Liquid Dielectric Resonator Antenna with Circular Polarization ...https://www.researchgate.net/...Polarization.../Liquid-Dielectric-Resonator-Antenna-With...

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAP.2017.2762005, IEEE Transactions on Antennas and Propagation

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Liquid Dielectric Resonator Antenna with Circular Polarization Reconfigurability Zhe Chen, Student Member, and Hang Wong, Senior Member, IEEE

Abstract—A novel liquid dielectric resonator antenna (LDRA) with circular polarization (CP) reconfigurability is investigated in this communication. The fluidic dielectric for this design is ethyl acetate (εr = 6.6) which is held by a container fabricated by 3D printing technology and excited by a single probe. To realize the CP reconfigurability, the container is designed with two zones: left and right zones. Therefore, the proposed antenna can be switched between two different states: when the liquid solution is injected into the left zone, it can realize left hand circular polarization (LHCP), on the other hand, if the fluidic dielectric is pumped into the right zone, it can obtain right hand circular polarization (RHCP). Consequently, the CP reconfigurability is obtained by flowing liquid control of the ethyl acetate solution. For demonstration, the proposed antenna is design at 2.4 GHz for RFID application with a broad impedance bandwidth (SWR < 2) of 35.6 % which fully cover the wide axial ratio (AR) bandwidth (AR < 3 dB) of 16.3 %. Finally, good agreement is achieved between the measurement and simulation. Index Terms—circular polarization reconfigurable DRA, broadside beam, liquid DRA, 3D printing technology.

I. INTRODUCTION In recent years, owing to the attractive electrical characteristics of reconfigurable antennas [1]-[10] such as frequency tunability, polarization reconfigurability, radiation pattern beam switching control, or combinations of them, reconfigurable antenna technologies are exhibiting outstanding performance in different wireless systems. Thereinto, a reconfigurable antenna based on PIN diodes [1]-[6] is the most traditional design with good property such as agile tuning speed, compact switching system and mature process technology. However, the presence of the PIN diodes also leads to drawback in narrow operating bandwidths and significant power loss which causes a lower radiation efficiency. Recently, liquid metal based [7] and liquid DRA based [8] reconfigurable antennas without using PIN diodes are proposed. Compared to the PIN-diode type reconfigurable antennas, these antennas [7]-[8] would have an enhanced bandwidth and better radiation efficiency. What’s more, the research on liquid based reconfigurable antennas also provides the possibility to explore more novel liquid materials to realize reconfigurability. Polarization reconfigurable antennas have been applied to various of wireless systems due to their prominent contribution to enhance the performance. Some of them can mitigate detrimental fading loss driven by multipath effects in navigation system [9]. Others can effectively increase the Manuscript received 17 March 2017. This project was supported in part by the Research Grant Council of the Hong Kong SAR, China under Project CityU11216915. Zhe Chen and Hang Wong are with the State Key Laboratory of Millimeter Waves, Department of Electronic Engineering, City University of Hong Kong, (email: [email protected]).

capacity and quality of channel in multiple input multiple output (MIMO) system [10]. Moreover, some polarization reconfigurable antennas can provide an efficient modulation scheme in wireless local area networks (WLAN) system [4]. In this communication, we are going to introduce a circular polarization (CP) reconfigurable liquid dielectric resonator antenna (LDRA). For the CP characteristic, the truncated corner liquid dielectric resonator (LDR) [11] is excited by a single probe with radiated Eθ and EΦ components from two orthogonal TEδ11 modes of the LDR. Broadside CP fields can be obtained when Eθ and EΦ components are equal in magnitude but different in phase by 90o. Finally, the proposed LDRA successfully obtains CP reconfigurability with a number of attractive features such as low loss, high radiation efficiency, and simple excitation [12]. This communication introduced a new design by applying fluidic dielectric to realize radiation and reconfiguration. Initially, the liquid solution can be injected into arbitrary side of the container, the LDRA will perform a corresponding CP characteristic (left zone for LHCP, right zone for RHCP). Then the CP reconfigurability is achieved through flowing liquid control of the ethyl acetate solution between the two zones. To the best of our knowledge, this work is the first demonstration of a truncated liquid typed DRA with reconfigurability. Unlike patch, dipole, and slot antennas, the conventional technique of using PIN diode for reconfigurable antennas is hard to apply to the DRA. Since the radiation of the DRA mainly comes from the dielectric resonator excited by a probe or slot, the additional PIN diodes on the DRA will cause unwanted radiation and reduce the radiation efficiency. To devote a new technology for realizing a reconfigurable DRA, we proposed to use the liquid injection method to form DRA. The proposed LDRA integrated with a 3D-printed container providing access for liquid solution to be pumped in and out conveniently. More importantly, it has a wide impedance bandwidth of 35.6 % which fully cover the broad axial ratio bandwidth of 16.3 %. Besides, the proposed CP reconfigurable LDRA has a better radiation efficiency and wider AR bandwidth than most reported reconfigurable antennas with PIN diodes. This communication is organized as follows. Section II introduces the design principle and fabrication of the LDRA. Then the antenna performances are presented in Section III. In section IV, a parametric study of the proposed LDRA was carried out using HFSS. Finally, the conclusion will be drawn in Section V. II. ANTENNA DESIGN AND FABRICATION The resonant frequency of TEδ11 mode of the LDRA is calculated by the formula in [13] and then simulated and optimized by Ansoft HFSS [14].

