L-shaped Stub Research Articles

Design and development of low-profile hybrid reconfigurable antenna for 5G sub-6 GHz applications

This paper reports a low-profile hybrid reconfigurable antenna for 5G sub-6 GHz applications, measuring 14 × 15 × 0.787 mm3. A hybrid, frequency-and pattern-reconfigurable antenna with a semi-circular patch makes up the design. The Rogers RT5880 substrate, having a dielectric constant of 2.2, is used to build the design. Two PIN diodes are employed in the top layer to reconfigure frequency, and two diodes are used in the bottom layer to achieve pattern reconfigurability. Inverted L-shaped stubs and a defective ground structure (DGS) are put onto the antenna's ground plane. The ground plane uses the DGS to cover the necessary sub-6 GHz frequency spectrum. The suggested design covers two distinct frequency bands having −10 dB impedance bandwidth of 260 MHz for 3.4 GHz-3.6 GHz when the top layer diodes are ON and 270 MHz for 3.6 GHz-3.8 GHz when they are OFF. In addition, the suggested design is manufactured and tested, and the simulation and measurement resultsshow good association.

Design of a compact wideband bi-directional pattern antenna for 5G applications

In this research, a wideband bi-directional pattern antenna implemented by a circular monopole encircled with an enforced-radiation circular ring incorporated with inversed L-shaped stub is designed to operate over the mid-band of 5G applications ranging from 2 to 6 GHz. It is contrived of a copper overlaid on FR4 substrate with relative permittivity of 4.3 and height of 1.6 mm. This proposed antenna is fed by a 50-ohm coplanar waveguide, which is printed on the same side of the radiated circular monopole. To further enrich the impedance matching, a pair of etched slots is added-on the ground plane near the fed line to reduce the return loss. In the study, the initial parameters are theoretically worked out, and then simulation is then performed by using an electromagnetic solutions tool to numerically discover the set of solution parameters. From the simulation results, this proposed antenna offers the |S11|<–10 dB covered the operating frequency running from 1.79 to over 8 GHz with fractional bandwidth 126.90 % and 1.74 to 7.07 GHz with fractional bandwidth 101.04 % for the simulation excluded and included SMA, respectively. It provides a linear polarization with total efficiency better than 81.5 %. After that, an antenna prototype with compact dimensions of 45×45×0.6 mm3 was fabricated and testified to validate the simulation results. The measurement results provide a stability bi-directional pattern with peak gain of 5.54 dBi covering a 10 dB return loss bandwidth of 118.5 % (1.93–7.54 GHz). Simulated |S11|, 2D radiation pattern and gain are reasonably in good agreement with experimental results. Furthermore, this proposed antenna is compared with the current compact, wideband and 5G antenna to indicate its prospective for the interested bands

A Co-Linearly Polarized Shared Radiator-Based Full-Duplex Antenna With High Tx-Rx Isolation Using vias and Stub Resonator

In this paper, a co-linearly polarized shared radiator (SR) based in-band full-duplex (FD) microstrip antenna with high Tx-Rx isolation is proposed. The Tx and Rx terminals of the proposed FD antenna are designed on a single patch, where a series of vias are loaded in the central line of the patch followed by two L-shaped stubs at either end, which leads to high Tx-Rx isolation (≈60 dB). The via loading makes the Tx and Rx antennas individually operate in TM0,1/2 mode. The proposed SR-FD antenna demonstrates Tx-Rx isolation of 60.8 dB at 5.9 GHz operating frequency. Both Tx and Rx terminals of the FD antenna exhibit identical radiation property with peak realized gain of 6.65 dBi and co-to-cross polarization isolation >18 dB. The working mechanism of the proposed FD antenna is explained by both EM and circuit simulation, as well as verified with measurements on the fabricated prototype. The proposed SR-FD antenna has the merits of being planar, reduced footprint, simple feeding mechanism, and desired isolation bandwidth for IEEE 802.11p which renders it suitable for V2X-ITS application.

