AWidebandWaveguide Antenna with Nearly Equal E-and H-Plane Radiation Patterns

A novel wideband waveguide antenna with excellent performance is proposed, which is composed of a coaxial-waveguide transition and an open-ended rectangular waveguide loaded with a pair of horizontal umbrella-shaped metallic brims. e brims perpendicular to two broad walls of the waveguide are constructed to modulate the antenna to radiate nearly identical Eand Hplane radiation patterns. Awideband impedancematching performance is achievedwith a fractional bandwidth of 40% through the introduction of short-stepped ladders. e antenna has the advantages of simple structure, symmetric radiation pattern, low-cross polarization, moderate back lobe, and almost constant beamwidth.


Introduction
e demand for the wideband, low-pro�le antennas with stable gain as well as symmetrical radiation patterns is on the rise with the fast growth of microwave and millimeter-wave wireless communication systems.Up to date, the pursuing of these high-performance antennas has attracted much attention and long-held interest.Microstrip patch antennas exhibiting the advantages of low pro�le, light weight, low cost, easy fabrication, and high integration with other devices have been widely adopted for electric systems.However, their impedance bandwidths are not sufficient, and also the gains are impossible to remain stable across a broad frequency range, which restricts considerably the practical applications.Although some impedance bandwidth enhancement techniques have been developed such as multilayer structure [1], U-slot loading [2], and L-probe feeding [3], the stability of radiation patterns are essentially difficult to be held.Some modi�ed planar monopole antennas [4,5] have been proposed with ultrawide bandwidths but they still do not satisfy the rigorous requirement because of their unstable radiation patterns.Other wideband antennas including the planar spiral, log-periodic, Vivaldi, Yagi antenna, and double-ridged horn have been implemented aer a survey of available literature.However, they are apparently with the drawback of large pro�le or complicated con�gurations.
Dipole is a fundamental radiator and is oen used as an equivalent source in the analysis of antenna.It is evident that unequal radiation patterns are achieved in the two principal planes for both an electric dipole and a magnetic dipole.is is because interchanged radiation patterns of �gure-o and �gure-8 are obtained between both dipoles.To implement equal E-and H-plane radiation patterns with low back radiation, Clavin and his coworkers presented the idea of complementary antennas [6,7] where nearly equal E-and H-plane radiation patterns were achieved by incorporating an electric dipole and a magnetic dipole with appropriate amplitude and phase.Recently, Luk et al. advanced a step forward who were enlightened by the concept of magnetoelectric dipole and proposed a series of wideband unidirectional antennas with stable gain.In their design, the antennas were mainly composed of a vertically oriented quarter-waveshorted patch and a horizontal planar dipole excited by Γshaped strip probes [8,9,10,11] or a coaxial feed [12].Of them, however, some structures are somewhat complicated especially for their feeding which is typically associated with International Journal of Antennas and Propagation a complicated design and thus may be hard to be popularized into practical applications, making an alternative, improved strategy a challenging and pressing task.
In this paper, a simpli�ed feed is introduced to excite the complementary antenna which is evolved from the openended rectangular waveguide antenna.Unlike the complicated corrugated conical horns [13], the proposed antenna not only overcomes the drawback of conventional openended rectangular waveguide antenna whose beamwidth in E-plane is usually unequal to that in H-plane [14] but also is with very simple structure which is oen related with an easy design and fabrication.It thus should be a good candidate in the modern wireless and satellite communication systems.In addition, due to its unique radiation characteristics, the proposed antenna can also be well applied to illuminate a circular aperture such as circular paraboloid [6] or lens.

