Differential Fabry–Perot Resonator Antennas

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4438 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 9, SEPTEMBER 2013 Differential Fabry–Perot Resonator Antennas Kai Lu and Kwok Wa Leung, Fellow, IEEE Abstract—The differential Fabry–Perot resonator (FPR) an- tenna is investigated for the rst time. It has advantages of suppressing the cross polarization and enabling integration with differential circuits. Its basic structure consists of two vertical parallel metal plates, which are connected by a horizontal ground plane. The differential FPR antenna is fed by a pair of differential -probes protruding from the ground plane. It is found that the basic differential FPR antenna has considerable sidelobes in the -plane. To suppress the sidelobes, a modied differential FPR antenna is proposed which has a pair of ridges at each side-opening of the parallel plates. In addition, a second modied differential FPR antenna is also proposed to reduce undesirable backward radiation. The second modied antenna has a pair of ridges placed at the top of each metal plate. It is found that all of the basic and modied antennas have low cross polarizations. The two modied differential FPR antennas were fabricated and measured, and the measurements agree reasonably well with HFSS simulations. The rst and second modied antennas have calibrated measured gains of 14.2 dBi and 15.4 dBi, respectively, with measured 10-dB impedance bandwidths of . Index Terms—Backward radiation reduction, cutoff structure, differential antennas, Fabry–Perot resonator antennas, sidelobe suppression. I. INTRODUCTION O WING to the advantages of its high directivity, high efciency, low prole and ease of fabrication, the Fabry–Perot resonator (FPR) antenna has received tremendous attention in the last decade [1]–[5]. A conventional FPR an- tenna has a metal ground plate and a parallel partially reective plate, along with a primary radiator. Its resonance frequency is determined by the separation between the parallel plates [5]. To improve the performance of the FPR antenna, some design techniques have been introduced to the ground plane and partially reective surface. For example, an articial magnetic conductor or high impedance surface has been used in place of the metal ground plane to reduce the antenna height [6]–[8]. To broaden the bandwidth, the partially reective surface can have non-uniform patterns [9], [10], multi-layer structures [11], or even non-planar shapes [12]. Usually, the partially reective surface of a FPR antenna has a very high reectivity (smaller than but close to 1), resulting in a highly directional radiation pattern with a narrow beam [2], [4]. For mobile Manuscript received July 25, 2012; revised March 30, 2013; accepted June 03, 2013. Date of publication June 07, 2013; date of current version August 30, 2013. This work was fully supported by a GRF research grant from the Research Grants Council of Hong Kong SAR, China (Project No.: CityU 116609). The authors are with the State Key Laboratory of Millimeter Waves and De- partment of Electronic Engineering, City University of Hong Kong, Kowloon, Hong Kong. (e-mail: [email protected]; [email protected]). Color versions of one or more of the gures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identier 10.1109/TAP.2013.2267196 communications, however, a broad-beam [13] or fan-beam [14] antenna can provide larger coverage than a narrow-beam [15] antenna and should therefore be more attractive. Over the past years, some FPR antennas with moderate gains have been proposed [6], [16]–[18], such as fan-beam FPR antennas with rectangular radiating apertures [17], [18]. The beam solid angles of the antennas in [16] and [17] are 650 (25 26 ) and 576 (12 48 ), respectively, where the superscript is the square degree of a solid angle [19]. However, it is dif- cult to obtain a larger solid angle from the conventional FPR antenna because of its inherent narrow-beam characteristic. To broaden the beamwidth, a new class of FPR antennas has been recently proposed [20], which can provide a wider beam solid angle of 896 (16 56 ). The new FPR antenna has two vertical parallel metal plates, which are connected by a horizontal ground plane. The strongest radiation direction of this FPR antenna is normal to the ground plane, instead of the parallel plates as found in a conventional FPR antenna. Since the new FPR antenna simply employs solid conducting plates instead of partially reective plates, its design and fabrication are very much easier than for the conventional FPR antenna. The differential signaling technique is widely used in modern radio-frequency/microwave circuit designs because it can pro- vide high signal-to-noise ratios. Also, it can improve radiation patterns when applied to antennas, such as reduce the cross-po- larized eld [21] and eliminate the tilting angle [22]. Further- more, it enables direct integration of antennas with differential circuits. As a result, a number of differential antennas have been investigated over the last decade [21]–[27]. In this paper, the differential FPR antenna is investigated for the rst time. The basic differential FPR antenna is based on the recently proposed design [20]. This generic structure, however, undesirably produces signicant sidelobes in the -plane. To suppress the side lobes, a modied differential FPR antenna is introduced which has a pair of ridges fabricated at each side- opening of the parallel plates. The modied antenna can reduce the sidelobe level at by about 22 dB. For a unidirectional antenna, it is desirable to reduce its backward radiation to avoid wasting energy. An approach in achieving this is to make the main beam more directional. In general, this can be done by enlarging the radiating aperture, which can be realized in [20] by increasing the spacing between the parallel plates. However, changing the spacing will also affect the operating frequency of the FPR antenna. In this paper, a second modied differential FPR antenna for suppressing backward radiation is also introduced. It has a pair of ridges located at the top of the parallel plates. The spacing between the top ridges is wider than that between the parallel plates to provide a larger radiating aperture. Since it is needless to change the spacing between the parallel plates, there is no virtual effect on the resonance frequency of the FPR antenna. 0018-926X © 2013 IEEE