Design of Novel Ultrabroadband Printed Antenna and Its Efficient Optimization Using Self-Adaptive Hybrid Differential Evolution Algorithm

A novel compact ultra-broadband-modified fork-shaped printed antenna is optimized efficiently by using a self-adaptive hybrid differential evolution (SHDE) algorithm. Firstly, a novel compact ultra-broadband-modified fork-shaped printed antenna structure is proposed. The antenna with more compact size consists of a modified fork-shaped radiator and a modified ground plane, which can cover a very wide operating frequency band. The antenna is fed by a step-shaped microstrip line, and the modified ground plane consists of some rectangular slots and an L-shaped stub. Then, the SHDE algorithm is used to determine structural dimensions of the proposed antenna, and the antenna’s performance is optimized while maintaining a cost-effective computation time. The optimized antenna with only 11.8 mm × 19.7 mm size covers -10 dB reflection coefficient bandwidth of 147.6% from 3.08 to 20.46 GHz. Finally, the antenna prototype is fabricated, and the measured results basically agree with the simulated ones. The proposed antenna can be viewed as an excellent candidate for realizing ultrabroadband transmission technology.

Wideband Single-Fed Circularly Polarized Stacked Patch Antenna With L-Shaped Stub

A wideband single-fed circularly polarized (CP) stacked patch antenna with an L-shaped stub is presented. The CP antenna is made up of the bottom gradient microstrip transmission line, middle driven patch and top square radiation patch. The driven patch with an L-shaped stub and opening slot can achieve a wideband CP radiation which is different from a conventional patch. The presented CP stacked patch antenna maintains good directional radiation, while featuring wideband CP radiation. The final tested results indicate that the presented CP antenna has significant performance with a −10 -dB impedance bandwidth of 42.1% (4.26-6.53 GHz), a 3-dB AR bandwidth of 26.0% (4.36-5.66 GHz) and broadside peak gain of 8.6 dBic. Moreover, the fifth-generation (5G) N79 band (4.4-5.0 GHz) and 5G wireless local area network (WLAN) band (5.15-5.35 GHz) can be covered by the operating bandwidth of the presented CPantenna.

A 22–28 GHz Polarization-Reconfigurable Flat-Panel 8 × 8 Tx/Rx Phased Array Antenna With Uniquely Arranged Novel Radiating Elements for CubeSat Communication

In this paper, a wideband (22-28 GHz), polarization reconfigurable, flat panel, 8x8 transmit (Tx)/receive (Rx) phased array antenna (PAA) is proposed. The array offers a realized gain of 22-23 dBi/dBic in the broadside direction and scans to approximately ±50° while maintaining 3dB gain drop/scan loss, low cross-polarized fields, and axial ratio (AR) below 3dB (in case of circular polarization (CP)) over the entire bandwidth within the given scan range. By utilizing the amplitude and phase control mechanism of the Radio Frequency Integrated Circuits (RFICs) employed for the beamforming network (BFN), each single radiating element of the array can work in four polarization cases such as horizontal (X-), vertical (Y-), left-hand circular and right-hand circular polarizations. The single element is a novel stacked patch configuration with L-shaped stubs at the two opposite corners of the driven patch and stubs on radiating edges of both the driven and parasitic patches. The radiator offers a wideband performance in addition to resolving the poor isolation between the two ports, thereby improving the cross-polarized fields and AR over the entire bandwidth. The radiating elements are arranged in a unique way in the array such that the benefit of element mirroring is achieved during the dual linear cases, whereas the benefit of sequential rotation of elements is achieved in dual CP cases, which further improves cross-polarized fields and AR. The simulated results are validated through the measurement results for a fabricated PAA prototype for the scanned radiation patterns for all four polarizations in receive mode, antenna gain-to-noise temperature (G/T) in receive mode, and effective isotropic radiated power (EIRP) in transmit mode.

A Compact UWB Monopole Antenna with Triple Band Notches

This article presents an ultra-wideband (UWB) monopole antenna with triple band notch characteristics. The proposed antenna consists of an octagonal patch, fed with a 50 Ω line, which occupies a compact size of 40 mm × 29 mm (0.36λ × 0.26λ, λ is computed using 2.7 GHz frequency) and resonances at a relatively low frequency (2.94 GHz). Specifically, an L-shaped stub, an inverted C-shaped slot, and a pair of U-shaped resonating structures are introduced into the design, which allow antenna to generate three band notches at 3.22-3.83 GHz, 4.49-5.05 GHz and 7.49-8.02 GHz, corresponding to WiMAX band, Indian national satellite (INSAT) band, and X-band satellite frequencies, respectively. In the center of the notched band, the antenna has lower efficiency and gain, essentially indicating that the antenna has good interference rejection performance. To evaluate its performance, the proposed antenna has been fabricated and measured, and the relevant functional parameters, such as S-parameters, voltage standing wave ratio (VSWR) and radiation property, have been studied.

