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Abstract
In this paper, we propose a concept of combining the methodology of phase coding modulation with frequency selective surface (FSS) inspired transmitarray (TA) to achieve the ability of dynamical beamforming and gain control in microwave regime. The TA element composed of five-layer stacked bandpass FSS units separated by small air gaps. Each FSS unit comprises a metallic octagon slot with a pair of varactor diodes loaded along the polarization direction. The elaborately designed feeding network makes it possible to modulate the transmission phase of each element. Different phase coding sequences are performed through changing the bias voltage configurations, then the radiation far field of the proposed TA can be tailored in real time. Dynamic beamforming and gain control under different encoding arrangements are exhibited to demonstrate the physical mechanism of electromagnetic (EM) manipulation with this method. The proposed strategy is verified by numerical simulations and experiment. This work adds new function for TA and can reshape its application prospect, such as reconfigurable beam emitter for multilink data transmission, long range point-to-point (PTP) wireless links and radio frequency energy harvesting.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Phase array antenna plays a vital role in wireless communication and evolved greatly over the past few decades. Conventional architecture composed of T/R modules are still used to implement the functions of high gain acquisition, EM focusing and dynamic beam steering. Accompanied by its relatively good EM manipulating performance, drawbacks of complex structure and high costs limit its application in wireless communications. The emergence of reflectarray and TA has attracted enormous researchers’ interests due to their intriguing characteristics, such as the low-profile, low costs and remarkable performance in radiation or scattering steering [1–8].
Compared with reflectarray, TA can eliminate the blockage of feed source, which makes it easier to achieve low profile and conformability with various planar platform. Spatial feeding is often adopted for the TA excitation. When EM wave impinges the surface of TA, the superimposed transmitted waves of all the elements can realize EM focus, flexible beam scanning and polarization control [9–13]. Generally, current reconfigurable TA can be realized by two means. One typical TA comprises three parts: the receiving structure, the phase shifter and the radiation structure. The incident wave is received and converted to guided wave signal by the receiving structure, then the signal phase is tuned by the active phase shifter. Finally the signal is transmitted to the radiation structure and radiated into the space. A large amount of designs were proposed to explore the ability of EM manipulation of this kind of TA architecture. 1-bit based beam scanning schemes were put forward by researchers but they suffered from low aperture efficiency caused by coarse phase resolution [14–17]. To improve phase resolution and performance of beam steering, TAs based on 2-bit and continuous phase modulation have been developed in Refs. [18–22].
The other kind of typical TAs use reconfigurable FSSs for phase modulation. Reconfigurable FSS generally consists of periodic metallic structure and the loaded active elements. Single layer FSS often cannot achieve $\textrm{36}{\textrm{0}^\mathrm{^\circ }}$ phase shift, so multi-layer cascaded structure incorporate with air gaps is usually adopted to meet the phase shift requirements. Five-layer bandpass structures with large air gaps were used in Refs. [10] and [23], and the insertion losses of them are about 3 dB. Four-layer cascaded structure realized $\textrm{18}{\textrm{0}^\mathrm{^\circ }}$ phase shift and lower thickness at X band in Ref. [14].
Most existing TA designs focus on beam scanning, almost few of them involves gain control or beamforming. To some extent, relatively simple function limits the applications of TA for various scenarios. With the development of wireless communication, adaptability and multifunctionality of systems are receiving more and more attentions from researchers. Antenna systems can change the responses in real time according to communication requirements are urgently needed [24,25]. For example, in unfavorable weather conditions, it is necessary to adjust the beam direction to offset the interference of beam misalignment caused by equipment shaking in MIMO scenario; multiple beams are required to improve data transmission rate, spectrum utilization and SNR; in the scenarios such as cellular systems and PTP transmission, it is necessary to control the gain to reduce the overlap under the premise of coverage. Besides, radio frequency energy harvesting also requires controlling the radiation patterns of the antenna system [26–28].