0018-926X (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.


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a0  2.57  0.8(W / 2H )  0.42(W / 2H )  0.05(W / 2H ) (A3) (A4) a1  2.71(W / 2 H ) (A5) a2 = 0.16 In these formulas, W is the side length of square undersurface of the rectangular DRA and H is the height of DRA. As a result, W = H = 30 mm are obtained by the calculation in terms of the setting of W = H. Since two opposite corners of the rectangular DRA are removed, the effective dielectric constant of the DRA reduces. Therefore, the resonant frequency of the DRA shifts upward. According to the simulation by Ansoft HFSS, the target resonant frequency can be restored by increasing W and H. After optimization, the dimension parameters are listed in Table I. 2

3

y

H

x

εr

H

y Probe

TE δx11

x

y

E-Field H-Field

x

y

TE δx11

TE δx11

Probe

L

H

D

36 mm

22.48 mm

12.73 mm

18 mm

34 mm

120 mm

x To verify two orthogonal electric fields from TE δ11 and

TE1yδ1 modes excited in the LDRA, the resonant electric field distribution of the LDRA was simulated by HFSS. Fig. 2 (a) shows the side view of simulated electric field of STATE 1. It is clearly shows that the fundamental TEδ11 mode is excited. In Fig. 2 (b), the top view of simulated electric field distribution of the LDRA at STATE 1 is shown. Obviously, the electric field in the LDRA rotates clockwise which implies LHCP. Since the antenna structure is symmetrical, the electric field distribution of STATE 2 is not included here for brevity. Fig. 3 shows the configuration of the proposed CP reconfigurable LDRA. Two identical truncated corner LDRs

Probe

Truncated Corner RDRA

Top View

Fig. 1. Fields distribution of a probe excited rectangular DRA and truncated corner DRA.

t=0

t = T/4

t = 3T/4

t = T/2

Z X

Y

X

Y

(a) Side View (b) Top View Fig. 2. Simulated resonant electric field inside the CP reconfigurable LDRA at STATE 1: (a) Side View and (b) Top View. Air Part Liquid DR

Y

Feed

Y X

Ground

X

Top View Air Part Liquid DR Z

L

S

E-Field

TE 1yδ 1

Z X

C

Probe

Side View

Rectangular DRA

TABLE I DESIGN PARAMETERS OF THE PROPOSED LDRA W

E-Field W

H

excited by the probe. By tuning the size of the truncated corner and the position of the probe, 90-degree phase difference between the orthogonal electric fields can be achieved. As a result, a circularly polarized field is realized. According to the target resonant frequency f0 = 2.4 GHz and dielectric constant εr = 6.6 of the fluidic solution, the dimension of the rectangular DRA can be calculated by the following formula [13]: 2  W  f 0   r (A1) F c (A2) F  a0  a1  (W / 2H )  a2  (W / 2 H ) 2

z

z

S

x In Fig. 1, a rectangular DRA is fed by a probe, a TE δ11 mode is excited in the rectangular DRA with the fields distribution shown in top view and side view, which would radiate like a short magnetic dipole in the z-directions. The design in this communication is an extension of a rectangular DRA. To the best of our knowledge, a truncated corner patch antenna can generate circularly polarized radiation. Therefore, a similar design is applied on a DRA. For the truncated corner rectangular DRA (RDAR), a top view with the electric distribution is shown in Fig. 1. Two x orthogonal electric fields from TE δ11 and TE1yδ1 modes are