Mutual coupling reduction for monopole MIMO antenna using l-shaped stubs, defective ground and chip resistors

In this paper, a symmetrical and compact monopole multiple input multiple output (MIMO) antenna is designed with two feeding ports. To reduce the mutual coupling between antenna elements, the l-shaped stubs and the defective ground structure (DGS) are used, and additionally the chip resistors are loaded. By optimizing the length of stub, the elements isolation can be improved remarkably. Then, two rectangular slots are etched on the metal ground as DGS to change the path of electric current so as to enhance the isolation further. Also, through loading the chip resistors to control the coupling current on the stubs, the isolation can be strengthened once more. The simulation and measurement results show that this antenna has the mutual coupling of −36 dB, the envelope correlation coefficient (ECC) of 0.002 and the diversity gain (DG) of 9.99 dB at resonance along with the radiant peak gain of 4.03 dBi.

Triple-band stub loaded patch antenna with high gain for 5G Sub-6 GHz, WLAN and WiMAX applications using DGS

Microstrip antennas have become ubiquitous in today's wireless communication world due to their low profile, low cost, and simplicity in fabricating on circuit boards. However, poor performance characteristics, such as limited bandwidth, low power handling capabilities, and low gain, limit their applicability in various instances. Path loss will be substantial in 5th generation (5G) wireless communication due to the utilization of high-frequency bands. A high-gain antenna with a small size is necessary to address this issue. A compact tri-band, slotted monopole antenna with high and consistent gain employing a defected ground plane structure (DGS) has been investigated and implemented in this study. This proposed antenna uses three inverted L-shaped stubs connected to the radiating element to cover the desired bands while keeping the antenna size small. The designed antenna has two key characteristics: (i) wide bandwidth and (ii) reasonable gain. The antenna covers 2.45 and 5.6 GHz WLAN, 2.4 GHz Wi-Fi, 2.5 and 5.2 GHz WiMAX and 3.7 GHz Sub-6 GHz of 5G for mobile communication. The overall substrate size of the antenna is 30 ? 17 ? 1.6 mm3and the electrical dimensions are 0.49 ?L ? 0.28 ?L ? 0.026 ?L, where ?L is the free space wavelength at 2.45 GHz. The measured reflection coefficient (S11 < -10dB) covers 2.4 - 2.52 GHz (bandwidth 112 MHz) and 3.4 - 4.1 GHz (bandwidth 700 MHz) and 5.2 - 6.6 GHz (bandwidth 1359 MHz) with a fractional bandwidth of 5.1 % at lower frequency band, 18.6 % at mid frequency band and 23.7 % at high frequency band. A prototype antenna has also been developed using an inexpensive, low-profile 1.6 mm thick FR-4 (?r = 4.4) substrate. The measured peak gains achieved are 1.35 dB at 2.45 GHz, 2.55 dB at 2.65 GHz and 3.8 dB at 5.5 GHz. The simulated results have been validated against actual experimental measurements, and the outcomes are consistent and match with certainty. The proposed antenna design is very compact and easy to fabricate due to the absence of vias.

Third- and Fifth-Order Mode Compression of a Dipole Antenna

This communication proposes a novel tri-mode wideband dipole antenna with mode compression. Tri-mode operation and wide bandwidth (BW) are obtained by compressing the third- and fifth-order modes simultaneously and combining them with the first-order mode. The third-order mode is compressed using an elliptical loop formed by loading two identical semi-elliptical stubs at the current-null points of the third-order mode. The overlap area and size of the loop play a critical role to compress/shift the mode. Two symmetrical pairs of L-shaped stubs loaded at the second current-null points of the fifth-order mode compress the fifth mode. The amount of compression depends on the stubs’ length. The stub width and position affect the impedance matching. The proposed antenna has an operational BW from 2.75 to 7.43 GHz that equals to 91.9% BW. The peak gain and electrical size are 3.8 dBi and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.32\lambda _{L}\times 0.14\lambda _{L}$ </tex-math></inline-formula> , respectively. The radiation pattern is omnidirectional over the entire impedance BW. A prototype was developed, and the experiments were performed to validate the design concept and computational results. The experimental results are well within the range of the simulation results.

