A Broadband 1-Bit Single-Layer Reconfigurable Reflectarray Unit Cell Based on PIN Diode Model

Microstrip reconfigurable reflectarray antennas (RRAs) have great potential for advanced systems including satellite communications and the 6th generation (6G) wireless mobile communication networks. However, as a type of microstrip antennas, RRAs generally exhibit an intrinsic issue of narrow bandwidths. This issue is further deteriorated by complicated structures for phase shifting and DC supplying in RRAs. PIN diodes have been used in recent works to control the phases of RRA elements. However, modelling them is still costly and time consuming. In this work, a simple but novel method for modelling PIN diode SMP-1340-040 is developed by using waveguides and modified simulation approaches. Based on the obtained model, a broadband 1-bit unit cell using only one substrate is also proposed, and it achieves a simulated bandwidth of 40.6% and 33.8% for linear and circular polarizations, respectively. The experimental results show an excellent agreement with the simulation, which confirms the accuracy of the proposed PIN diode model. Moreover, the performances of the unit cell demonstrate that it can be used for designing RRAs in bands X and Ku.


I. INTRODUCTION
Microstrip reflectarrays (RFAs) are considered a combination of reflectors and phased array antennas with notable advantages, including affordability, light weight, and low profile with a planar structure. Compared to phased array antennas, their air-feeding mechanism avoids high loss in the feeding network. Furthermore, RFAs do not require radio frequency (RF) modules, analog-to-digital converters (ADCs), and digital-to-analog converters (DACs), rendering RFAs less complicated and more affordable than phased array antennas. Given these advantages, RFAs have been employed for satellite communications [1], [2], [3], radars, point-to-point terrestrial links, 5G [4], [5], and beyond. However, as a type of microstrip antenna, RFAs generally exhibit limited The associate editor coordinating the review of this manuscript and approving it for publication was Davide Comite .
RRA is a variant of RFA, which can steer using phaseshifting elements. They are adopted for modern wireless communication systems with the requirement of beam steerings, such as satellite communication systems, radars, and base stations [10]. Recently, passive RIS (reconfigurable intelligent surface) or intelligent reflecting surface (IRS), which operates similarly to RRAs without horn antennas, is proposed as a promising candidate for next-generation antennas [11], [12], [13], [14]. The steering capability of RRAs is realized by devices, including MEMs (Microelectromechanical Systems), varactor diodes, PIN diodes, graphene, and liquid crystals, which tune the reflective phases of elements. Among these devices, MEMs, varactors, and PIN diodes are used more frequently. MEMs present several advantages, VOLUME 11, 2023 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ such as small size, low insertion loss, and low power consumption [15], [16], [17], [18], although fabricating them is unpopular and requires a high expense. Varactors can produce smoother reflective phases, but the expense of manufacturing a RRA with these devices is high because of the cost of the control board [19], [20], [21]. Indeed, each cell in RRAs using varactors is controlled independently by a circuit that includes a digital-to-analog converter (DAC) and some passive devices besides register shifters, microcontrollers (MCUs), or FPGAs [22], [23], which makes the control board extremely complicated and high-cost, especially when using fast-settling ADCs such as MAX5592. This problem is more critical for array with hundreds or thousands of elements which are employed for 5G [24], 6G [14], [25] and satellite [26], [27], [28], [29]. Of a particular note, PIN diodes are preferred for RRAs given their low cost, diversity, and ready availability on the market [22], [23], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. Moreover, the control boards for PIN-diode RRAs are simpler and more affordable than those for RRAs using varactors, especially for large RRAs. Most PIN-diode RRAs adopt 1 bit [22], [23], [26], [27], [30], [31], [32], [33], [39], [41], [42], [43], [44] or 2 bits [35], [36], [37] to shift reflective phases, but those using 1-bit are given more attention because of the ease of design (simple structures) [34] although their performance in terms of sidelobe levels and gains are worse (but acceptable) than those using 2 bits as a trade off. To date, characterizing PIN diodes for RRA unit cells is still deemed a challenge, and there have been a few studies on modelling PIN diodes. Largely, PIN diode models are affected by various factors, including operating frequencies, diode mounting substrates, and controlling currents and voltages. Most types of PIN diodes have their own models provided by manufacturers; however, these models can not be applied to RRAs because they are developed under specific conditions with different substrates. Indeed, the microstrip line, which is generally used by manufacturers for the measurement of the PIN diode parameters, greatly differs from the electromagnetic conditions for the RRAs unit cell with various angles of incidence. A recent work [27] has succeeded in modelling a PIN diode by measuring a full RRA, but this method is costly and time-consuming. Another work [41] has used a waveguide to measure the reflective parameters of the RRAs unit cells; however, the method to determine the model of the PIN diodes has not been described in this literature.