In this paper, a multifunctional reconfigurable TA based on cascaded FSSs is designed, incorporating the functions of gain control and dynamic beam forming. Through changing the coding sequence by varying the bias states, the number of the radiated beams from the TA can be switched among one, two and four, and the gain tunable range of the main beam can reach above 8 dBi. In addition, it can be inferred from the simulations that the designed TA has the ability of one-dimensional beam scanning from $\textrm{ - 3}{\textrm{0}^\mathrm{^\circ }}$ to $\textrm{3}{\textrm{0}^\mathrm{^\circ }}$. However, it is not the focus of this work, thus omitted here for brevity.
2. Design and analysis
In this geometry, octagon slot is adopted as the unit cell of FSS, as illustrated in Fig. 1(a). The metallic patterns are bonded on a 1.6 mm-thick F4BM substrate with a relative permittivity of 2.2 and a loss tangent of 0.001. The other parameters of the octagon slot are ${p = 33 mm}$, ${{w}_{o}}{ = 1 mm}$, ${{l}_{o}}{ = 32}{.2 mm}$. Two varactor diodes SMV-1405-040LF from Skyworks are loaded on the y-direction of the unit. The capacitance variation range of the diode is from 0.63 pF to 2.67 pF. Small air gap (${{t}_{a}}\textrm{ = 1}\textrm{.5 mm}$) and five layers cascaded structure is used in this design, as shown in Fig. 1(b). The octagon patches in the middle of the unit are connected together by the via holes with diameters of 1 mm and the feeding line. The other parts of the element are also connected as the ground. The equivalent circuit of one-layer FSS unit cell is illustrated in Fig. 1(c). ${{L}_{\textrm{FSS}}}$ and ${{C}_{\textrm{FSS}}}$ represent the inductance and gap capacitance of the metallic octagon slot. The equivalent circuit model of the varactor is shown by the parts circled by the red rectangle. ${{L}_{\textrm{sv}}}$, ${{C}_{\textrm{sv}}}$, ${{R}_{\textrm{sv}}}$ and ${{C}_{j}}$ correspond to the parasitic inductance, package capacitance, resistance and junction capacitance of the diode. The transmission phase changes greatly near the resonance frequency. Varying the junction capacitance of varactor ${{C}_{j}}$ yields a change of the whole circuit capacitance, hence the resonance frequency can be tuned according to the equation ${{f}_{r}}\mathrm{\ =\ 1/2\pi }\sqrt {{LC}} $.
Fig. 1. Schematic plot of the proposed TA unit cell. (a) The front side. (b) The 3D view. (c) The equivalent circuit model of the FSS.
Generally, single layer FSS can’t acquire sufficient phase shift and stacking several layers of FSS unit cells separated by air gaps can increase the phase shift range of TA element [10,29]. Increasing the number of layers can broaden the passband of element transmission coefficient [23]. The thickness of air gap has a great influence on the transmission characteristics of TA unit. Figure 2 depicts the simulated transmission coefficients of the five-layer FSS unit with different air gaps when the varactor capacitance is set at 2.67 pF and 0.63 pF. Table 1 shows the simulated phase shift and corresponding insertion loss of the TA unit with different air gaps within the variation range of the varactor capacitance. As can be seen from Fig. 2 and Table 1, enlarging the air gap leads to more phase shift. On the contrary, decreasing the air gap can reduce the phase shift range and increase the oscillation of the transmission amplitude. The insertion loss of the TA unit fluctuates with the increasing air gap due to changes in impedance matching caused by the variation of air gap. Besides, according to the simulations, large air gap may enhance the coupling between adjacent TA units, and result in operation frequency shift under unit cell and open boundary conditions.
Fig. 2. The transmission coefficients of five-layer FSS unit with different air gaps and varactor capacitance settings.