Transcript of Differential Fabry–Perot Resonator Antennas

4438 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 9, SEPTEMBER 2013

Differential Fabry–Perot Resonator AntennasKai Lu and Kwok Wa Leung, Fellow, IEEE

Abstract—The differential Fabry–Perot resonator (FPR) an-tenna is investigated for the first time. It has advantages ofsuppressing the cross polarization and enabling integration withdifferential circuits. Its basic structure consists of two verticalparallel metal plates, which are connected by a horizontal groundplane. The differential FPR antenna is fed by a pair of differential-probes protruding from the ground plane. It is found that thebasic differential FPR antenna has considerable sidelobes in the-plane. To suppress the sidelobes, a modified differential FPR

antenna is proposed which has a pair of ridges at each side-openingof the parallel plates. In addition, a second modified differentialFPR antenna is also proposed to reduce undesirable backwardradiation. The second modified antenna has a pair of ridges placedat the top of each metal plate. It is found that all of the basic andmodified antennas have low cross polarizations. The two modifieddifferential FPR antennas were fabricated and measured, andthe measurements agree reasonably well with HFSS simulations.The first and second modified antennas have calibrated measuredgains of 14.2 dBi and 15.4 dBi, respectively, with measured 10-dBimpedance bandwidths of .

Index Terms—Backward radiation reduction, cutoff structure,differential antennas, Fabry–Perot resonator antennas, sidelobesuppression.

I. INTRODUCTION

O WING to the advantages of its high directivity, highefficiency, low profile and ease of fabrication, the

Fabry–Perot resonator (FPR) antenna has received tremendousattention in the last decade [1]–[5]. A conventional FPR an-tenna has a metal ground plate and a parallel partially reflectiveplate, along with a primary radiator. Its resonance frequencyis determined by the separation between the parallel plates[5]. To improve the performance of the FPR antenna, somedesign techniques have been introduced to the ground plane andpartially reflective surface. For example, an artificial magneticconductor or high impedance surface has been used in place ofthe metal ground plane to reduce the antenna height [6]–[8].To broaden the bandwidth, the partially reflective surface canhave non-uniform patterns [9], [10], multi-layer structures[11], or even non-planar shapes [12]. Usually, the partiallyreflective surface of a FPR antenna has a very high reflectivity(smaller than but close to 1), resulting in a highly directionalradiation pattern with a narrow beam [2], [4]. For mobile