2

Ground Feed

D

X

Side View

(a) STATE 1 (b) STATE 2 Fig. 3. The two working states of the presented CP reconfigurable LDRA: (a) STATE 1 and (b) STATE 2.

are fed by a single axial probe for exciting the fundamental TEδ11 mode of the LDRA. As shown in Fig. 3 (a), in STATE 1, the liquid solution is injected into the left zone of the container and it will obtain a left hand circular polarization (LHCP). In addition, it will realize a right hand circular polarization (RHCP) when the liquid solution is injected in to the right zone of the container as shown in Fig. 3 (b) of STATE 2. B. Material Selection and Fabrication The liquid dielectric is called ethyl acetate, a kind of organic compound. This liquid dielectric is a sort of non-electrolyte and the feed probe doesn’t have direct contact with the liquid



> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < dielectric. It is applied as a LDRA due to its low cost, low toxicity and stable dielectric constant through the target frequency band. What’s more, the freezing point of ethyl acetate is below -89.3 ℃ . This characteristic provides a possibility for the LDRA to work at low-temperature environment. The measured dielectric constant and loss tangent of the ethyl acetate at different temperature have been investigated in section IV. They were measured by Agilent 85070D Dielectric Probe Kit Product [15]. Considering the additional pipes would affect the performance of the antenna, four pipes are integrated into the skin of the container and provide access for the solution. For convenience, 3D printing technology [16] is introduced for the fabrication of container. Recently, the 3D printing technology has received a surge of attention owing to its attractive performance in fabrication, such as it can provide a possibility to fabricate arbitrary shape in three dimensions with high precision. The 3D printer used for fabricating the container is OBJET30 Scholar. The printed material is VEROBLUE RGD840 (εr = 3.08). In Fig. 4, with four pipes passing through the holes of the gourd, the container is integrated with the ground and fixed by the slot properly. Meanwhile, the glue is used to seal the seam between the container and the ground to prevent the dielectric liquid flowing out. Finally, a SMA connector is launched underneath the ground plane to connect with a feeding probe for antenna excitation. The probe is inserted into the feeding hole to avoid touching the liquid. C. Switch Control Compared to the DC-bias switch control for PIN-diode-type reconfigurable antenna, the CP reconfigurability is achieved through flowing liquid control of the ethyl acetate solution in this design. Therefore, a pump was integrated with the antenna as a practical design in Fig. 5. This is a demonstration of our reconfigurable idea on DRA. In the real application, the switching system will be integrated well with the whole system with a compact design. Firstly, the liquid solution was injected into left side of the container, which is equivalent to STATE 1 for LHCP. As shown in Fig. 5, the two pipes for liquid in/out were connected to the pump and the two pipes for air in/out were connected by a transparent hose. When the pump is turned on, the ethyl acetate solution will be extracted from the left side and injected into the right side until the left side is empty and the right side is filled up. Then the antenna will change to STATE 2 for RHCP. Meanwhile, the pump could also extract the solution back to the left side when reversed signal of the pump is activated through the control of the switching rod of the pump panel. Finally, by changing the control of injection and extraction of the solution, we could realize the antenna to operate at either STATE 1 or STATE 2 accordingly that results in having a CP reconfigurability in this proposed antenna. In addition, there is a speed adjuster which can adjust the speed of the pump and control the switch speed of the antenna. The maximum speed of the pump is 1300 ml/min. Considering

3

Fig. 4. Exploded view of the CP reconfigurable LDRA.