Table 1. Simulated phase shift and insertion loss of the TA unit with different air gaps
To investigate the transmission properties of the proposed TA, full wave simulations based on CST 2020 Microwave Studio are performed. Figure 3(a) and 3(b) show the transmission amplitude and phase of one layer unit cell. When the capacitance of varactor varies from 0.63 pF to 2.67 pF, the resonance frequency of the unit changes from 4.2 GHz to 4.87 GHz, and the transmission amplitude is higher than -3 dB within the frequency range of 4.61 to 4.78 GHz, while the phase shift is between $\textrm{6}{\textrm{0}^\mathrm{^\circ }}$ and $\textrm{7}{\textrm{6}^\mathrm{^\circ }}$. Noted that the transmission amplitude is over -2 dB and the corresponding phase shift is $\textrm{7}{\textrm{0}^\mathrm{^\circ }}$ at 4.65 GHz. In order to overcome the shortcomings of insufficient phase change of single-layer structure, multiple layers need to be cascaded. The transmission amplitude and phase of the five-layer cascaded structure are illustrated in Fig. 3(c) and 3(d). Obviously, the passband of five-layer unit cell becomes wider and flatter. The frequency band where the transmission amplitude of the unit cell is higher than -3 dB can be maintained at 0.6 GHz under different varactor capacitance settings, enabling the transmission amplitude can reach above -3 dB within the entire range of diode capacitance variation at the frequencies from 4.85 to 4.9 GHz. And in this frequency band, the insertion loss of the unit is comparable with Refs. [10] and [23], but the phase shift is smaller than them due to smaller air gap is introduced in this design after making a compromise among the operation frequency shift, the ripple (oscillation) in the transmission amplitude and the phase shift.
Fig. 3. The transmission characteristics of one-layer and five-layer FSS units. (a) and (b) are the transmission amplitude and phase of one-layer unit. (c) and (d) are the transmission amplitude and phase of five-layer unit.
3. Results and discussions
3.1 Dynamic beamforming
Traditional TAs seldom involve the function of beamforming, however, antennas enabling flexible beamforming often have many advantages such as improving data transmission rate and spectrum utilization in practical applications. In this design, the EM manipulation method of coding metasurface is drawn into TA to change its radiation characteristics.
According to the coding metasurface theory, different phase encodings for array elements can achieve various scattering or radiation properties. Herein, 1-bit phase coding is adopted for dynamical beamforming. According to the simulations, the transmission amplitude of the unit cell is about 0.8 when the diode capacitance is set at 0.66 pF and 1.33 pF, and the phase difference is $\textrm{18}{\textrm{0}^\mathrm{^\circ }}$. Therefore, we define the unit with working capacitance of 0.66 pF as “0” element, and the unit with working capacitance of 1.33 pF as “1” element.
Suppose that a metasurface comprising M × N equal-sized coding elements under plane waves’ normal illumination, the radiation far field can be described by the equation [30],
The azimuth angle and the elevation angle of the radiated beam can be obtained by the following function,
To explore the tunability of the proposed concept, a TA composed of $\mathrm{8\ \times 8}$ units is designed. Figure 4(a) and 4(b) show the complete structure of the TA and the two-dimensional feeding network. The horn antenna with the gain of 15 dBi acts as a plane wave feeding source to illuminate the array normally.
Fig. 4. (a) The complete geometry of the proposed TA. (b) The feeding network on the rear side of the geometry. (c) The schematic diagram of radiation steering using the proposed TA.
For the proposed TA, when the coding sequence is “00000000” or “11111111”, a single beam perpendicular to the surface can be achieved because ${{p}_{x}}$ and ${{p}_{y}}$ trend to infinity, and $\mathrm{\theta =\ }{\textrm{0}^\mathrm{^\circ }}$ according to Eq. (4). Figure 5 shows the phase coding arrangement and the simulated radiated field patterns. Noted that stronger single-beam radiation can form at 4.9 GHz and 4.95 GHz, and the gains of them are 13.4 dBi and 13.1 dBi respectively, compared with the gain of the horn antenna itself is reduced by 1.6 dBi and 1.9 dBi. The loss mainly caused by the overflow of energy when spatial feeding is performed, and insertion loss of the proposed TA, including resistive loss of the active elements, dielectric loss and metal loss.