Manuscript received July 25, 2012; revised March 30, 2013; accepted June03, 2013. Date of publication June 07, 2013; date of current version August 30,2013. This work was fully supported by a GRF research grant from the ResearchGrants Council of Hong Kong SAR, China (Project No.: CityU 116609).The authors are with the State Key Laboratory of Millimeter Waves and De-

partment of Electronic Engineering, City University of Hong Kong, Kowloon,Hong Kong. (e-mail: [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TAP.2013.2267196

communications, however, a broad-beam [13] or fan-beam[14] antenna can provide larger coverage than a narrow-beam[15] antenna and should therefore be more attractive. Overthe past years, some FPR antennas with moderate gains havebeen proposed [6], [16]–[18], such as fan-beam FPR antennaswith rectangular radiating apertures [17], [18]. The beam solidangles of the antennas in [16] and [17] are 650 (25 26 )and 576 (12 48 ), respectively, where the superscriptis the square degree of a solid angle [19]. However, it is diffi-cult to obtain a larger solid angle from the conventional FPRantenna because of its inherent narrow-beam characteristic.To broaden the beamwidth, a new class of FPR antennas hasbeen recently proposed [20], which can provide a wider beamsolid angle of 896 (16 56 ). The new FPR antenna hastwo vertical parallel metal plates, which are connected by ahorizontal ground plane. The strongest radiation direction ofthis FPR antenna is normal to the ground plane, instead of theparallel plates as found in a conventional FPR antenna. Sincethe new FPR antenna simply employs solid conducting platesinstead of partially reflective plates, its design and fabricationare very much easier than for the conventional FPR antenna.The differential signaling technique is widely used in modern

radio-frequency/microwave circuit designs because it can pro-vide high signal-to-noise ratios. Also, it can improve radiationpatterns when applied to antennas, such as reduce the cross-po-larized field [21] and eliminate the tilting angle [22]. Further-more, it enables direct integration of antennas with differentialcircuits. As a result, a number of differential antennas have beeninvestigated over the last decade [21]–[27].In this paper, the differential FPR antenna is investigated for

the first time. The basic differential FPR antenna is based on therecently proposed design [20]. This generic structure, however,undesirably produces significant sidelobes in the -plane. Tosuppress the side lobes, a modified differential FPR antenna isintroduced which has a pair of ridges fabricated at each side-opening of the parallel plates. The modified antenna can reducethe sidelobe level at by about 22 dB.For a unidirectional antenna, it is desirable to reduce its

backward radiation to avoid wasting energy. An approach inachieving this is to make the main beam more directional. Ingeneral, this can be done by enlarging the radiating aperture,which can be realized in [20] by increasing the spacing betweenthe parallel plates. However, changing the spacing will alsoaffect the operating frequency of the FPR antenna. In this paper,a second modified differential FPR antenna for suppressingbackward radiation is also introduced. It has a pair of ridgeslocated at the top of the parallel plates. The spacing betweenthe top ridges is wider than that between the parallel platesto provide a larger radiating aperture. Since it is needless tochange the spacing between the parallel plates, there is novirtual effect on the resonance frequency of the FPR antenna.

0018-926X © 2013 IEEE

LU AND LEUNG: DIFFERENTIAL FABRY–PEROT RESONATOR ANTENNAS 4439

Fig. 1. Configuration of basic differential FPR antenna. (a) Side view. (b) Topview.

In this study, ANSYS HFSS was used to simulate the basicandmodified differential FPR antennas. Parametric studies weredone to characterize the two modified FPR antennas. The mod-ified antennas were fabricated and measured, and reasonableagreement between the measured and simulated results was ob-served. The basic differential FPR antenna will be investigatedin the next section first, whereas the modified designs will bepresented in Sections III and IV.

II. BASIC DIFFERENTIAL FPR ANTENNA

Fig. 1 shows the configuration of the basic differential FPRantenna. With reference to the figure, two vertical parallel metalplates having a separation of are connected by a horizontalmetal plate that functions as the ground plane of the antenna.Each vertical plate has a length of , a height of , and a thick-ness of . The thickness of the ground plane is . To ex-cite the FPR antenna, a pair of differential -probes protrudefrom the ground plane. The probes are placed back-to-back witha separation of . For each -probe, the vertical- and hori-zontal-arm lengths are given by and , respectively. TheFPR antenna can be fabricated from a single metal block. It wasfound that the antenna performance is not sensitive to the thick-nesses , , therefore thick metal plates can be used to obtaina robust antenna structure. It is worth mentioning that the radi-ation mechanism of this FPR antenna is different from that ofa conventional one. For a conventional FPR antenna, the waveis leaked through the partially reflective plate and the strongestradiation direction is normal to the plate. However, for our pro-posed antenna, the radiation takes place at the opening of the

