affecting the reflected wave fronts during the measurements. It needs to be mentioned that the lumped elements in the proposed design are small compared to the incident radiation wavelength, leading to only a minor difference between S 11 and S 22 . However, this may change depending on the grid periodicity and the size of the applied active component.
Contrary to the EQC, the inductivity of the matching RLC boundary is far below the expected value. This is first because of the RLC boundary's intrinsic inductance [17], and second, due to additional inductivities from the pads. The difference of the tunable capacitance between the EQC and the simulation might arise from an additional parallel capacitance between the pads. Obviously, the aforementioned effects were not considered in the RLC boundary. A corresponding modified circuit is shown in Fig. 4(b), where the additional inductance and capacitance is represented by L s and C p , respectively.
With reasonable EQC parameters at the full-wave simulations, it is possible to further investigate the reflector behavior, where especially the effects of oblique incident waves on the resonance frequency need to be verified. Fig. 5 depicts the obtained resonances for C sim = 0.305 pF and C sim = 0.105 pF under different incident angles θ. The deviation of the reflection minimum remains weak as the varactor contributes  stronger to the resonance than the top grid capacitance. Nevertheless, according to EQC approaches as, e.g., [18], C t increases with θ, and thereby, reduces the reflection minimum frequency.
The realization of a 2-D periodic reflector without continuous back plane implies difficulties regarding the control of the varactor diodes. Nevertheless, it is possible to vapor deposit ultrathin metal layers on plastics, which are on the one hand transparent to RF radiation and provide sufficient conductivity to control varactor diodes on the other hand. If such layers are properly structured, they can be used to bias 2-D active reflectors. Such devices enable more application freedom and are, therefore, worth consideration via simulations. In Fig. 6, a corresponding unit cell and resulting frequency responses for three different varactor capacitances are shown. Here, the bottom metal layer was omitted completely. As expected, the frequency responses of the 2-D arrays are similar to the 1-D configurations. Only the gaps between the patches overall reduce the grid capacitance resulting in slightly higher reflection minimum frequencies.

IV. INFLUENCE OF BIAS VOLTAGE TO REFLECTION
To present the reflector's capabilities in more detail, its reflection coefficient is plotted over bias voltage in Fig. 7(a). For 24 GHz, the magnitude can be tuned within a nominal range of 9 dB and reaches the minimum of −10 dB at 6 V. The remaining radiation power is transmitted and absorbed as shown in Fig. 3(b) and (c), respectively. If the device is used as a tunable absorber, the excess transmission can be absorbed behind the back. Besides tuning the reflection magnitude, the active surface can also be used to switch reflection phase shifts. Biasing the reflector with 1 V results in a relatively high reflection magnitude of −2.2 dB with a phase shift of ψ + = 198 • . Applying 10 V, gives a similar magnitude but ψ − = 148 • . In Fig. 7(b), reflection patterns of the tunable surface at different applied biasing states are shown. The colored curves depict the frequency dependence of the reflection pattern without bias, whereas the solid black one represents the low-reflectivity state for 24 GHz at 6 V. The remaining curves correspond to the patterns for the bias states shown in Fig. 7(c)-(e), where the effect of a scattering phase difference between certain reflector parts is investigated. Depending on the separation of the reflection centers d, the resulting beam direction can then be switched according to At small reflection areas, the reflected power maximum decreases while the beam width increases. Obviously, it is not possible to perform universal beam steering with the proposed reflector, as it cannot provide the needed 360 • phase variation. However, the scattering experiments give a valuable proof of concept, which is needed for further investigation.

V. CONCLUSION
This letter presents a concept for a tunable reflector that is capable of manipulating radiation within the K-band. A prototype was verified through an EQC model, full-wave simulations, and measurements, where this first design exhibited a good reflection tuning range and shifted the phase of reflected waves according to theory. In Table I, its characteristics are compared to other active reflectors operating at high frequencies. All of these references utilize pin diodes to tune the reflectivity over a broad bandwidth with partly high switching dynamic. However, the presented design's simplicity in combination with low parasitic varactor diodes enables control at even higher frequencies. As the concept potential was not fully exploit in the presented prototype, better performance and further applications like, e.g., beam switching are feasible.