Compact UWB MIMO antenna with dual band-notch characteristics

ABSTRACT This article describes a quad-port ultra-wideband multiple-input multiple-output (MIMO) antenna with dual-band notch characteristics that is very compact and highly isolated. The compactness and high isolation of this design are achieved by etching a modified Minkowski fractal structure and an inverted L-shaped stub made available by the partial ground plane. Simply by incorporating ‘C’- and ‘U’-shaped slots in the radiating patch, it is possible to obtain dual-band rejection characteristics that are very suitable for wireless local area network band and X-band downlink satellite communication of 5.0–5.9 GHz and 7.1–7.9 GHz, respectively, in this proposed structure. The entire design is housed in a very compact size of 30 mm × 30 mm. A few key parameters, such as channel capacity loss (CCL), envelope correlation coefficient (ECC), diversity gain (DG) and total active reflection coefficient (TARC), are examined to ensure that the MIMO system meets its requirements. Furthermore, a mutual coupling value of less than −22 dB and an operating frequency band of 3.1–12 GHz allow the design to be very effective in a multipath channel environment.

High-Isolation wideband MIMO antenna with offset T-Shaped slots for 5G/WLAN applications

A broadband multiple-input multiple-output (MIMO) antenna with high isolation operating in 3.14–5.42 GHz (2.28 GHz, 53.3%) is proposed for 5G smartphones. An offset T-shaped slot with dual functions is employed to improve the bandwidth of one antenna element and enhance the isolation. Then, the double L-shaped stubs are loaded to improve the impedance matching of the other antenna in the MIMO antenna. Finally, the 2 × 2 MIMO antenna is constructed by four T-shaped monopole antennas, two double L-shaped stubs, and two offset T-shaped slots. The proposed MIMO antenna is first simulated and then experimentally tested with a good agreement. High isolation of greater than 15 dB, high antenna efficiency of more than 54%, and low envelope correlation coefficient (ECC) of smaller than 0.08 are realized within 3.14–5.42 GHz. These good performances indicate that the proposed antenna can be applied for MIMO applications in smartphones.

DGS based miniaturized wideband MIMO antenna with efficient isolation for C band applications

Abstract A wideband multiple-input multiple-output (MIMO) antenna for C-band applications is presented in this paper. It consists of 2 × ${\times}$ 1 hexagonal motifs which serves as radiating elements. The side of each hexagonal element is 5.73 mm and the overall dimension of the proposed MIMO antenna is 30 × ${\times}$ 20 × ${\times}$ 1.6 mm3. The hexagonal motifs are embedded on inexpensive FR-4 lossy substrate. Thereafter, a circle with radius 1 mm is etched at the center of each hexagonal motif. Inverted L-shaped stubs are employed to attain efficient isolation between the nearby antenna elements. Four inverted L-shaped stubs are included to further enhance the isolation and eliminate the antenna size increment simultaneously, by suppressing the surface waves. Before using the decoupling approach, the MIMO antenna had an impedance bandwidth of 6.7 GHz and an isolation of −20 dB. The suggested antenna’s impedance bandwidth and isolation are 5.83 GHz and −52 dB, respectively, after using a decoupling approach (inverted L-shaped stub). The proposed MIMO antenna had a peak gain and radiation efficiency of 3–7 dBi and better than 90% (with decoupling), 2.75 to 6 dBi and greater than 60% (without decoupling). To verify the proposed design, a prototype was developed to compare the simulated parameters with the measured one. The envelope correlation coefficient (ECC) was less than 0.05, and channel capacity loss (CCL) less than 0.3 was achieved with DGS. Besides, scattering matrix such as return loss S 11 and transmission coefficient S 21 between two elements, radiation pattern, and current distribution was also favorable. Thus, the proposed MIMO antenna is advantageous to be used for C-band applications such as developing new generation air-borne and space-borne radars, as well as X-band applications.