Fig. 5. Photo of the reconfigurable LDRA prototype.

the volume of the truncated LDRA is 26.9 ml. Therefore, the minimum switching time from LHCP to RHCP is 1.2 s. For the DC power consumption of such pump switch system in comparison to a PIN diode switch system, it is explained as below. On one hand, according to the datasheet [17] of the PIN diode used in reference [6], the total power dissipation of a PIN diode is 250 mW. There are 64 PIN diodes used in the polarization reconfigurable antenna in [6], it means that, the total power dissipation of 64 PIN diodes is about 16 W. What’s more, there are some inductance elements in the DC circuit, it means that, the total power dissipation of the DC bias in [6] is more than 16 W. For the electric pump which used in this design, the maximum power consumption is 24 W. It turns out that, the difference of power consumption between these two kinds of reconfigurable antennas is little. On the other hand, when talking about the power consumption, the working time in the different practical applications should be considered. The DC bias system of PIN-diode-type reconfigurable antenna should be kept on during the whole working time, while the pump switching system only needs to be turned on when the antenna needs to be



5

3.0

5

2.5

4

2.5

4

2.0

3

1.5

2

AR (dB) SWR

3.0

SWR

2.0

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2

STATE 1 STATE 2 1.0 1 1.0 1 2.0 2.2 2.4 2.6 2.8 3.0 2.0 2.2 2.4 2.6 2.8 3.0 Frequency (GHz) Frequency (GHz) Simulated SWR Simulated AR Measured AR Measured SWR 0

Fig. 6. The measured and simulated SWR and AR of the LDRA. z

III. ANTENNA PERFORMANCE

B. Radiation Pattern The radiation patterns at 2.4 GHz for the two states are shown in Fig. 7. For the convenience of comparison, the black solid and dash lines are for the simulated LHCP and RHCP and the red solid and dash lines are for the measured LHCP and RHCP, respectively. With the reference of Fig. 7, the measured and simulated results are matched very well. For STATE 1, the LHCP is co-polarization while for STATE 2, the RHCP is co-polarization. Clearly, broadside radiation patterns have been obtained in two states. However, the co-polarization and cross-polarization is asymmetrical and the maximum radiation pattern is slightly shifted. This is caused by the fact that the ground is asymmetrical for either state. Meanwhile, the asymmetric probe feed also contributes to the asymmetrical radiation patterns. As expected, the proposed CP reconfigurable LDRA can achieve broadside radiation patterns in its different operating

x

φ = 90° o LHCP

0 330

330

30

300

60

-30 -20

-10

240

90

-30 -20

210

330

LHCP

LHCP

-30 -20

240

-10

90

60

-30 -20

270

240

120

-10

90

120 210

150

Simulated LHCP

30

300

60

180

150 180 0

RHCP

300

210

90

120

(a) STATE 1

30

270

-10

240

150 180 0

330

60

270

120 210

30 RHCP

300

270

y

0

RHCP

180 (b) STATE 2 Simulated RHCP Measured LHCP

150 Measured RHCP

Fig. 7. The measured and simulated radiation pattern of the LDRA: (a) STATE 1 and (b) STATE 2. 10

100

10

100

8

80

8

80

6

60

6

60

4

40

4

40

2

20

2

20

Efficiency (%) CP Gain (dBic)

A. Standing Wave Ratio Fig. 6 shows the simulated and measured results of the SWR and AR for both two states. It is shown a good agreement between the simulation and measurement. The black solid and dash lines are for simulated and measured SWR and the red solid and dash lines are for simulated and measured AR, respectively. For STATE 1, the LDRA is LHCP. The impedance bandwidth (SWR < 2) is wide enough for covering the axial ratio bandwidth (AR < 3 dB). On the basis of measured results, the effective bandwidth (SWR < 2 & AR < 3 dB) for STATE 1 is 16.7 % from 2.31 to 2.73 GHz. For STATE 2, the LDRA is switched to RHCP. Due to the symmetrical structure of two states, the corresponding results is similar to STATE 1. Based on the measured results, the effective BW is 16.3 % from 2.31-2.72 GHz. Finally, the coincident effective BW for the two states is 16.3 % from 2.31-2.72 GHz.