Fig. 5. (a) The coding arrangement of “11111111”. (b) and (c) are the simulated radiation far field patterns of the proposed TA at 4.9 GHz and 4.95 GHz.
When the coding sequence is switched to “11110000/11110000”, ${{p}_{x}} = {4p}$ and ${{p}_{y}}$ still tends to infinity, hence $\mathrm{\theta =\ 13}\textrm{.}{\textrm{4}^\mathrm{^\circ }}$ and $\mathrm{\varphi =\ }{\textrm{0}^\mathrm{^\circ }}\textrm{,}\; \textrm{18}{\textrm{0}^\mathrm{^\circ }}$ according to Eq. (3) and (4). Subsequently, two beams are formed along the x-direction. Figure 6 illustrates the phase coding sequence on the array and simulated far field patterns at 4.9 GHz and 4.95 GHz. Due to opposite phase response (the phase difference is $\textrm{18}{\textrm{0}^\mathrm{^\circ }}$) is introduced into the array, the coupling between different coding elements makes the working frequency of the array slightly shifted. Hence, under dual-beam working state, beamforming effect at 4.95 GHz is better than that at 4.9 GHz. Besides, the transmission amplitude of the units with diode capacitance of 0.66 pF differs by 10%-20% with that of 1.33 pF, thus resulting in a difference (about 1.8 dB) in the gain of the two beams. And due to the energy dispersion effect, the gains of the dual beams are about 3 dB lower than that of the single beam.
Fig. 6. (a) The coding arrangement of “11110000/11110000”. (b) and (c) are respectively the simulated radiation far field patterns of the proposed TA at 4.9 GHz and 4.95 GHz.
Then switching the coding sequence to 11110000/00001111, therefore ${{p}_{x}} = {{p}_{y}} = {4p}$ under this coding state, and $\mathrm{\theta =\ 19}\textrm{.}{\textrm{1}^\mathrm{^\circ }}$, $\mathrm{\varphi =\ 4}{\textrm{5}^\mathrm{^\circ }}\textrm{,}\; \textrm{13}{\textrm{5}^\mathrm{^\circ }}$, $\textrm{22}{\textrm{5}^\mathrm{^\circ }}$, $\textrm{31}{\textrm{5}^\mathrm{^\circ }}$ according to the analytical model. The coding arrangement and corresponding radiation pattern of the proposed TA is shown in Fig. 7. The lobe gains of four beams are reduced by around 3 dB compared with that of dual beams. Besides, the effect of beamforming at 4.95 GHz is also better than at 4.9 GHz.
Fig. 7. (a) The coding arrangement of “11110000/00001111”. (b) and (c) are simulated radiation far field patterns of the proposed TA at 4.9 GHz and 4.95 GHz, respectively.
3.2 Gain control
Gain control has potential applications in radio frequency energy harvesting, WLAN, long range PTP wireless links and cellar base stations. In this section, a pseudorandom coding arrangement is designed firstly, and subsequently the far field pattern of transmitted wave can be steered dynamically from pencil-like radiation to diffusion-like radiation through modulating the phase response of some elements of the proposed TA. Whereafter, the gain of the main beam radiated from the array can be tuned in real-time.