The bandwidths of RRAs are affected by two factors: the structures of RRAs and the bandwidth of unit cells [6], [45]. The air-feeding structure of RRAs causes oblique effects, which deteriorate their bandwidth. This is considered an intrinsic feature of RRAs. The bandwidths of RRAs are also noticeably dependent on unit cells. Even in the cases of oblique incidences, if unit cells produced sufficiently large bandwidths, they would enlarge the bandwidths of RRAs. However, unit cells largely exhibit the narrow bandwidths which are typical for microstrip antennas. Moreover, active devices and DC-bias structures cause parasitic parameters and insertion losses, which in turn degrade the performance of unit cells considerably.
Recently, intensive effort has been made to improve the bandwidth of the RRA unit cell. In [39], a unit cell using delay lines with two PIN diodes achieved a bandwidth of 10.5%, from 13.5 GHz to 15 GHz for a phase shift of 180 • ± 20 • . Another unit cell formed from two patches and a PIN diode is presented in [23], which obtained a 180 • ± 20 • bandwidth of 12% at the center frequency of 5 GHz. Reference [43] proposed a polarization-turning element with a complicated structure, which used four layers and four PIN diodes for polarization turning, DC isolating, and impedance matching. This element operated at the center frequency of 13.25 GHz and achieved a bandwidth of nearly 20%. Reference [33] adopted a ''microstrip line-slot line-microstrip line'' structure and two PIN diodes to design a broadband unit cell. This unit cell had a bandwidth of 20.8%, from 11.6 GHz to 14.3 GHz. Because the unit cells had narrow bandwidths, RRAs achieved bandwidths still lower than RFAs, lower than 22.5% [34] compared to approximately 33.52% [8] (1-dB gain bandwidth).
Most recent works adopt multi-layer PCBs for RRAs [27], [30], [38], [39], but such structures elevate the cost of RRAs. Moreover, a multi-layer PCB uses different materials, such as PTFE and FR4 [27], [38] and some types of prepregs, which causes inhomogeneity and loss because the prepregs and FR4 typically have higher dielectric constants than PTFE [46]. This structure will also be unstable over time, resulting from the difference in thermal expansion between prepregs and other substrates [47].
In this paper, the authors focus on proposing a novel but simple method to accurately model the PIN diode. Unit cells were designed, fabricated, and tested to validate the proposed PIN diode model. Subsequently, a new structure of broadband unit cells using only one substrate and the determined PIN diode model were presented. The obtained results demonstrate that the new structure can be a viable replacement for multilayer unit cells with a number of benefits, including low cost, high stability, and reduced loss. This paper includes four sections. Section II presents the method of modelling the PIN diode model. Section III shows the design of a broadband unit cell using the PIN model obtained in Section II and its performance. Section IV is the conclusions.

II. PIN DIODE MODELLING
The PIN diode includes metal pads, P + and N + layers and an intrinsic region (I-region) as illustrated in Fig. 1a. The characteristics of a PIN diode mainly depend on the geometrical properties of the metal pads and the properties of the I-region. In the RRAs, PIN diodes work as a switch with two states: ''ON'' and ''OFF''. The ''ON/OFF'' states are turned when driving it by a forwarded current or supplying a reversed bias voltage, respectively. The general model of PIN diodes in these two states is outlined in Fig. 1b [48]. At the ''ON'' state, the PIN diodes are modelled as a resistor R ON in series with an  inductor L d . The R ON is the property of the I-region injected with holes and electrons, while the inductor L d models the metal pads [48]. The PIN diode models at the ''OFF'' state are described as a series of a resistor (R OFF ), a capacitor (C d ) and an inductor (L d ) where R OFF and C d reflect the properties of the I-region with no stored charge while L d , presents the metal pads.