Fig. 2. Simulated radiation patterns of the basic differential FPR antenna at24.1 GHz: , , , ,

, , , and .

structure, with the strongest radiation direction being parallel tothe parallel plates.Ideally, a FPR with an infinite plate size will resonate when

the spacing is equal to a multiple of half-wavelength [28, p.329], or

(1)

where and are the resonance frequency and wavelength,respectively, and is the speed of light in vacuum. The funda-mental FPR mode is considered in this study and therefore the-oretically . However, since practically a finite platesize is used, an approximate relationship of is foundin our designs.As a demonstration, a basic differential FPR antenna is de-

signed using HFSS. It operates at 24 GHz for ISM-band (in-dustrial, scientific and medical) applications (24.0–24.25 GHz).Fig. 2 shows the simulated radiation pattern of the optimizedbasic differential FPR antenna operating at 24.1 GHz. With ref-erence to the figure, very low cross-polarized fields are obtainedas a result of using the differential feed. However, strong side-lobes around are observed in the -plane and a tech-nique to reduce them is needed.

III. MODIFIED DIFFERENTIAL FPR ANTENNA FOR SIDELOBESSUPPRESSION

To reduce the sidelobe, first note that for the fundamentalmode ( ), we have

(2)

when a finite plate size is used. It is interesting to note thatis also the -mode cutoff frequency of a parallel-plate wave-guide with a plate separation of [28, p. 118]. Therefore, theproposed antenna can be viewed as a parallel-plate waveguideantenna operating near the cutoff frequency of the mode.Given the same operating frequency, the wave will be cut offif the plate separation is reduced. Based on this observation,

4440 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 9, SEPTEMBER 2013

Fig. 3. Configuration of the modified differential FPR antenna. (a) Side view.(b) Front view. (c) Top view.

a pair of ridges can be placed at each side-opening of the par-allel plates to obtain the cutoff effect in the ridge region. Sincethe wave will be attenuated near each side-opening, radiationfrom the side-opening can be suppressed and, thus, the side-lobes can be reduced. Fig. 3 shows the modified differentialFPR antenna with a pair of ridges at each side-opening. Eachridge has a length of and a thickness of . Compared witha TEM-mode parallel plate waveguide antenna, the proposedantenna has a much lower sidelobe.To validate the idea, field distributions of the original and

modified differential FPR antennas were simulated and the re-sults are compared in Fig. 4. With reference to Fig. 4(a), theoriginal FPR antenna has considerable fields near each side-opening. But after the side ridges are added (Fig. 4(b)), the fieldgradually decays in the ridge region and becomes very weak ateach side-opening. In this case, the field mainly concentrates atthe central region.The modified differential FPR antenna is also designed to

operate at 24 GHz for ISM-band applications. Each parallel

Fig. 4. Simulated -field plots (side view) of the basic and modified differen-tial FPR antennas at 24.1 GHz: , , ,

, , and . (a) Basic differential FPRantenna: and . (b) Modified differential FPRantenna: , , , and .

plate has a size of 50 25 ( ) and a thick-ness of . The ground plane has a thickness of .A commercial 3-dB 180 hybrid coupler was used to providethe differential signals for far-field measurements. For all thedesigns in this paper, the distance between the two -probeswas given by , which was determined by theport separation of the commercial hybrid coupler. Other param-eters including the ridge were optimized as ,

, , and . At themid-frequency of 24.125 GHz, the free-space wavelength isgiven by and therefore the separation betweenthe two parallel plates should be ideally . Butdue to the effects of the probe loading and finite plate size, theoptimal was found to be 6.60 mm, which was 5.8% higherthan the ideal value (6.22 mm).

A. Results and Discussions

The modified differential FPR antenna was fabricated andmeasured. Its photos are given in Fig. 5.In this paper, the differential reflection coefficient was

measured using an Agilent E8361A vector network analyzer,whereas the radiation pattern and antenna gain were measuredusing an NSI 700S-20 near-field measurement system.Fig. 6 shows the measured and simulated of the modi-

fied differential FPR antenna, which were obtained by using thefollowing odd-mode formula [21]:

(3)

LU AND LEUNG: DIFFERENTIAL FABRY–PEROT RESONATOR ANTENNAS 4441

Fig. 5. Photos of the modified differential FPR antenna. (a) Perspective view.(b) Top view. The parameters are the same as in Fig. 4(b).