φ = 0° o

CP Gain (dBic)

To verify the design, the CP reconfigurable LDRA was fabricated and measured by using the optimized parameters. The photo of the prototype is presented in Fig. 5. In the measurement, the standing wave ratio (SWR) of the two states was measured by an Agilent network analyzer 8753, meanwhile, the axial ratio (AR), radiation pattern, realized antenna CP gain, and radiation efficiency of the two states were measured by using a Satimo StarLab system.

z

STATE 1: LHCP 0 2.2 2.4 2.6 2.8 3.0 Frequency (GHz) Simulated CP Gain Measured CP Gain

0 2.0

Efficiency (%)

switched, then it is turned off. Therefore, when the practical application needs a dynamic switching reconfigurable antenna, the PIN-diode-type antenna is suitable. However, when the practical application need a static switching reconfigurable antenna, the pump-switching-type antenna is appropriate. Compared with the bulky integration of a pump, most of the PIN-diode-type reconfigurable antenna should be integrated with battery as shown in [6], it also looks bulky. The size of the pump used in this design is 49× 100 ×68 mm3.

4

AR (dB)

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2 1.5 1 1.0 2.0

εr = 2.5

2.2

εr = 3.0

58 % Around 70% 45-55 % NULL LP: 23.8-31.9 % CP: 22.7-24.5 % NULL

14.6 % 1.8 % NULL 8.8 %

15.4 %

NULL 18 % 25 % 7% LP: 15.5 % CP: 22.6 % 28.6 %

> 70 %

16.3 %

35.6 %

However, the efficiency of these two kinds of reconfigurable antennas should be compared according to different practical applications. For the PIN-diode-type reconfigurable antenna, it is suitable for a dynamic switching system which needs agile switching but not high radiation efficiency. Compared with the PIN-diode-type reconfigurable antenna, this design is great for a system which doesn’t needs dynamic switching but high radiation efficiency. IV. PARAMETRIC STUDY In this design, different kinds of materials and fabrication technologies have been applied. Therefore, the effects of different parameters have been investigated in this section. A. Different Permittivity of Container The permittivity of the container would affect the performance of the antenna. As shown in Fig. 9 the impedance bandwidth (SWR < 2) and AR bandwidth (AR < 3 dB) of the LDRA shift a little from upwards to downwards with the increase of the permittivity of the container. The CP gain and efficiency also shows the same variation trend. However, as the wide impedance bandwidth and AR bandwidth, the antenna

90

4

80

0 3.0

2.4 2.6 2.8 Frequency (GHz)

70 εr = 2.5

0 2.0

2.2

εr = 3.0

εr = 3.5

60 3.0


3.0

6

8

100

6

90

4

80

2

70

4 2.0

3 2

1.5 1 1.0 2.0

2.2

0 3.0


0 330

60

-20

-10

ddd 240

-30

270

-20

60

-10

240

120 210

30

RHCP

300

90

y

φ = 90° o

30

-30

60 3.0

z

LHCP

RHCP

300


x

0 330

2.2

(a)

z

φ = 0° o

0 2.0

Efficiency (%)

2.5

AR (dB) CP Gain (dBic)

5

120

AR bandwidth

150

210

90

150

NULL 180 NULL D = 80 mm D = 160 mm 47 % Fig. 10. (a) Simulated SWR, AR, CP Gain and Efficiency (b) Simulated 45 %-55 % radiation pattern of LDRA with different ground size. 3.0 6 7.5 0.20 >50% 180

(b) D = 120 mm

5

7.0

0.16

6.5

0.12

6.0

0.08

5.5 2.0

2.2

0.04 3.0


2.5 4 2.0

NULL

2 1.5 1 1.0 2.0

2.2


(a) Temp. [ ]

3

AR (dB)

[1] [2] [3] [4]

6

2

εr = 3.5

SWR

Impedance BW

100

Fig. 9. Simulated SWR, AR, CP Gain and Efficiency with different permittivity of container.

Dielectric Constant

AR BW

0.3 %

3

Loss Tangent

Radiation Eff.

[6] Our work

2.0

270

Ref.