The PIN diode models are affected by the mounting techniques, operating frequencies, and other conditions as aforementioned. Table 1 shows the models of some kinds of PIN diodes. Most of these models are different, especially in capacitors at the ''OFF'' state, although some of them are the same type. Take SMP-1340-040 as an example. Its capacitor C d is adjusted from 100 fF to 202 fF, corresponding to the center frequencies from 2.3 GHz to 9 GHz. Therefore, modelling PIN diodes at their operating frequencies and substrate is necessary before designing the unit cells and RRAs.
In this work, the PIN diode SMP1340-040 from Skywork is selected for modelling. This kind of PIN diode is low cost although its characteristics are more nonlinear and lossy than MA4AGP907 and MADP-000907 from MACOM. With such a low price, SMP1340-040 is an appropriate selection for RRAs with hundreds or thousands of elements. The PIN diode SMP1340-040, with general equivalent circuits as shown in Fig. 1b, is modelled according to four steps as follows (see Fig. 2): Step 1 (Section II-A): Design the unit cell using an initial PIN diode model extracted from [27], which operates at the center frequency of 9.2 GHz and uses substrate TLX-08 (thickness of 1.58 mm) (See Table 1). The values of the elements in the initial model are as follows: L d = 500 pH, C d = 100 fF, R ON = 1 , and R OFF = 10 . However, the operating conditions of the unit cell in this work are not VOLUME 11, 2023 similar to those in [27]. Indeed, this unit cell uses a single thicker substrate and operates at frequencies from 9 GHz to 16 GHz. Therefore, the real model of the PIN diode in this paper will be different to the initial model. Fig. 3. Thus, the real model in relation to the initial model is expressed as follows: where L d , R ON , C d , and R OFF are adjustments of the parameters L d , R ON , C d , and R OFF due to the different operating frequencies and substrate properties. Note that the values of these parameters can be positive (an upward adjustment) or negative (a downward adjustment). Function (1) reveals that the errors in the model will result in differences between simulated and experimental results. However, the initial model is still used to design the unit cell because the real model is unknown.
Step 2 (Section II-B): Simulate, fabricate, and measure the unit cell designed in Step 1. In this step, the unit cell (version 1) is simulated by the periodic method with a plane wave to obtain the reflective coefficients and phases. Then, it is fabricated and measured by Keysight Vector Network Analyzer (VNA) N5242A in cooperation with a waveguide to achieve the S-parameters. The difference between experimental and simulated results is used to adjust L d , R ON , C d , and R OFF (in Step 4). The difference between measured and simulated results mostly comes from the wrong PIN diode model and the wrong simulation method configuration. Therefore, the simulation method is configured before adjusting errors of the PIN diode models (Step 3).
Step 3 (Section II-C): Configure the simulation methods. In this section, the simulation configurations are adjusted to be analogous to the real conditions in the waveguide, where the angle of incidence is varied according to the frequencies and the reference plane is set at the surface of the unit cell.
Step 4 (Section II-D): Implement simulation-adjustmentsimulation loops to obtain the PIN diode model. Errors ( L d , R ON , C d , and R OFF ) are adjusted gradually in loops to obtain agreements between simulated and measured reflective coefficients.

A. UNIT CELL DESIGN
The authors use the initial PIN diode model to design the unit cell (version 1) for modelling the PIN diode. The structure  of the unit cell is presented in Fig. 4 with dimensions of 12 mm × 12 mm, less than half of the wavelengths of the center frequency (12 GHz). Only one substrate (Duroid RT5880, ε r = 2.2) with a thickness of 3.175 mm is used for the unit cell. The detailed dimensions of the structure are shown in Table 2. The unit cell has two copper layers. The top metallic layer including four rectangle patches and slots works as the main resonant component, which mostly defines the characteristics of the unit cell. Each couple of patches is connected by a PIN diode mounted on the top layer. Thus, switching states ''ON'' and ''OFF'' of four PIN diodes alters the main resonant structures of the unit cell, creating a phase shift. The slots support fixing the position of the PIN diodes. They also work as variable structures for optimizing the unit cell. The ground layer is slotted around the vias, creating four isolated patches. Two DC wires and two GND wires are soldered onto these patches to control four PIN diodes. The bottom layer is also a ground layer, working as a reflective surface. To close this surface in terms of RF signal, four 27 pF capacitors are employed to connect the four isolated patches to the remaining area, which creates a perfect reflective layer. The advantage of this DC-supplying method is an excellent isolation between the DC and the RF signals, which contributes to creating a broadband unit cell.