Fig. 6. Measured and simulated differential reflection coefficients of the mod-ified differential FPR antenna. The parameters are the same as in Fig. 4(b).

With reference to the figure, reasonable agreement be-tween the measured and simulated results is observed.The measured and simulated 10-dB impedance bandwidths( ) are (23.90–24.49 GHz) and

(23.91–24.29 GHz), respectively, entirely coveringthe 24-GHz ISM band (1.04%, 24.0–24.25 GHz).As mentioned before, a commercial 3-dB 180 hybrid

coupler was used in the far-field measurements. Fig. 7 showsthe measured and simulated radiation patterns at 24.1 GHz. Itshould be mentioned that the measured radiation patterns aregiven in the upper half plane only as limited by the NSI system.With reference to figure, the measured 3-dB beamwidths ofthe - and -plane results are given by 19 and 67 (beamsolid angle: ), respectively. The measuredco-polarized field is stronger than the cross-polarized coun-terpart by in the boresight direction ( ). It isworth mentioning that the simulated cross-polarized fields aretoo small to be observed from the figure. With reference tothe figure, however, the simulated backward radiated fields arequite significant for the -plane result. It is caused by the factthat the -plane radiation pattern is rather broad due to thenarrow plate separation . Increasing can reduce the -planebeamwidth but will then change the operating frequency as

. A viable method that alleviates the problem will bediscussed in the next section.The level of the cross-polarized field in the diagonal plane

was also studied, with the cross-polarized field defined usingLudwig’s third definition [15], [29]. Fig. 8 shows the diagonal

Fig. 7. Measured and simulated radiation patterns of the modified differen-tially FPR antenna at 24.1 GHz. The parameters are the same as in Fig. 4(b). (a)-plane. (b) -plane.

Fig. 8. Simulated radiation pattern of the modified differentially FPR antennain the diagonal plane at 24.1 GHz. The parameters are the same as in Fig. 4(b).(a) Top view of the structure showing the cut of the diagonal plane. (b) Simulatedradiation pattern.

plane and the simulated radiation pattern. As can be observedfrom the figure, the co-polarized pattern is very similar to that ofthe -plane result. Again, the cross-polarized field is very weak.It is at least 30 dB weaker than the maximum co-polarized field,showing the effectiveness of the differential excitation.The measured and simulated antenna gains in the boresight

direction are shown in Fig. 9. With reference to the figure, themaximum measured gain of 11.7 dBi is found at 24.3 GHz.However, a much higher simulated antenna gain of 14.0 dBiis found at this frequency. The difference of 2.3 dB betweenthe measured and simulated results is mainly caused by theloss of the hybrid coupler. Let and be the insertionloss (0 output port) and coupling factor (180 output port)of the hybrid coupler, respectively [30], then ideally we have

and . In re-ality, however, both and are less than due toloss of the coupler, and is usually not equal to180 . The following calibration formula for the gain measure-ment was used to take the loss and unbalance into account:

(4)

where and are the calibrated and original measured an-tenna gains, respectively. The derivation of (4) is very straight-

4442 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 9, SEPTEMBER 2013

Fig. 9. Measured and simulated antenna gains of the modified differential FPRantenna. The parameters are the same as in Fig. 4(b).

forward and is therefore not included here for brevity. For easeof comparison, the calibrated gain is also plotted in Fig. 9. Fromthe figure, it can be seen that the simulated and calibrated mea-sured gains are in good agreement.The two differential -probes have been placed back-to-back

in this design. It is also possible to place the two -probesface-to-face. The latter case has also been simulated and the re-sult is somewhat similar to that of the former one. Practically,however, the back-to-back design should be more useful sinceit allows a wider range of probe separation .