As can be seen from Eq. (2), varying $\mathrm{\varphi (m, n)}$ can change the value of ${F}({\mathrm{\theta ,\;\ \varphi }} )$. If $\mathrm{\varphi (m, n)}$ is a constant (such as 0 or $\mathrm{\pi }$), it means that the transmission phases of all the elements are the same, therefore, the far field pattern of TA which derives from the superposition of the transmitted waves of all the constituent elements is pencil-like radiation. Furthermore, if $\mathrm{\varphi (m, n)}$ varies with the element location [m, n], the value $\mathrm{\varphi (m, n)}$ of is determined by the coding sequence. Consequently, continuously shaping the radiated wave patterns can be achieved only by changing the transmission phase of some coding elements.
To obtain the best ability of manipulating the transmitted waves, genetic algorithm (GA) is utilized to optimize the coding matrix of the array. During the optimization, an initial matrix containing 10% “0” elements and 90% “1” elements is defined firstly, and subsequently updated by changing the values and positions of arbitrary elements. The fitness value can be calculated by the following fitness function,
Figure 9 shows the coding arrangement of the pseudorandom sequence and the gain tunability of the proposed TA at 4.9 GHz. We denote the working capacitances of all the “0” elements in the array as Cv0, and the working capacitances of all the “1” elements as Cv1. When Cv0 and Cv1 are set at 1.33 pF, all the elements have the identical transmission phase. The transmitted waves of all the constituent elements are superimposed to form a pencil-like beam in the z direction, and the gain of the beam is 13.4 dBi, as shown in Fig. 9(b). Then keep Cv1 unchanged, gradually decrease the capacitance Cv0 by increasing the bias voltage supplied on the diodes, and the transmission phases of “0” elements will change accordingly. When Cv0 is set at 0.73 pF, the phase difference between “0” element and “1” element can reach about $\textrm{9}{\textrm{0}^\mathrm{^\circ }}$. Due to the elements arranged in a pseudorandom sequence, destructive interference among different elements is invoked, hence the radiation energy of superimposed wave of all the elements becomes weaker in the normal direction of the array, and in other directions the radiated energy enhanced. The lobe gain in the z direction reduces to 8.02 dBi, as illustrated in Fig. 9(c). When Cv0 is decreased to 0.66 pF further, the phase difference of the transmitted wave between two kinds of elements is $\textrm{18}{\textrm{0}^\mathrm{^\circ }}$, the transmitted beam in the z direction is almost destroyed, accompanied by random divergence of energy into multiple directions in space. The maximum gain of the radiated wave is further reduced to 3.28 dBi, as depicted in Fig. 9(d).
Fig. 9. (a) The coding arrangement of pseudorandom sequence. (b), (c) and (d) are respectively the simulated far field patterns of the proposed TA at 4.9 GHz when Cv0 is set at 1.33 pF, 0.73 pF and 0.66 pF.
For the pseudorandom sequence, through tuning the capacitances of the loaded diodes, the phase responses of one kind of elements (“0” or “1”) can be changed, subsequently, dynamic radiation steering is realized and the gain of the main lobe can be controlled. The gain tunable range can reach 10.12 dBi at 4.9 GHz. Table 2 shows the simulated gain of the main beam under different transmitarray working states and gain tunable range at different frequencies. It can be observed that gain tunable range can reach above 8 dBi in the frequency band from 4.8 GHz to 5.05 GHz.
Table 2. Gain tunable range of main beam at different frequencies
4. Fabrication and experiment verification
To experimentally validate the proposed multi-functional TA, a prototype was fabricated. Firstly, the metallic patterns of the FSS were etched on the F4B laminates covered by 35 µm thick copper using PCB technology and then the diodes were mounted on each FSS. At the second stage, the patches of each element were connected by metallic wires and accessed to via holes on the bottom FSS. Finally, all the FSSs are bonded together by nylon screws and separated by gaskets. Figure 10 shows the fabricated sample and the designed feeding network. The size of the top four active FSSs are $\mathrm{364\ \times 364\;\ m}{\textrm{m}^\textrm{2}}$, and that of the bottom FSS is $\mathrm{364\ \times 401\;\ m}{\textrm{m}^\textrm{2}}$. Noted that the size of area occupied by all the elements is $\mathrm{264\ \times 264\;\ m}{\textrm{m}^\textrm{2}}$. The redundant areas of each FSS are covered by copper and connected by the via holes around the array to work as the ground when the diodes are biased. The cathodes of all the diodes can be biased independently under this feeding configuration. Masking tape were covered on the diodes to protect them from shedding.