To understand the operating principle of the unit cell more clearly, the authors model it by two equivalent circuits as illustrated in Fig. 5. Because of powerful and effective electromagnetic simulation softwares, these circuit models is used to explain the physical mechanism of the unit cells rather than optimizing or validating them [52]. For the top layer, each of the four patches is modelled as an inductor L p series with a capacitor C p . Each patch is connected to the ground layer by a via to control the PIN diodes. The via is modelled as an inductor L v , paralleled to the patch-modelled circuit. Each pair of patches is connected by a PIN diode and modelled by two equivalent circuits in correspondence with the ''ON'' and ''OFF'' states. Because of the direction of the electromagnetic field (see Fig. 3), the coupling between the patches in the y-axis direction is weak and could be ignored. When the PIN diodes turn ''ON'' or ''OFF'', the equivalent circuit of the unit cell is altered, respectively, which results in changing the resonant frequencies and shifting the reflective phase around 180 • .

B. SIMULATION AND MEASUREMENT
The unit cell is simulated by the periodic method with a plane wave (incident angle of 0 • ) in CST Studio. A couple of unit cells with dimensions of 24 mm × 12 mm are fabricated, as illustrated in Fig. 6. To mimic the walls in the simulation environment (boundary conditions), two rings of vias are employed to shut off the radiation leakage. Moreover, four holes for pinning the steel plate for solder paste printing and four holes for fixing the position of the board on the waveguide are added. Capacitors and PIN diodes are also mounted on the PCB board.
The authors intend to adopt a waveguide WR-75 to measure the unit cells, but it is not large enough to cover these double unit cells. Therefore, a couple of tapered waveguides that convert from WR75 dimensions (19.05 mm × 9.525 mm) to dimensions of 24 mm × 12 mm are designed and fabricated. They are combined with WR75 coaxial-waveguide adapters to form a set of waveguides, as illustrated in Fig. 7a. The waveguide set is calibrated by the thru-reflect-line (TRL) method [53], defining the plane of the open end (24 mm × 12 mm) of the waveguide as a reference plane. As shown in Fig. 7d, the reflection coefficient of the tapered waveguide closed by the short sheet is nearly 0 dB after calibrating, which demonstrates that the reference plane of the waveguide is calibrated. The mechanical tolerance between the two  waveguides leads to some minor peaks of less than 0.2 dB. However, they affect the reflective parameters of the unit cell slightly.
The unit cells are placed at the reference plane to measure reflection parameters by a VNA through an RF cable (see Fig. 8) with a measurement schematic, as depicted in Fig. 9a. The unit cells are switched ''ON/OFF'' by a DC signal from the DC supplier. The forward current is set up by a current limiter (four resistors of 560 ) in cooperation with the DC supplier and is monitored by a multimeter as in Fig. 9b. Due to the similarity of the two unit cells, Fig. 9 just presents a single DC-control schematic for one unit cell as a representation. Four PIN diodes are controlled through four wires (two GND  and two V+ wires), which connect DC signals from the current limiter to the pads 1, 2, 3, and 4 as shown in Fig. 6 and Fig. 9b. An output voltage of 6.5 V is provided to turn ''ON'' the PIN diodes simultaneously with a forward current of around 5 mA for each of them. A reverse voltage of −12 V is supplied to the diodes to turn them ''OFF''. Because the I-region in the ''OFF'' state (see Fig. 1) is modelled as a capacitor series to a resistor, the reverse current is nearly zero as illustrated in Fig. 8.