B. Parametric Study

A parametric study was carried out to characterize the dif-ferential FPR antenna. The effect of the side ridges on the an-tenna performance is discussed first. Fig. 10(a) shows the effectof the ridge thickness on the differential reflection coeffi-cient. With reference to the figure, introducing the ridges shiftsthe resonance frequency upward from 23.85 GHz to 24.09 GHz,which can be expected since adding the ridges reduces the cen-tral resonance volume (it is well known that a smaller resonatorhas a higher resonance frequency). It can be observed from thefigure that the ridge thickness does not affect the resonancefrequency significantly because it can hardly change the cen-tral resonance volume. Fig. 10(b) shows the effect of on the-plane radiation pattern. The -plane result is not shown here

because it was found that the side ridges have negligible effectson it. As can be observed from the figure, the side ridges sub-stantially reduce the sidelobe level from 4.7 dB to at

when . But the sidelobe level converselyincreases as increases further, which should be due to strongdiffractions when large side ridges are used. With reference tothe figure, satisfactory sidelobe levels can be obtained at both

and by using , which is there-fore used in our prototype design.Fig. 11(a) shows the effect of the ridge length on the differ-

ential reflection coefficient. With reference to the figure, the res-onance frequency increases with because the central volumedecreases as increases. Fig. 11(b) shows the effect ofon the -plane radiation pattern. As can be observed from the

Fig. 10. Simulated differential reflection coefficients and co-polarized -planeradiation patterns of the modified differential FPR antenna as a function of ele-vation angle for different side-ridge thickness of , 0.5, 1.0, and 2.0mm. Other parameters are the same as in Fig. 4(b). (a) Differential reflectioncoefficients. (b) Co-polarized -plane radiation patterns.

figure, the sidelobe level monotonically decreases with an in-crease of . This is expected because a larger provides alonger attenuation path and, thus, the wave becomes weaker atthe side-openings. It can also be observed from the figure thatthe beamwidth increases with an increase of . This is, again,expected because increasing effectively shortens the radi-ating aperture along -direction, leading to a broader radiationpattern and a wider beamwidth.The effect of the -probe separation on the antenna per-

formance is also studied. It was found that the impedance leveland radiation pattern are insensitive to . This is a positive re-sult because it can increase the flexibility of the circuit layout.

IV. SECOND MODIFIED DIFFERENTIAL FPR ANTENNA FORSUPPRESSING BACKWARD RADIATION

In this section, a second modified design is investigated tosuppress backward radiation.

A. Antenna Configuration

Fig. 12 shows the configuration of the second modified dif-ferential FPR antenna. With reference to the configuration, the

LU AND LEUNG: DIFFERENTIAL FABRY–PEROT RESONATOR ANTENNAS 4443

Fig. 11. Simulated differential reflection coefficients and co-polarized -planeradiation patterns of the modified differential FPR antenna as a function of el-evation angle for different side-ridge lengths of , 3.0, 6.0, and 9.0mm. Other parameters are the same as in Fig. 4(b). (a) Differential reflectioncoefficients. (b) Co-polarized -plane radiation patterns.

new design has a pair of ridges located at the top of the par-allel plates. Each top ridge has a thickness of and a heightof from the top of the original parallel plate. When the par-allel plates are very long (i.e., is very large), the -mode-field of a parallel-pate waveguide can be approximated by

(5)

where is the aperture field at the top of the parallel platesand is its constant amplitude. Since the -plane backwardradiation is much stronger than the -plane counterpart (seeFig. 7), only the former is suppressed in our design. With theaperture field given by (5), the new aperture width can becalculated as [31]

(6)

where is the beamwidth between first nulls of an -planefield pattern. To avoid having sidelobes in the upper half plane,the first nulls are set at , giving . At 24.1GHz, we have and thereforefrom (6). The width of the top ridge is then given by

, which is the initial design value.

Fig. 12. Configuration of the second modified differential FPR antenna. (a)Side view. (b) Front view. (c) Top view.

We do not expect this initial value to be very accurate because ofthe rough analysis. For example, (6) requires the aperture fieldto be equiphase but obviously this condition is not satisfied atthe plane due to the discontinuity at . UsingHFSS, the optimized values of and were found to be 4.0mm and 6.0 mm, respectively. Other parameters of this designremain the same as before.To verify the idea, -field distributions of the first and second

modified designs are shown in Fig. 13. With reference to thefigure, the top ridges of the second modified design effectivelyconcentrate the energy over the top of the antenna, leading to areduction of backward radiation.

B. Result and Discussion

The second modified differential FPR antenna was fabricatedand measured. Its photos are shown in Fig. 14.

