Beam Tilt-Angle Estimation for Monopole End-Fire Array Mounted on a Finite Ground Plane

Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2015, Article ID 351439, 8 pages http://dx.doi.org/10.1155/2015/351439

Research Article Beam Tilt-Angle Estimation for Monopole End-Fire Array Mounted on a Finite Ground Plane

Jia Cao, Zhenghui Xue, and Meng Cao

School of Information and Electronics, Beijing Institute of Technology, 5 South Zhongguancun Street, Haidian District, Beijing 100081, China

Correspondence should be addressed to Zhenghui Xue; [email protected]

Received 2 October 2014; Revised 2 December 2014; Accepted 15 December 2014

Academic Editor: Ana Alejos

Copyright © 2015 Jia Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

A modified method for the beam tilt-angle estimation of monopole end-fire array mounted on finite ground plane is proposed. In the simplified model, the monopole array and ground plane are approximated to two line sources of transverse and longitudinal electric current, respectively. It is deduced that the beam tilt angle is a function about the length of ground plane in front of array 𝐿𝑔, the length of monopole array 𝐿𝑎, and the phase constant 𝛽𝛼. After verifying the optimizing principle of monopole end-fire array, a 10-element monopole Yagi-Uda antenna satisfying Hansen-Woodyard condition is designed and measured for the analysis. By comparison and analysis, the value of 𝛽𝛼 is demonstrated to be the key point of the proposed method. And a slow wave monopole array is proved to be able to achieve a low beam tilt angle from end-fire with only a short-length ground plane.

1. Introduction line source of magnetic current and electric current, respec- tively. As a result, the beam tilt 𝜃𝑡 was proved to be a function End-fire antennas are useful in all applications that require of both 𝐿𝑎 (given antenna length) and 𝐿𝑔 (effective ground low profile, for example, in airborne and vehicular envi- ∘ plane length). For small values of beam tilt (𝜃𝑡 ≤20), this ronments. After decades of research and developing, the function reduced to performance of end-fire antennas has been greatly advanced 49 in several fields, like broadband, gain enhancement, and 𝜃 ≈ , 𝑡 1/2 (1) pattern reconfiguration1 [ –4]. However, those end-fire anten- [(𝐿𝑎 +𝐿𝑔)/𝜆] nas mounted in or on a finite ground plane suffer from a serious problem: the main beam is tilted at some angle from where 𝜃𝑡 is in degrees [6]. the horizontal plane by diffraction effects from conductive Nevertheless,thismethodwithhighaccuracyisnotsuit- ground, which prevents a true end-fire condition. able for the monopole end-fire array vertical to the ground By image theory, the conclusion can be easily obtained plane. That is not only because of the model abstracted that the beam tilt angle will disappear when ground plane from the flush-mounted end-fire antenna which is akind extends to infinite. Meanwhile, as a majority of radiation of aperture antenna parallel to the ground, but also due to power distributes in the positive half-space, the value of the no consideration about the influence from phase constant’s beam tilt angle mainly depends on the effective ground plane varying. Thus in the former research, the beam tilt-angle length in front of end-fire antenna. This phenomenon was analysis of this kind of monopole end-fire array could only first described by Elliott in 1954 [5]. be obtained by whole model simulation using simulation BasedonHuygens’principle,asimplifiedmethodfor software, far-field measurement, or numerical calculation determining the effect of finite ground plane was demon- method [7], with high cost, long time, and various operations. strated by Walter in his book, by which the aperture of A beam tilt-angle estimation method, which is modi- antenna and the ground plane were simplified to a uniform fied for the monopole end-fire array mentioned above, is 2 International Journal of Antennas and Propagation