Compact CPW fed Four Port MIMO Antenna for UWB applications with Wi-Fi/ISM/WLAN Band Notch Characteristics

A compact UWB with WLAN notch-based four-element CPW fed MIMO/diversity antenna is presented in this paper. Multiple elements facilitate the design to transmit and receive the signal from all directions enhancing the channel capacity and diversity performance. The inverted L-shaped stub attached to the ground enhances the impedance bandwidth (10 dB) and provides the UWB response. Plus and cross-shaped decoupling structure is accomplished to diminish the surface current and enhances the isolation between antenna elements and it is more than 20.2 dB from port-1 to port-4 without affecting the impedance bandwidth and radiation pattern. A complimentary split ring resonator (CSRR) in the radiator is utilized to eliminate the Wi-Fi/WLAN band. The |S11| of UWB MIMO antenna varies from 3.26 GHz to 14 GHz which can be utilized in portable, Radar, Satellite, and wireless applications. The simple decoupling structure is used to correlate and isolate the antenna elements, therefore acceptable ECC and CCL parameters are achieved.

Quad-Band Circular Polarized Antenna for GNSS, 5G and WIFI-6E Applications

A quad-band circularly-polarized antenna, for applications of a global navigation satellite system (GNSS), 5G, and WIFI-6E, is designed, fabricated, and measured. The proposed antenna is formed by an L-shaped radiator, a rectangular frame ground with an L-shaped stub, and a rectangular strip at the opposite corner. The microstrip antenna can generate four frequency bands, covering WIFI-6E (5925–7125 MHz), 5G n77 (3300–4200 MHz), n78 (3300–3800 MHz), and the GNSS bands. This antenna generates right hand circular polarization (RHCP) waves in the low frequency band (0.95–2.11 GHz), covering GPS, BDS, GLONASS, and GALILEO applications. Moreover, an L-shaped aperture and three rectangular slits are cut on the ground to broaden the axial-ratio bandwidth at the upper band. A prototype is fabricated and measured to verify the performance of this design. It is shown that the agreement between the simulation and measurement is satisfactorily good. The measured −10 dB bandwidths for each band are 75.8% (0.95–2.11 GHz), 55.8% (3.05–5.39 GHz), 39.9% (5.84–8.19 GHz) and 10.3% (9.14–10.68 GHz), respectively. While the measured 3 dB axial-ratio bandwidths are 59.4% (1.16–2.14 GHz), 35.8% (3.23–4.64 GHz), 8.4% (5.70–6.20 GHz), and 2.6% (7.51–7.71 GHz), the measured gains are 4.56, 2.28, 4.26, and 4.30 dBi at 1.5 GHz, 3.8 GHz, 6 GHz, and 7.6 GHz, respectively.

Design of an Analog RFID-Based Tag Antenna with Opened Circuited L-Shaped Stubs for Applications in Localization

This paper presents a new analog design for a radio-frequency identification (RFID) tag antenna with a long-read range oriented to localization applications. The actual work focuses on the analog input characterization of antenna impedance by studying the capacitive effect, created by the gaps, and the effect of the introduced opened circuited L-shaped stubs, on the RFID tag characteristics. Numerical and measured results confirm that proposed tag antenna performances are significantly improved by introducing gaps and stub structures and after optimizing their dimensions, such as length and width. The introduced stubs with optimum dimensions provide good impedance matching, and improved return loss values. Furthermore, two operating frequency bands have been created when the antenna is excited by a 50 Ω port: a low-frequency band around 837 MHz and a higher one around 927 MHz. These results have been validated by measured ones. The proposed RFID antenna is mainly composed of three split rectangular resonators (SRR) where introduced structures concern only the larger SRR. The optimized antenna has an area of 76 × 24.6 mm2 and is printed on the Taconic RF-60A substrate with a dielectric constant of 6.12, a thickness of 1.6 mm, and a loss tangent of 0.025. Simulation results show interesting communication performances, of the proposed tag antenna, with a return loss of −22.3 dB around 916 MHz and a long-read range up to 25 m when it is fed by an industrial Mping M730 chip with a power sensitivity of −24 dB and an output impedance Zchip = 16 − j194 (Ω) at 916 MHz