4444 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 61, NO. 9, SEPTEMBER 2013

Fig. 13. Simulated -field plots (front view) of the differential FPR antennaswithout and with top ridges at 24.1 GHz: , ,

, , , , ,, , and . (a) ,

(no top ridges). (b) , .

Fig. 14. Photos of the second modified differential FPR antenna. (a) Perspec-tive view. (b) Top view: The parameters are the same as in Fig. 13(b).

Fig. 15 shows the measured and simulated differential reflec-tion coefficients of this modified antenna. As can be found fromthe figure, the measured and simulated impedance bandwidthsare given by (23.90–24.46 GHz) and (23.93–24.30 GHz), respectively. The results are nearly the same asthose of Fig. 6, indicating that the top ridges do not affect theimpedance matching. The result is very positive.Fig. 16 shows the measured and simulated - and -plane

radiation patterns of the second modified antenna at 24.1 GHz.With reference to the figure, the -plane backward field is nowsignificantly suppressed as compared with those of the basic

Fig. 15. Measured and simulated differential reflection coefficients of thesecond modified differential FPR antenna. The parameters are the same as inFig. 13(b).

Fig. 16. Measured and simulated radiation patterns of the second modified dif-ferential FPR antenna at 24.1 GHz. The parameters are the same as in Fig. 13(b).(a) -plane. (b) -plane.

and first modified designs. As shown in the figure, the measured3-dB beamwidth of the -plane result is found to be 45 , whichis 22 less than that of the first modified antenna. However, themeasured 3-dB beamwidth of the -plane result remains un-changed at 19 (beam solid angle: ). With ref-erence to the figure, the measured co-polarized field is strongerthan its cross-polarized counterpart by in the boresightdirection. The simulated cross-polarized fields are too weak tobe observed from the figure.Fig. 17 shows the measured and simulated antenna gains in

the boresight direction. Both direct and calibrated measure-ments are shown in the figure. With reference to the figure,the simulated result and the calibrated measured result are inreasonable agreement. The maximum calibrated measured gainof 15.4 dBi is found at 24.3 GHz. This peak gain is 1.2 dBhigher than that of the first modified antenna, which is expectedbecause the second modified antenna suppresses unwantedbackward radiation.

C. Parametric Study of the Top Ridge

Fig. 18 shows the effect of the ridge width on the -planeradiation pattern. As compared with the case without any top

LU AND LEUNG: DIFFERENTIAL FABRY–PEROT RESONATOR ANTENNAS 4445

Fig. 17. Measured and simulated antenna gains of the second modified differ-ential FPR antenna. The parameters are the same as in Fig. 13(b).

Fig. 18. Simulated co-polarized -plane radiation patterns of the second mod-ified differential FPR antenna as a function of elevation angle for differenttop-ridge widths of , 2.0, 4.0, and 6.0 mm. Other parameters are thesame as in Fig. 13(b).

ridges ( ), the top-ridge designs with and4 mm can suppress backward radiation substantially. Also,the top-ridge designs have narrower beamwidths. It is becausethe aperture width, which is inversely proportional to thebeamwidth as seen from (5), can be made wider by using thetop ridges. For example, when there are no ridges, the aperturewidth is equal to the distance ( ) between the twoparallel plates. But the aperture width significantly increasesto for the top-ridge case with .However, as increases, the aperture width decreases andthe beamwidth will conversely increase. It can be noted fromthe figure that the backward radiation undesirably increases asincreases from 4 mm to 6 mm. It is because increasing

reduces the size of the radiation aperture and, thus, broadensthe beamwidth, leading to increased backward radiation.A parametric study of the top ridge height was carried out.

Four cases of , 3, 6, and 9 mm were simulated. It wasfound that the beamwidth of the -plane radiation pattern de-creases as increases until reaches 6.0 mm. A further in-crease of to 9 mm has no significant effect on the beamwidth.

The effects of the top ridge dimensions on the impedance leveland -plane radiation pattern were also investigated. It wasfound that the effects are negligible.