8

Efficiency (%)

SWR

4

AR (dB) CP Gain (dBic)

2.5

TABLE II COMPARISON FOR ANTENNA PERFORMANCE

[5]

6 5

SWR

based on the measured results in Fig. 11 at room temperature. It was measured by Agilent 85070D Dielectric Probe Kit Product [15]. By using this method, the accuracy is provided in [15] by the Agilent as ± 5% for dielectric constant and ± 0.05 for loss tangent. Consequently, the difference between the measured and simulated results is acceptable. With reference to the gray area in Fig. 8, for both two states, the measured LHCP and RHCP gains are 5 and 5.5 dBic, respectively, across the effective BW. Meanwhile, the radiation efficiencies of both two states are over 70 % across the effective frequency band. As key performance of the reconfigurable antennas, radiation efficiency has attracted much attention. As mentioned in the introduction, due to the presence of the PIN diodes, the antenna may have a lower radiation efficiency. The comparison between the reported reconfigurable antennas and the proposed antenna for radiation efficiency is shown in Table II. It is clear that, the radiation efficiency is higher than most reported reconfigurable antennas realized by PIN diodes. In the further research, for the liquid with appropriate dielectric constant, the radiation efficiency can be further increased with low-loss dielectric fluids.

5

0 3.0

(b) -10

0

10

15

20

25

Fig. 11. Measured permittivity and loss tangent of the liquid and corresponding simulated SWR and AR at different temperature.

still can cover the target frequency band properly. For the variation trend of the SWR and AR, it can be explained by the formula A1 in II-A. When εr increases, f0 will decrease, and vice versa (provided that F and W unchanged). B. Ground Size Selection To select the ground plane size, the performances of the LDRA with different D (D is the diameter of the ground plane as shown in Fig. 3) were studied. In Fig. 10 (a), when the ground plane size increases, the impedance bandwidth does not change. Although the AR bandwidth may be narrower due to the change of ground size, the achieved AR bandwidth still covers the targeted frequency range. The CP gain of the antenna goes up with the ground plane size. This is due to beamwidths of the radiation pattern narrowed, as shown in Fig. 10 (b).



> REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < To select an appropriate ground size, AR, SWR, and gain performances of the antenna should be considered. Therefore, the diameter of the ground size D = 120 mm is chosen to optimal above electrical characteristics of the antenna. C. Temperature Effect The dielectric constant and lost tangent of the ethyl acetate at the temperature of -10 ℃, 0 ℃, 10 ℃, 15 ℃, 20 ℃, and 25 ℃ are measured and the results are shown in Fig 11 (a). Clearly, the dielectric constant and loss tangent of the liquid decrease slightly with temperature increased. In addition, the simulated SWR and AR results with corresponding permittivity and loss tangent of the liquid at -10 ℃, 10 ℃, and 25 ℃ are shown in Fig. 11 (b). The SWR is insensitive to the temperature change. This is due to the broadband property of the antenna and stable permittivity of the liquid. The AR would shift slightly to higher frequencies when the temperature increased. From the obtained result, this proposed antenna can operate with wide impedance bandwidth as well as the AR bandwidth even the temperature is varied. The ethyl acetate is volatile at room temperature and has a boiling point of 77 ℃. However, in this design, the ethyl acetate is stored in an enclosure space. Therefore, the vaporization would not affect the performance. In general, the hermetically sealed structure design and broadband property of the antenna, together with the natural low freezing point and stable permittivity characteristic of the liquid, provide additional robustness for this liquid DRA.

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

V. CONCLUSION A novel CP reconfigurable LDRA has been investigated. The proposed LDRA successfully demonstrate how to realize switch ability between LHCP and RHCP by flowing liquid control of the ethyl acetate solution pumping in and out between the two zones of the 3D printed container. Good agreement between the measured and simulated results have been obtained. The antenna obtained a broadband characteristic with the wide operating bandwidth of 35.6 % ranged from 2.08 to 2.98 GHz which fully cover the wide 3dB AR bandwidth of 16.3 % ranged from 2.31 to 2.72 GHz. As expected, the CP reconfigurability is achieved in two states across the working bandwidth. Moreover, it has a better radiation efficiency and wider AR bandwidth than most reported reconfigurable antennas with the PIN diodes. For the potential application, the proposed LDRA could be applied as a reader antenna for RFID system in one CP state and as a Wi-Fi hotspot with another CP state. According to the good CP polarization reconfigurability across a wide AR bandwidth, the proposed antenna can be applied as a receive antenna in the mobile satellite communication system in vehicle.

6

[11]

[12] [13] [14]

[15]

[16] [17]

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ACKNOWLEDGMENT This project was supported in part by the Research Grants Council of the Hong Kong SAR, China (Project No. CityU 11216915).