Antenna Structure and Design
2.1.Geometry of the Waveguide Antenna. Figure 1 illustrates the structure and the geometrical dimensions of the proposed waveguide antenna which consists of an open-ended rectangular waveguide, stepped ladders along the broad walls, and umbrella-shaped metallic brims.Notice that beamwidth of the conventional open-ended rectangular waveguide in E-plane is wider than that in H-plane.To obtain an equal E-plane and H-plane radiation pattern, a complementary antenna with beamwidth in E-plane narrower than that in H-plane is necessary.For this purpose, the rectangular waveguide is loaded with a pair of horizontal umbrellashaped metallic brims which functions as a planar electric dipole whose beamwidth in E-plane is narrower than that in H-plane (see Figure 4).In the present work, the antenna is designed to operate in the whole Ku-band ranging from 12 GHz to 18 GHz.e geometrical parameters are optimized and detailed in Figure 1, in which  and  are the length and width of the waveguide cross-section,  and ℎ are the height and length of the stepped ladder, and  in conjunction with  are the thickness and length of the metallic brims, respectively.
e rectangular waveguide antenna is simply excited by a coaxial probe with the diameter of 1.27 mm, which is accompanied by a dielectric and a coaxial-waveguide transition.e dielectric in the SMA connector covering the probe has a relative permittivity of    0.e metal that is utilized in the design and fabrication is copper with the conductivity of     0  S/m, and silver is adopted to cover the surface inside the waveguide to reduce the transmission loss.

Input Impedance Matching Performance. As an antenna
, a conventional open-ended rectangular waveguide cannot be well matched to free space over the entire operating frequency band [15].Hence extensive simulations have been performed, which demonstrate that the impedance bandwidth of the waveguide antenna is determined by two factors.e �rst factor is the transition from coaxial to rectangular waveguide.e second is the re�ection at the end of the waveguide which exhibits a capacitive reactance.To show the corresponding result, the relative input impedance of conventional openended WR62 waveguide on a Smith chart obtained from commercial EM full-wave simulator HFSS is shown in Figure 2. As can be seen, an obvious capacitive reactance is con�rmed.Moreover, the real part of input impedance approximates to unity.According to the transmission line theory, the complex input impedance including the real (resistive) and imaginary (reactive) components can be transformed to a pure resistive one through a portion of transmission line with appropriate length.In this particular case, a pair of stepped ladders along the broad walls is introduced, and the length ℎ of them is selected about one eighth of the waveguide wavelength (  ) corresponding to the center frequency 15 GHz to cancel out the capacitive reactance.Moreover, the stepped ladders considerably counteract the resulting capacitive reactance in a broad band.
To corroborate the elucidation, Figure 3 depicts the simulated voltage standing-wave ratio (VSWR) against the frequency as a function of ℎ (see Figure 3(a)) and  (see Figure 3(b)), respectively.It is clearly observed that the VSWR of the designed antenna decreases as ℎ increases from zero to 3.5 mm stepped by 1.75 mm ( is �xed as 2.1 mm).Remark that the case ℎ = 0mm corresponds to the open-ended waveguide antenna without ladders.From Figure 3(b), it can be clearly observed that the VSWR of the designed antenna does not always reduce as  increases (ℎ is �xed as 3.5 mm); instead, it initially reduces and then deteriorates, which demonstrates that the introduced stepped ladders play an important role in determining the matching performance of the antenna and are able to improve the matching providing an appropriate dimension.In fact, the VSWR is minimum around  =  mm and is below 1.2 over the entire band.In the �nal fabricated prototype, the value of  is selected as 2.1 mm to consider the tradeoff between the impedance match and the equality of the beamwidths in E-plane and Hplane within the entire Ku-band.In the �nally implemented antenna (ℎ = 35 mm (nearly   /8 at 15 GHz) and  =  mm), numerical results indicate that the VSWR is better than 1.4 across the whole Ku-band.