Z ∫h sin jkzcos 𝜃 f= 0 Im (k(h − z))e dz Y 0

−10 h1 X h2 h3 ··· hn ··· hN ) (dB) 𝜃

( −20 f

S −30

−40 W Normalized pattern Normalized −50 La Lg L −60 Figure 1: 𝑁-monopole end-fire antenna vertically mounted on a 0 10 20 30 40 50 60 70 80 90 ∘ finite ground plane. 𝜃 ( ) Ideal dipole h = 0.2𝜆 h = 0.1𝜆 h = 0.25𝜆 proposed in this paper. Firstly, a simplified source model Figure 2: Radiation patterns of 0.1𝜆, 0.2𝜆,and0.25𝜆 monopoles and is applied to this kind of antenna. The key point of this of ideal dipole. model simplification is evaluating the phase constant 𝛽𝑎 of the surface wave along monopole end-fire array. Secondly, monopole Yagi-Uda antenna is introduced to validate the La =NS validity and accuracy of this method. The estimated tilt Ideal dipole angles present a good agreement with CST simulation results. S Furthermore, comparison between the proposed method zÎ Δl zÎ Δl zÎ Δl zÎ Δl zÎ Δl in this paper and Walter’s method shows an advantage of 1 2 3 n N monopole end-fire antenna with slow wave characteristic. X ̂ Transverse current zJz(x)dx Thisadvantage,thatalowtiltanglecanbeachievedwitha line source short ground length, is demonstrated by the experimental results of the 10-element monopole Yagi-Uda antenna. Figure 3: Ideal dipole array and transverse current line source corresponding. 2. Simplified Model for Monopole End-Fire Array and Ground Plane height of monopole, the radiation pattern can be derived Figure 1 shows the configuration of an 𝑁-monopole end- by (2). Figure 2 exhibits the curves of 𝐸-plane (𝑋𝑍-plane) firearraymountedonagroundplanewithcertainsize normalized patterns of ideal dipole, 0.1𝜆 monopole, 0.2𝜆 (𝑊𝐿). Assume it is working at the frequency point 𝑓,witha monopole, and 0.25𝜆 monopole, respectively. It is suggested wavelength 𝜆,and𝜔 is the corresponding angular frequency. thatidealdipole’sradiationpatternisquitesimilartotheones Consulting the original method in [6], the simplified model of monopoles with height less than or equal to 0.25𝜆,sothis should be composed of two parts: one line source approx- approximation has no serious loss in accuracy: imated from the monopole array current distribution and another one approximated from the current on the ground ℎ 𝑋𝑍 𝑗𝑘𝑧 cos 𝜃 plane. Note that only far-field patterns in -plane are taken 𝑓=∫ 𝐼𝑚 sin (𝑘 (ℎ−𝑧)) 𝑒 𝑑𝑧. (2) into account for the beam tilt-angle problem, as the main 0 lobe direction is always in this plane when the ground is symmetric about the 𝑋-axis. Secondly, as shown in Figure 3, the array of ideal dipoles with electric current amplitude and phase offset as (𝐴𝑛,𝜑𝑛) on each is approximated by a transverse electric current 2.1. Simplification for Monopole End-Fire Array. Firstly, the line source lying on the 𝑋-axis, with amplitude 𝐴(𝑥) and array elements, electric monopoles with heights {ℎ𝑛},are phase velocity V(𝑥) in 𝑋 direction. For the line source length, approximated by a series of ideal dipoles. Ideal dipole is 𝑗𝜑 ̂ ̂ 𝑛 𝐼 assume that each ideal dipole 𝑧𝐼𝑛Δ𝑙 = 𝑧𝐴𝑛𝑒 lying on 𝑥𝑛 defined as a Hertz dipole with uniform electric current 𝑠 on the total length Δ𝑙 ≪, 𝜆 and its radiation pattern corresponds to a segment (spacing between two adjacent function is 𝑓=sin 𝜃. Usually, monopole height is less elements) in length, so the whole length of line source will be than or equal to 0.25𝜆. Assuming the current distribution on monopole is 𝐼(𝑧)𝑚 =𝐼 sin(𝑘(ℎ − 𝑧)),whereℎ is the 𝐿𝑎 =𝑁𝑠, (3) International Journal of Antennas and Propagation 3 where 𝑁 is the number of elements. Therefore, let the current According to the considerations about both simplicity and source be accuracy,thephaseconstantinG1isvaluedbytheaverage 𝛽 𝑘 −𝑗𝛽(𝑥)𝑥 of 𝑎 and . The estimation for the phase constant in G1 𝐽𝑧 (𝑥) =𝐴(𝑥) 𝑒 0≤𝑥≤𝐿𝑎, (4) is another special progressing in the novel method, because in previous work only the ground in front of the end-fire where aperture, corresponding to G2 in our case, is taken into 𝜔 account [5, 6]. 𝛽 (𝑥) = V (𝑥) (5) Thus, the simplified line source can be expressed as is the phase constant on the line source. For small element spacing (one-half wavelength or less) the distinction between 𝐽𝑥 array and continuous source tends to disappear. So when 𝑠≤ −𝑗((𝛽 +𝑘)/2)𝑥 0.5𝜆,thisapproximationworks. 𝐴 𝑒 𝑎 0≤𝑥≤𝐿 { 𝑔 𝑎 Finally, simplify the line source expressed by (3) to a { (9) line source with a constant amplitude 𝐴𝑎 and uniform phase = −𝑗[𝑘(𝑥−𝐿 )+((𝛽 +𝑘)/2)𝐿 ] {𝐴 𝑒 𝑎 𝑎 𝑎 𝛽 { 𝑔 constant 𝑎. For beam-tilting estimation, only a relative −𝑗(𝑘𝑥+((𝛽 −𝑘)/2)𝐿 ) =𝐴 𝑒 𝑎 𝑎 𝐿 <𝑥≤𝐿 +𝐿 . value of 𝐴𝑎 is needed, and this work will be introduced in { 𝑔 𝑎 𝑎 𝑔 Section 2.3. Meanwhile the value of 𝛽𝑎 is evaluated as