The measurement of far field patterns was implemented in a microwave anechoic chamber, as illustrated in Fig. 11. Two standard gain horn antennas about 6 meters apart were connected by a vector network analyzer. The prototype, two DC sources and the transmitting antenna were fixed on the mechanical turntable which can be controlled to rotate from $\textrm{ - 9}{\textrm{0}^\mathrm{^\circ }}$ to $\textrm{9}{\textrm{0}^\mathrm{^\circ }}$ by computer to perform omnidirectional far field measurement. Two DC sources supplied desired bias voltage for different elements of the prototype. It should be noted that the fabricated TA and two horn antennas were inclined at $\textrm{4}{\textrm{5}^\mathrm{^\circ }}$ when measured the far field of quad-beam radiation, and put them horizontally for other radiation states.
According to the official data sheet, we biased the varactor with 3.5 V for the “1” element, and 26 V for the “0” element. Correspondingly, the diode capacitances are respectively 1.33 pF and 0.66 pF under these two biasing states. Figure 12 presents the measured far field patterns of beamforming at 4.9 GHz and 4.95 GHz, and gain control at 4.9 GHz. As can be seen from Fig. 12(a) and 12(b), along the horizontal direction and the diagonal line of the sample, the radiated field patterns exhibit two beams under dual-beam and quad-beam working states, and the amplitude of the lobe for quad-beam case is 3 dBi lower than that of dual-beam case, which is in good consistence with the numerical simulations. Some angle deviations and the larger side lobes may be caused by the overall stability of the diodes, the fabrication tolerance and the experiment environment. Figure 12(c) shows the measured patterns of gain control. When the bias voltage on all the elements is 3.5 V, a main beam can be observed and its amplitude decreases when increasing the bias voltage on the “0” elements. The measured gain tunable range is about 7 dBi, which is smaller than the simulated results, the above factors may also lead to the deviations. In addition, the gain tunable range of the main beam at the frequencies of 4.8 GHz, 4.85 GHz, 4.95 GHz, 5 GHz, and 5.05 GHz was measured. And the results are all above 7 dBi, which agrees with the numerical simulations well.
Fig. 12. (a) and (b) are respectively the measured far field patterns of dual-beam and quad- beam under beamforming state at 4.9 GHz and 4.95 GHz. (c) The measured patterns under gain control state at 4.9 GHz.
5. Conclusion
In conclusion, a strategy of introducing phase coding into TA and dynamic radiation steering digitally is realized. The proposed TA comprises five-layer cascaded FSS with loaded varactor diodes and the corresponding two-dimensional feeding network. With electrically controlling the capacitances of the diodes, the elements phase responses can be modulated, and the far field pattern of the transmitted wave of the proposed TA can be tailored in real time. Feeding the TA according to the coding sequences of “11111111”, “11110000/11110000” and “11110000/00001111”, the number of radiated beams can be tuned freely among one, two and four, hence dynamic beamforming is realized. Subsequently, feeding the array according to the pseudorandom coding sequence optimized by GA, gain tunable range of the main beam radiated from the TA can reach above 7 dBi. The measured results are in good accordance with the numerical simulations. This design integrates the functions of beamforming and gain control, and is meaningful for manifold applications ranging from multilink wireless communication to radio frequency energy harvesting.
Funding
National Key Research and Development Program of China (2020YFA0709800); National Natural Science Foundations of China (61971340); Chinese Aeronautical Establishment (2022Z062053002); Key Research and Development Projects of Shaanxi Province (2023-YBGY-246).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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