Radiation Characteristics.
To investigate the operation mechanism of the proposed waveguide antenna, the surface current distributions of the antenna excited in the case of different phases ( and the inside surface current of TE 0 mode along the broad and narrow wall of the waveguide are demonstrated in Figure 4. From the inside surface current distribution of the dominant mode TE 0 , we obtain that the longitudinal components and the transverse ones change alternately.In the case of  = 0 ∘ , the transverse components of inside surface current of TE 0 mode on the aperture are dominative while the longitudinal ones are minimized (see Figure 4(e)).e aperture current mainly concentrates around the aperture and forms a circular loop with two components �owing along opposite directions, resembling a "one-wavelength" loop antenna.On the contrary, in the case of  = 0 ∘ , the current along the horizontal umbrella-shaped metallic brims is up to the maximum while the one around the aperture is minimized, corresponding to the case when longitudinal current of TE 0 mode is dominative.erefore, an electric dipole has been effectively excited as claimed in the previous section.Similar to the �rst case, the current around the aperture at  = 80 ∘ is dominative; however, its direction is opposite to that in the case of  = 0 ∘ .In the case of  = 0 ∘ , the electric dipole is excited again, and the resulting current direction is opposite to that in the case of  = 0 ∘ .In summary, the proposed antenna is capable of exciting a complementary antenna by means of alternately exciting aperture current along two orthogonal directions.
From the observation of the operation mechanism of the proposed antenna, we can conclude that the current distribution on the aperture is mainly determined by the geometrical shape of the aperture.Although the distribution of the inside surface current for the TE 0 mode of rectangular waveguide is determined when its transverse size is given, we still can control the aperture current distribution by changing the shape of the aperture.In this case, it is particularly interesting to study the relation between the dimensions of metallic brims and radiation performance of the antenna.e study would afford us a useful guideline in the design of the waveguide antenna with equal E-and H-plane radiation patterns by exciting simultaneously the complementary antenna with appropriate amplitude and phase.Figure 5 illustrates the simulated beamwidth in E-and H-planes as a function of .We remark that  = 0 mm corresponds to the conventional waveguide antenna without brims.Following the �gure, it is evident that nearly equal E-and H-plane radiation patterns are engineered at three selected representative frequencies when  =  mm.However, the uniform radiation patterns degrade to a certain degree when  takes other values.Particularly, in the condition when  takes zero, the beamwidth in E-plane is much wider than that in H-plane, implying a large discrepancy of the radiation patterns.e mechanism can be simply explained as follows: the variation of  affects the amplitude and phase of the equivalent electric dipole.To obtain identical radiation patterns in the two principal radiation planes,  is chosen as 2.7 mm in the �nal design and fabrication.
Note that the width of the brim is selected equal to that of the waveguide in the above analysis.For comprehensive study, extensive simulations have also been performed in the case when -directed brims (perpendicular to the narrow walls of the waveguide) are introduced.For analysis convenience, the length of the -directed brims that extends the waveguide is de�ned as   .Not to lose generality, a typical value of   = 3 mm is selected.e corresponding simulated results are also afforded in Figure 3 and Table 1.As can be seen, the VSWR is nearly invariable, and the gain is slightly increased when brims are introduced in  direction.Moreover, the back radiation levels change slightly.However, the beamwidths in E-and H-planes are decreased considerably.To illustrate the effect of the length of the metallic brims  on the radiation performance, Figure 6   E-plane @ 12 GHz H-plane @ 12 GHz E-plane @ 15 GHz H-plane @ 15 GHz E-plane @ 18 GHz H-plane @ 18 GHz     = 0 mm represents the situation that the width of the brim is equal to the width of the waveguide.
radiation patterns versus different .It can be observed that the metallic brims introduced here can suppress the back radiation of the waveguide antenna.According to Figure 6, the back radiation has been signi�cantly suppressed when  increased from 0 to 10 mm.Moreover, the back radiation levels can be reduced to below −20 dB across the whole Kuband when  takes 10 mm.is level of back radiation is very comparable to that reported in [6,7,8,9] with a ground plane.However, in this case the beamwidth of the far-�eld pattern in E-plane is wider than that in H-plane.Since the equal Eand H-plane radiation patterns are the main concentration in this paper,  is �nally chosen as 2.7 mm.In this case, the back radiation level of the proposed antenna is less than −11 dB within the whole Ku-band.