∑𝑁 (𝜑 −𝜑 ) 𝑛=2 𝑛 𝑛−1 And its relative far-field is 𝛽𝑎 = . (6) 𝐿𝑎

𝛽𝑎 is just the key point of this new method, owing to 𝑋 𝑋 𝑗𝑋 sin 𝑔1 𝑗𝑋 sin 𝑔2 𝛽 𝜃𝐸̂ = 𝜃𝐴̂ (𝑒 𝑔1 𝐿 +𝑒 𝑔3 𝐿 ) 𝜃, the fact that the difference between the value of 𝑎 and the 𝑔 𝑔 𝑋 𝑎 𝑋 𝑔 cos wavenumber in free space 𝑘 cannot be ignored in many cases. 𝑔1 𝑔2 The further explanation will be given in Section 3. (10) According to the simplification above, the line source expression is deduced to where −𝑗𝛽𝑎𝑥 𝐽𝑧 (𝑥) =𝐴𝑎𝑒 0≤𝑥≤𝐿𝑎 (7) whoserelativefar-fieldinelevationplane(𝑋𝑍-plane) is 𝐿𝑎 𝛽𝑎 +𝑘 𝑋𝑔1 = (𝑘 sin 𝜃− ), 𝑗𝑋 sin 𝑋𝑎 2 2 𝜃𝐸̂ = 𝜃𝐴̂ 𝑒 𝑎 𝐿 𝜃, 𝑎 𝑎 𝑋 𝑎 sin (8) 𝑎 𝐿𝑔 𝑋 = 𝑘 ( 𝜃−1) , (11) 𝑔2 2 sin where 𝑋𝑎 =(𝐿𝑎/2)(𝑘 sin 𝜃−𝛽𝑎). 𝐿 𝑘−𝛽 𝑋 =(𝐿 + 𝑔 )𝑘( 𝜃−1) +𝐿 𝑎 . 2.2. Simplification for Ground Plane. In electromagnetic field 𝑔3 𝑎 2 sin 𝑎 2 analysis, a ground plane can be replaced by a current sheet with its induced current components (𝐽𝑥,𝐽𝑦) distributed on. Based on the mirror symmetry of end-fire antenna’s structure 2.3. Superposition of Far-Field Patterns. The total estimated in Figure 1, 𝐽𝑦 on the current sheet has no contribution to the radiation is the superposition of the far-fields of the two line far-field in 𝑋𝑍-plane, so it can be ignored in the beam tilting sources introduced in Sections 2.1 and 2.2. Good results are estimation. Thus the simplified model for the ground plane obtained in practice by letting the sources be in-phase at should be a line source of longitudinal electric current on 𝑋- the origin and with amplitudes adjusted so that their pattern axis. maxima are equal by Walter’s method [6]. Therefore the same This line source is divided into two parts: the part assumption is made in this paper. ∘ representing the ground plane just under the monopoles (G1) Field 𝐸𝑎 will have maximum value at 𝜃=90.Setting and the part representing the ground plane in front of end- |𝐸𝑎|max =|𝐸𝑔|max gives firearray(G2).Thecurrentamplitudesareassumedtobe 𝐴𝑔, equal and constant on both parts. However, the phase 𝛽(𝑥) constant shouldnotbeuniformalongthewholeline 󵄨 sin 𝑋𝑎 󵄨 source. The current in G2 is close to the current induced by 𝐴 𝐿 󵄨 𝑎 𝑎 𝑋 󵄨 monopoles’ far-field, so the phase constant in G2 is close to 𝑎 󵄨𝜃=90∘ 𝑘 . Meanwhile, the current phase constant in G1 approaches 󵄨 𝑋 𝑋 󵄨 󵄨 𝑗𝑋 sin 𝑔1 𝑗𝑋 sin 𝑔2 󵄨 to 𝛽𝑎 because of the constraint by monopole array’s near- =𝐴 󵄨(𝑒 𝑔1 𝐿 +𝑒 𝑔3 𝐿 ) 𝜃󵄨 . 𝑔 󵄨 𝑋 𝑎 𝑋 𝑔 cos 󵄨 field but regresses to 𝑘 at the end of array because of the 󵄨 𝑔1 𝑔2 󵄨max continuity of 𝛽(𝑥) on the boundary between G1 and G2. (12) 4 International Journal of Antennas and Propagation