The measured and simulated results, as plotted in Fig. 10, are not correlated especially in reflection coefficients. For the measured reflection coefficients, there are two peaks at around 11.9 GHz for the ''ON'' state and two peaks at approximately 13.5 GHz and 15,1 GHz for the ''OFF'' state, whereas there are no peaks for the simulated results. The reflective phases also show a disagreement between measured and simulated results with deviations from 40 • to 0 • , especially at the ''OFF'' state. The simulated phase at the ''OFF'' state has no phase drop at 15 GHz compared to the measured one.
These errors mostly derive from the PIN diode model errors ( L d , R ON , C d , and R OFF and the incorrect simulation configuration. The errors of the PIN diode models are explained above, while simulation configuration is needed to clarify. Indeed, the current simulation configuration just uses the plane wave to excite the unit cell, which does not reflect accurately the realistic incident angle. Generally, the wave propagates in the tapered waveguide at various incident angles in correspondence with the operating frequencies. These oblique incidences excite the unit cell, creating responses greatly different from the plane wave and thus, causing errors between the simulation and the measurement. Hence, it is necessary to configure the simulation correctly and remove the errors of the diode models to match the simulated outcomes to the experimental ones.
The slotted ground layer and capacitors could affect the performance. However, this factor is excluded because the measured loss of the bottom layer is approximately 0 dB, as shown in Fig. 10a.

C. SIMULATION METHODS
To configure the simulation conditions equivalent to the real measurement conditions correctly, the process of the electromagnetic wave travelling in the tapered waveguide has to be clarified in advance. In principle, the electromagnetic wave propagates in the waveguide at various angles θ, which depend on frequency as expressed in Function (2) [54].
where f cutoff is the cut-off frequency of the waveguide; f is the operating frequency. The waveguide, in this case, includes two components: the waveguide adapter (WR75 adapter) and the tapered waveguide (WR75 to 24 × 12 taper), as indicated in Fig. 7. Sine the waveguide is tapered, when the wave reaches the unit cell  surface, the incident angles θ turn into φ as shown in Fig. 11. Hence, determining the angle of incidence for each frequency is a crucial factor to simulate the unit cell accurately.
As depicted in Fig. 11, the dimensions of the whole waveguide (including the WR75 adapter) are as follows: The distance from the phase center of the adapter WR75 to its open end is l a = 20 mm; The length of the tapered waveguide is l t = 71 mm; The broad side dimension of the WR75 adapter is d a = 19.05 mm, while that of the wider open end of the tapered waveguide is 2a = 24 mm.
Based on the structure and the dimensions of the whole waveguide, and thanks to the geometrical method, the authors calculate a set of angles ϕ for a set of discrete frequencies from 9 GHz to 16 GHz.
Both methods, namely waveguide method and periodic method, are utilized to simulate the unit cell, as depicted in Fig. 12. For the periodic method, the set of pre-calculated angles ϕ are used to define the angles of incidence of the Floquet port. In contrast, the angles of incidence in the waveguide method are fixed to angles θ by the software because this method mimics a standard waveguide rather than a tapered waveguide. The length of the waveguide in the waveguide method is set to 91 mm (l t + l a ), similar to the actual dimension (see Fig. 12b). The reference planes of both methods are set at the surface of the unit cell as presented in the measurement setup in Section II-B (12 × 24 mm plane).
The Floquet port in the periodic method just creates a plane-wave mode, but it just slightly affects the performance of the unit cell compared to the TE10 mode in the real waveguide [52]. For the waveguide method, the boundary conditions of this method (four walls) are set to E t = 0 to trigger the TE10 mode.