Results and Discussions
For numerical characterization, the proposed antenna is simulated using commercial soware Anso HFSS.For ver-i�cation, a prototype of the antenna is fabricated (see Figure 1) and measured using an Agilent N5230C network analyzer.e measured VSWR is also shown in Figure 3 and is in reasonable agreement with the simulated one.Measured result implies that the impedance bandwidth (VSWR < 1.4) covers the whole Ku-band.erefore, the matching performance of the waveguide antenna across the operating bandwidth has been improved dramatically by the introduction of the stepped ladders with appropriate dimensions.e antenna radiation patterns are measured through the far-�eld measurement system in an anechoic chamber.Figure 7 illustrates the simulated and measured radiation patterns.As can be seen, the proposed antenna presents nearly identical beamwidths in E-and H-planes.Both simulated and measured results indicate that the cross-polarization (normalized to the copolarization) is considerably low in the entire frequency range.Furthermore, the backward radiation levels are less than −11 dB across the entire operating band and are smaller in the upper frequency band than those in the lower frequency band.It is worth mentioning that the simulated cross-polarization levels are all less than −35 dB while the measured ones are less than −25 dB across the entire operating frequencies.e relatively large cross-polarization levels in measurements may be attributable to three factors: the �rst factor is the received wea� signal which is on the order of the system noise and this is especially true for measuring the very low cross-polarization; the second factor is the large cross-polarization that is inherently induced by the transmitting horn, and this is especially true for the doubleridged horn which is used for measurement; the third factor is the tolerances of the pose for the transmitting and measured antennas which are impossible to be placed rigorously orthogonal.e tolerances can be reduced; however, they are  hard to be eliminated.e detailed antenna performances including the gains and 3-dB beamwidths for both E-and H-planes at 12, 15, and 18 GHz are summarized in Table 1.Clearly, the 3-dB beamwidth of the proposed antenna varies within 10 degrees across the observed frequency range, and the gain varies less than 2 dB when the frequency changes from 12 to 18 GHz.erefore, the antenna exhibits a stable performance.

Conclusion
A novel open-ended rectangular waveguide antenna has been proposed, which features wide bandwidth, low crosspolarization, moderate backward radiation, and uniform pattern bandwidth (almost identical E-and H-plane patterns) across the whole Ku-band.Furthermore, the proposed antenna exhibits a simple structure and is conceptually easy to design.Hence, it can be widely employed as an efficient feed for circular-aperture antennas to obtain the desired pencil-beam radiation patterns.

F 1 :
e fabricated prototype and topology of the proposed antenna.(a) e photograph of the prototype antenna.(b) e cut-open view of the proposed antenna.(c) e cross-section along E-plane of the proposed antenna.e detailed dimensions (unit: mm) are   ,   ,   ,   ,   ,   ,   , ℎ  ,   , and   .

5 F 2 :
Simulated relative input impedance of conventional openended WR62 waveguide without ladders within entire Ku-band. portrays

F 3 :F 4 :
Simulated and measured VSWRs of the proposed antenna versus the dimensions of the stepped ladders (a) as a function of ℎ, (b) as a function of .J surf (A/m) Surface current distributions of the proposed antenna in the case of different excitation phases.Aperture current distributions in the case of (a)    ∘ ; (b)    ∘ ; (c)    ∘ ; (d)    ∘ ; and (e) inside surface current of TE  mode in the case of    ∘ .

F 5 :
Comparison of beamwidths in E-and H-planes as functions of .T 1: Simulated and measured 3-dB beamwidths and gains of the proposed antenna.

F 6 :
Study of variations in radiation patterns versus the changes of lengths of metallic brims at 12, 15, and 18 GHz, respectively.(a)-(b) E-plane and H-plane at 12 GHz, (c)-(d) E-plane and H-plane at 15 GHz, and (e)-(f) E-plane and H-plane at 18 GHz.