Thus the total far-field is Table 1: Parameter for monopole Yagi-Uda antenna.

𝐸𝑡 =𝐸𝑎 +𝐸𝑔 Variables Values 𝑟 2 󵄨 𝑋 𝑋 󵄨 (mm) 󵄨 𝑗𝑋 sin 𝑔1 𝑗𝑋 sin 𝑔2 󵄨 =𝐴 󵄨(𝑒 𝑔1 𝐿 +𝑒 𝑔3 𝐿 ) 𝜃󵄨 𝑠 (mm) 20 𝑔 󵄨 𝑋 𝑎 𝑋 𝑔 cos 󵄨 󵄨 𝑔1 𝑔2 󵄨max ℎ1 (mm) 23 󵄨 ℎ2 (mm) 21.5 𝑋𝑎 󵄨 𝑗𝑋 sin 𝑋𝑎 × 󵄨 𝑒 𝑎 𝜃 ℎ3 19 󵄨 sin (mm) sin 𝑋𝑎 󵄨 ∘ 𝑋𝑎 𝜃=90 ℎ4 (mm) 17 𝑋 𝑋 ℎ5 15.6 𝑗𝑋 sin 𝑔1 𝑗𝑋 sin 𝑔2 (mm) +𝐴 (𝑒 𝑔1 𝐿 +𝑒 𝑔3 𝐿 ) 𝜃. 𝑔 𝑎 𝑔 cos ℎ6 (mm) 15.5 𝑋𝑔1 𝑋𝑔2 ℎ7 14.5 (13) (mm) ℎ8 (mm) 10.67 The main lobe direction 𝜃𝑚 can be obtained by solving ℎ9 (mm) 6.83 (𝜕𝐸 /𝜕𝜃)| =0 𝜃 ℎ10 3 the equation 𝑡 𝜃=𝜃𝑡 ,andthebeamtiltangle 𝑡 has (mm) ∘ 𝜃𝑡 =90 −𝜃𝑚.So,𝜃𝑚 is proved to be a function of 𝐿𝑎, 𝐿𝑔,and 𝛽𝑎. Moreover, for the convenience of calculation, numerical computing for (12) to find the value of 𝜃 corresponding to |𝐸 | 𝑡 max is also a considerable solution. Thus, through this simulation experiment, the relation- ships between 𝛽𝑎 and array’s directivity and 𝛽𝑎 and array’s tilt 3. Simulation Analysis and Discussion anglewerebothobtained.TheblacksolidcurveinFigure 5 illustrates that the directivity 𝐷 ≈ 11.43 dB when 𝛽𝑎 = 1.25𝑘, A monopole Yagi-Uda antenna is taken as an example of anditisalmosttheoptimumdirectivityforthis10-element monopole end-fire array for the beam tilting analysis and dis- array. It demonstrates Hansen-Woodyard condition is still cussion. In most conditions, conventional Yagi-Uda antenna suitable for the monopole end-fire array case. is inherently a slow wave structure, and Hansen-Woodyard To be worthy of attention, the red solid curve in Figure 5 condition which is expressed by (14) is usually considered reveals the trend that beam tilt angle is decreasing while 𝛽𝑎 is as the optimization aim in this kind of antenna’s design increasing. for improving directivity [6]. Before antenna designing, a simulation experiment was implemented to verify that this optimizing principle applies to the monopole end-fire array 3.2. Beam Tilting Estimation to a Monopole Yagi-Uda Antenna. case. Consider A 10-element dipole Yagi-Uda antenna has been designed fol- lowing Hansen-Woodyard condition which has been verified 𝛽𝑎𝐿𝑎 =𝜋+𝑘𝐿𝑎. (14) above at 𝑓=3GHz. And the corresponding monopoles in the positive-𝑍-space are mounted on a finite ground plane to 3.1. Optimizing Principle in Monopole End-Fire Array. The constituteamonopoleYagi-Udaantenna.Theconfiguration simulation object is a 10-element monopole array like the is shown in Figure 6, and parameters of the monopole array model shown in Figure 1,workingat𝑓=3GHz. All the are given in Table 1. monopoles in this array have an equal height ℎ = 0.25𝜆 = According to (3), the monopole array’s length is 𝐿𝑎 = 25 mm and an equal radius 𝑟=2mm. The interspace between 200 mm. Substituting it in (14),thesolutionis𝛽𝑎 ≈ 78.54, adjacent elements is 𝑠=20mm, so the total length of array whose distinction with 𝑘 = 2𝜋/𝜆 ≈ 62.83 cannot be is 𝐿𝑎 = 200 mm. The finite ground size is 𝐿𝑎 = 200 mm, ignored. Thus only the length of ground plane in front of 𝐿𝑔 =30mm, and 𝑊=60mm. To satisfy Hansen-Woodyard 𝐿𝑔 isthevariableinthisanalysis.A𝜃𝑡-𝐿𝑔 curve is simply condition, the actual phase constant on the array’s current calculated by the estimation method proposed in Section 2. should be 𝛽𝑎 = 1.25𝑘. Meanwhile, there are two other 𝜃𝑡-𝐿𝑔 curves calculated by Every element was fed with an equal magnitude and a Walter’s method and simulated by CST Microwave Studio, uniform-step phase offset. By CST MWS simulating, the fed respectively. All the three curves are shown in Figure 7 for signal phase step Δ𝜑 between adjacent elements was taken as comparison. The estimated result by Walter’s method has a a variable, the array’s directivities and tilt angles with different clear distinction to the simulation one. Meanwhile a good Δ𝜑 were recorded, and the surface current data of monopoles agreement is achieved between the modified estimation and were exported for calculating the phase constant 𝛽𝑎 on this CST simulation. The accuracy of the proposed estimation array. method is illustrated to be much better than Walter’s for beam Specifically, Figure 4(a) shows the surface current distri- tilt angle of monopole end-fire array like this monopole Yagi- bution on monopoles with a certain phase step Δ𝜑0.Bymeans Uda antenna. of processing these current data in Matlab, the actual phase Furthermore, the estimated value of this new method is offsetofcurrentsourceoneachelement𝜑𝑛 was calculated in general lower than Walter’s when the finite ground plane is and Figure 4(b) shows the results. Substituting {𝜑𝑛} in (6),the short, and two curves trend to approximation and the length actual phase constant 𝛽𝑎 was derived. of ground plane increases. International Journal of Antennas and Propagation 5

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∘ 60 9.09 ( n

8.18 𝜑 7.27 6.36 0 5.45 Number 1 ⇢Number 10 4.55 3.64 2.73 Phase offset −60 1.82 0.909 0 −120 z Surface current (f=3) [simulation_1] (peak) x 3D maximum: 91.8 −180 Frequency: 3 0 246810 Phase: 0 Monopole number n (a) (b)

Figure 4: The current distribution on the 10-element monopole end-fire array with a finite ground 𝐿𝑎 = 200 mm, 𝐿𝑔 =30mm, and 𝑊= 60 mm at 𝑓=3GHzforacertainphasestepΔ𝜑0: (a) current vector on the surface, (b) actual current phase offsets of elements.