D. TUNING LOOP
Due to the oblique effects, the experimental reflection coefficients have some peaks, as shown in Fig. 10, which are marks for tuning. Generally, the reactances (L d and C d ) of the equivalent circuit affect the frequencies of the peaks, while the resistances (R ON and R OFF ) just influence the peak depths. Thus, each of them is adjusted in a loop to match the experimental result to the measured one. Because the measured results are ready, the loops are just executed to tune the simulated outcomes towards the measured ones. Note that before implementing the loops, the simulation methods must be configured correctly. Since the PIN diode model at the ''ON'' state just has two components L d and R ON , the loops for finding them are executed first. As shown in Fig. 13a, the measured reflection coefficient at the ''ON'' state just has one peak at 11.97 GHz. To determine L ′ d , a tuning loop is implemented, in which L d is adjusted step by step to tune the frequency of the peak towards 11.97 GHz. The loop stops when the simulated frequencies of the peaks reach 11.97 GHz, with L d = −378 pH and Similarly, R ON is adjusted in another loop to match the simulated amplitude of the peaks (11.97 GHz) to the measured one. However, due to the nonlinear characteristics of the PIN diode, the loop is terminated at R ON = 1.5 (R ′ ON = 2.5 ) to keep the amplitudes of all frequencies in the bandwidth close to those of the measurement. Thus, the final ''ON'' model is R ′ ON = 2.5 ( R ON = 1.5 ) and L ′ d = 122 pH ( L d = −378 pH). For the ''OFF'' state, there are two resonant points at 13.5 GHz and 15.1 GHz, but only the peak at 15.1 GHz is considered because the other is minor, thus skipped. As depicted in Fig. 1, the parameter L ′ d for ''ON'' is the same as the ''OFF'' state, so it is fixed at 122 pH. Only loops for determining C ′ d and R ′ OFF are executed. To find C ′ d , a loop is implemented by tuning C d gradually to move the frequency of the peak toward 15.1 GHz, and it exits when the frequency reaches that value with C d = 0.025 pF. Subsequently, R OFF is adjusted in another loop to determine R ′ OFF and the loop stops when the amplitude of the peak at 15.1 GHz relatively matches the measured one and also keeps balanced results for other frequencies in the bandwidth with ( R OFF = −5 ). Hence, the final ''OFF'' model are as follows: As shown in Fig. 13b, the simulated reflective phases have an excellent agreement with those of the measurement for both simulation methods, which validates the obtained model of the PIN diode, although the phase difference does not attain 180 • as expected.
Because the dimensions of the standard waveguides rarely fit the unit cell, the tapered waveguides are typically used to coordinate with VNAs for measuring unit cells. Hence, the periodic method with the set of angles of incidence is more appropriate to simulate the unit cell and obtain a better tolerance in comparison with the waveguide method.
Compared to other models of the previous works in Table 1, this model is slightly different, especially in R ′ ON , R ′ OFF , and L ′ d because the substrate, the operating frequencies, and the structure of the connecting pads are greatly different to other previous works. Regrettably, most previous works using this PIN diode do not measure unit cells. The capacitors and the gaps on the ground could be factors which affects the reflective parameters. However, the reflective characteristic of the ground layer is verified with a reflection coefficient of nearly 0 dB, as plotted in Fig. 13a, which demonstrates that it is a perfect reflective plane.

III. BROADBAND UNIT CELL
The authors re-design the unit cell in Section II-A with the obtained PIN diode model. Parameters l d , l v , g, w 1 and w 2 are tuned to reach a phase difference of around 180 • between   Table 3, and its operating principle is similar to the unit cell in Section II-A.

A. UNIT CELL PERFORMANCES
The unit cell (version 2) is simulated in the periodic environment with the Floquet port, which adopts a plane wave (linear or circular polarizations) to excite the unit cell. Unlike the periodic method in Section II-C, the angle of incidence is set to zero or not changed according to the frequency. The reflection coefficients and phases of the unit cell are plotted in Fig. 15. Since the structure of the proposed unit cell is symmetric, it maintains the same linear polarizations or circular polarizations as those of the exciting sources, and its performances for x-polarized and y-polarized incidences are not significantly different. Therefore, the authors just present the simulation results for left-hand circular polarization (LHCP) and y-polarization as representations for the circular and the dual linear polarizations, respectively.