A compact high isolation wideband MIMO antenna for multi-band applications

Ultra-wideband (UWB) multiple-input-multiple-output (MIMO) antennas promise a wide range of interesting applications in various radio frequency (RF) systems. However, the prime challenges in realizing such systems include achieving a wider bandwidth, significant isolation between the antennas and compactness. This research demonstrates a compact MIMO antenna having a prominent isolation level for portable UWB applications. The proposed antenna comprises two modified rectangular radiating elements with narrow slots in the ground plane, achieving an enhanced bandwidth from 2.1 to 16.9 GHz covering the S, C, X and Ku bands. Meanwhile, two inverted L-shaped stubs are introduced into the ground structure to obtain a higher isolation greater than 16 dB in the entire spectrum. The proposed antenna is of compact size (36 × 38 mm2) and exhibits excellent performance in terms of return loss, mutual coupling, envelope correlation coefficient (ECC), diversity gain (DG) and total active reflection coefficient (TARC).

Design of Dual-Band Notched UWB Antenna Loaded with Split Ring Resonators for Wide Band Rejection

ABSTRACT Nowadays, the design of a miniaturised ultra-wideband (UWB) antenna with wide dual band-notched characteristics gained widespread demand in wireless communications to reduce interference. The design of a planar CPW-fed circular UWB antenna loaded with split ring resonators and stubs is presented to eliminate two frequency bands. Two symmetrical circular split ring resonators are etched below the CPW feed at the backside of a circular UWB monopole antenna to suppress 3.61 GHz–5.57 GHz (sub-6 GHz band) wideband interference, whereas the 7.06 GHz–8.79 GHz (X-band uplinks and downlinks) band is suppressed by loading two L-shaped stubs. Slots are also made on the patch and ground to enhance impedance matching at a lower resonance frequency. The proposed notch band antenna has a compact size of 38 × 32 × 1.6 mm3 and has the highest gain of 5.75 dB at a frequency of 9 GHz. The parametric analysis has been performed to obtain optimised dimensions for better performance. The designed antenna is simulated, prototyped and tested to validate the antenna design.

A Pattern-Reversal Wideband Antenna Integrating Metal Rings, Diodes-Loaded Stubs and Defective Ground

The pattern reconfigurable antenna provides a new implementation scheme for expanding application in modern wireless communications. In this paper, a pattern-reversal wideband microstrip antenna is proposed. This antenna is composed of a radiation patch with attached rectangular metal rings connected by a microstrip line on the upper layer and a four-defects ground plane connecting two PIN-diodes-loaded L-shaped stubs on the bottom layer. In view of the Yagi-antenna feature of metal rings and L-shaped stubs, the ON-OFF of diodes controls directly the radiation direction of antenna. Under the joint action of multiple resonances of rings, slots and stubs, the bandwidth of antenna is surged so as to develop evident wideband radiation. Finally, the measured impedance bandwidth of -10 dB is about 20.1% from 4.54 to 5.55 GHz. The average gain of the antenna with the size of 0.75&#x03BB;0&#x00D7;0.75&#x03BB;0 reaches 4.92 dBi. With the diodes dependence, the pattern can really deflect in opposite direction. The designed antenna has much advantages, such as low cost, wider band, compact and simple structure along with explicit application scenarios.

A Design of Compact Wideband Antenna Based on Hybridization of Minkowski Fractal Curves on Hexagonal Patch and Partial Ground Plane with Truncated Corners

In this manuscript, a compact wideband antenna using a partial ground plane has been designed by the hybridization of Minkowski fractal curves on the hexagonal radiating patch. Further, the corners of this partial ground plane have been truncated and the Minkowski curves superimposed on each truncated corner. The L shaped stub has been employed to enhance the performance parameters of the antenna in terms of the number of frequency bands and impedance bandwidth. Different prototypes of an antenna have been compared and found that prototype with L-shaped stub and ground plane with truncated corners using Minkowski curve (proposed prototype) exhibits better antenna performance parameters. The proposed prototype of the antenna reveals the maximum bandwidth of 10.86 GHz (140.10%) with four distinct frequency bands 4.4, 7.1, 10.8, 16.3 GHz. Designed antenna has also been fabricated and tested for authentication of simulated results with measured results and found in reasonable agreement with each other. The proposed antenna uses a low-cost FR4 substrate with a compact size of 24 × 30 × 1.6 mm3. Due to the wider bandwidth, stable radiation pattern, and desired gain at the desired frequency points, the proposed antenna can be used for different wireless applications.