V. CONCLUSION

The differential FPR antenna has been investigated for thefirst time. It is fed by a pair of back-to-back -probes, withthe differential signals provided by an external hybrid coupler.By using the differential feed, the cross-polarized field can besuppressed substantially. The basic differential FPR antenna issimple in structure, but it produces large undesirable sidelobes.To solve this problem, a pair of side ridges have been introducedat each side-opening of the parallel plates. Since the plate sep-aration of the ridge region is effectively reduced, a cutoff phe-nomenon occurs and the wave is attenuated as it passes throughthe ridges. Consequently, the field reaching the side-opening isweakened and the sidelobe level can therefore be reduced. Thismodified differential FPR antenna was simulated using HFSS.A hardware prototype was fabricated and measured, and rea-sonable agreement between the measured and simulated resultshas been observed. It has been found that by using the modifieddifferential antenna, the sidelobe at can be reduced by

.A second modified differential FPR antenna has also been in-

troduced to reduce backward radiation. In this case, a pair ofridges are placed at the top of the parallel plates. The ridges areto provide a wider radiation aperture and, hence, decrease thebeamwidth of the radiation pattern. This technique avoids theneed of changing the parallel-plate spacing that will affect theoperating frequency of the antenna. The second modified differ-ential antenna was also fabricated and measured, and the mea-surement agrees reasonably well with the HFSS simulation. Ithas been found that backward radiation can be reduced effec-tively by using the modified FPR antenna.

ACKNOWLEDGMENT

The comments of the reviewers are gratefully appreciated.

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Kai Lu was born in Laoting, Hebei Province, China.He received the B.Eng. and M.Eng. degrees fromHarbin Institute of Technology, Harbin, China, in2006 and 2008, respectively, and the Ph.D. degree in2012 from City University of Hong Kong (CityU),Hong Kong, all in electronic engineering.From August 2008 to July 2009, he worked as an

Antenna Design Engineer in Beijing Skyway Tech-nologies Co., Ltd., China. He is currently working asa Senior Research Assistant at CityU. His researchinterests include Fabry–Perot resonator antennas, di-

electric resonator antennas, reflector antennas, microstrip antennas, millimeterwave imaging technology, and microwave theory.

Kwok Wa Leung (S’90–M’93–SM’02–F’11)was born in Hong Kong in 1967. He received theB.Sc. degree in electronics and the Ph.D. degree inelectronic engineering from the Chinese Universityof Hong Kong, Hong Kong, in 1990 and 1993,respectively.From 1990 to 1993, he was a Graduate Assistant

with the Department of Electronic Engineering, Chi-nese University of Hong Kong. In 1994, he joined theDepartment of Electronic Engineering, City Univer-sity of HongKong (CityU), as an Assistant Professor.

Currently, he is a Professor and an Assistant Head of the Department. From Jan-uary to June 2006, he was a Visiting Professor in the Department of ElectricalEngineering, The Pennsylvania State University, Philadelphia, PA, USA.Prof. Leung is a Fellow of HKIE. He received the International Union of

Radio Science (USRI) Young Scientists Awards in 1993 and 1995, awarded inKyoto, Japan and St. Petersburg, Russia, respectively, and the CityU ResearchExcellenceAward 2013 andDepartmental Outstanding Teacher Awards in 2005,2010 and 2011. He was the Chairman of the IEEE AP/MTT Hong Kong JointChapter for the years of 2006 and 2007. He was the Chairman of the TechnicalProgram Committee, 2008 Asia-Pacific Microwave Conference, Hong Kong,the Co-Chair of the Technical Program Committee, 2006 IEEE TENCON, HongKong, and the Finance Chair of PIERS 1997, Hong Kong. His research interestsinclude RFID tag antennas, dielectric resonator antennas, microstrip antennas,wire antennas, guided wave theory, computational electromagnetics, and mo-bile communications. He was an Editor for HKIE Transactions and a GuestEditor of IET Microwaves, Antennas and Propagation, and an Associate Editorfor the IEEE ANTENNASWIRELESS PROPAGATION LETTERS. He was also an As-sociate Editor for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATIONand received Transactions Commendation Certificates twice in 2009 and 2010for his exceptional performance. Currently he is the Editor-in-Chief of the IEEETRANSACTIONS ON ANTENNAS AND PROPAGATION. He is a Distinguished Lec-turer of the IEEE Antennas and Propagation Society.