The simulated results for y-polarization are plotted in Fig. 15a and Fig. 15c, while the results for LHCP are presented in Fig. 15b and Fig. 15d. The unit cell has an excellent performance for multiple polarizations. The 180 • ± 20 • phase-shift bandwidth of the linear polarization is 40.6% from 9.2 GHz to 13.9 GHz, and for LHCP, it is 33.8%, from 9.26 GHz to 13.03 GHz. In these frequency ranges, the reflection coefficients for Y-polarization and LHCP are   VOLUME 11, 2023 be estimated that the average radiation efficiencies of the unit cell are approximately 90% for both the ''ON'' and ''OFF'' states. The deviation of the average reflection coefficient in the bandwidths is minor (0.4 dB), which could make the unit cell a promising candidate for broadband RRAs. Moreover, the cross-polarization reflection coefficients and transmission coefficients are less than −40 dB for both Y-polarization and circular polarization. It is an excellent performance for a unit cell using such a low-cost PIN diode for frequencies up to 13.9 GHz and one layer with significantly low expense compared to a multi-layer unit cell.
This unit cell obtains a wide bandwidth because it uses a thick substrate and an appropriate structure. In fact, a shape of four patches and a thickness of 3.175 mm help the original unit cell (without PIN diodes) achieve a wideband feature because it has a more linear reflective phase [55], [56]. Four PIN diodes are placed in the middle of the unit cell to shift phase, and thus the unit cell avoids the mismatching between microstrip patches and delay lines that occurred in the previous works [22], [30]. Moreover, the proper DC-bias structures still keep the unit cell symmetrical and create an excellent isolation between DC and RF signals, while the single-layer structure also minimizes bad effects, such as nonlinear insertion loss and phase shift, compared to multilayer structures. All of these factors contribute to creating a broadband unit cell.
Since the oblique incidence influences the performance of the unit cell significantly, it is necessary to examine the response of the unit cell at various incident angles. The simulated performances for both oblique incidences of 20 • and 30 • are plotted in Fig. 16. For both y-polarization and LHCP, the reflection coefficients and reflective phases at 20 • and 30 • show a minor deviation in comparison with the normal incidence (0 • ). For cross polarizations, reflection coefficients still maintain excellent isolation for Y-polarization with a figure of less than −45 dB, while for LHCP, it is less than −15 dB in the bandwidth from 9.2 GHz to 13.3 GHz. For both polarizations, the reflective phase difference between the states ''ON'' and ''OFF'' has a narrow trend from 11.5 GHz with a maximum deviation of approximately 30 • for both oblique angles of 20 • and 30 • in comparison with the normal incidence.

B. FABRICATION AND MEASUREMENT
To verify the performance of the proposed structure, the double cells are fabricated. The virtual walls and holes are also employed on the board, as illustrated in Fig. 17. The unit cells are also controlled and tested as presented in Section II-B (see Fig. 18).
The measured results are compared with the simulated ones for both simulation methods (waveguide and periodic method), as shown in Fig. 19, in which the periodic method presents better errors. Indeed, for the ''OFF'' state, the periodic method detects a resonant point at 9.8 GHz, whereas the waveguide method ignores this point. However, there are still frequency deviations between simulated and measured  peaks, particularly at 9.8 GHz with around 100 MHz, and at 12.55 GHz and 13.4 GHz with nearly 500 MHz. The errors are caused by two factors: two versions of the unit cells are fabricated at two different factories, and the PIN diode is nonlinear, especially at high frequencies. There is an excellent agreement between the simulated and measured reflection phases, as shown in Fig. 19b, which validate again the obtained PIN diode models.
Although the measured results do not reflect the characteristics of the unit cell accurately because of oblique incidences in the waveguide, the experimental phase difference of 171 • to 203 • for a bandwidth from 9 GHz to 13.9 GHz indicates the ability to attain a phase-shift of 180 • between two states.    [39] and reflective coefficients of greater than −2 dB. The unit cell has the greatest performance in terms of bandwidth, although it uses a low-cost diode (SMP-1340) and its structure is more simple than other works. For the reflection coefficient, due to using four diodes, the insert loss is high but acceptable, similar to [33].

IV. CONCLUSION
This paper proposed a novel method to model a PIN diode using the periodic method for simulation and a waveguide for measurement. As a result, the model of the PIN diode SMP-1340-040 is determined. Based on this model, the authors proposed a broadband 1-bit unit cell with only one substrate layer. It achieves a wide bandwidth, from 33% to 40.6% for both polarizations, which promotes it as a promising candidate for developing a broadband RRA. The method of this work can be applied to model other PIN diodes and active devices to lower the cost of designing and fabricating RRAs.