11.5 50 Z Y 11.0 45

10.5 40 X ) h h h ∘ 1 2 3 h h ( 4 h 6 h h 10.0 35 5 7 8 h9 t h10 𝜃 9.5 30 Feeding point

9.0 25 S

Tilt angle Tilt Directivity (dB) Directivity

8.5 20

8.0 15

7.5 10 0.9 1.0 1.1 1.2 1.3 2r

Phase constant 𝛽a (k) Figure 6: Geometry for the 10-element monopole Yagi-Uda Directivity antenna. Tilt angle

Figure 5: The relationships between 𝛽𝑎 and directivity, 𝛽𝑎 and tilt angle for 10-element monopole end-fire array with a finite ground appropriate high value of 𝛽𝑎 canresultinalowbeamtiltangle 𝐿𝑎 = 200 mm, 𝐿𝑔 =30mm, and 𝑊=60mm at 𝑓=3GHz. in the range where ground plane is short. By changing the array’s feeding situation or structure parameters, the phase constant of monopole end-fire array 3.3. Discussion on the Significance of 𝛽𝑎 in Estimating. Based canbeadjustedinawiderange.Therefore,theevaluationof on the phenomenon shown above, we will explain the 𝛽𝑎 will determine the validity and accuracy of estimation. significance of wavenumber 𝛽𝑎 in the beam tilting estimation of monopole end-fire array. Setting 𝐿𝑎 =2𝜆,the𝜃𝑡-𝐿𝑔 curves when 𝛽𝑎 = 𝑘, 1.1𝑘, 1.2𝑘 4. Experiment for 10-Element Monopole and 1.3𝑘 are, respectively, shown in Figure 8 compared with Yagi-Uda Antenna thecurveofWalter’s.Thedistinctionbetweenthecondition 𝛽𝑎 =𝑘and Walter’s estimation, caused by the different According to the analysis in Section 3, for a 10-element vector current elements (𝐽𝑧,𝐽𝑥) and (𝐾𝑦,𝐽𝑥) [6], is not quite monopole end-fire array, when the total length of finite 𝐿=𝐿 +𝐿 = 2.3𝜆 remarkable.However,as𝛽𝑎 increases, the distinction is ground plane is about 𝑎 𝑔 ,thebeamtilt ∘ getting larger and 𝜃𝑡 with the same 𝐿𝑔 is getting lower. It is angle is about 27 when 𝛽𝑎 =𝑘. For the same length, when 𝛽𝑎 suggested that 𝜃𝑡-𝐿𝑔 relationship is sensitive to 𝛽𝑎,andan is satisfying Hansen-Woodyard condition the tilt angle can be 6 International Journal of Antennas and Propagation

30 30

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15 18

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Lg/𝜆 Lg/𝜆

Walter’s method Walter’s method Proposed method in this paper Proposed method in this paper Simulation by CST Simulation by CST

Figure 7: Beam tilt angles of the 10-element antenna when 𝐿𝑎 = 200 mm, got by the proposed method in this paper, Walter’s method, and CST simulating.

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Walter’s method 𝛽a = 1.2 k Walter’s method 𝛽a = 1.2 k k 𝛽 = 1.3 k 𝛽 = 1.3 k 𝛽a = a 𝛽a = k a 𝛽a = 1.1 k 𝛽a = 1.1 k

Figure 8: Estimated beam tilt angles of the 10-element monopole end-fire antenna when 𝐿𝑎 =2𝜆, 𝛽𝑎 = 𝑘, 1.1𝑘, 1.2𝑘 and 1.3𝑘 and Walter’s Method. International Journal of Antennas and Propagation 7

Figure 9: Photo for the 10-element monopole Yagi-Uda antenna mounted on a finite ground plane with size 𝐿 = 230 mm, 𝑊=60mm.

0 90 0 330 0 30 120 60

−10 −10 300 60 30 −20 −20 150 ) (dB) ) (dB) 𝜃 𝜃 ( (

f −30 f −30

−40 270 90 −40 180 0

−30 −30 Normalized pattern Normalized −20 240 120 pattern Normalized −20 210 330 −10 −10 210 150 0 0 240 300 180 270 (∘) ∘ 𝜃t 𝜃t ( ) CST CST Mea Mea

Figure 10: Measured radiation pattern for the 10-element monopole Yagi-Uda antenna shown in Figure 9.

∘ lowered to about 20 , which needs a ground plane whose total 5. Conclusion length 𝐿=𝐿𝑎 +𝐿𝑔 ≥ 4.5𝜆 when 𝛽𝑎 =𝑘. The 10-element monopole Yagi-Uda antenna, which sat- A modified method for the beam tilt-angle estimation of end- isfies this condition as mentioned in Section 3,isfabricated fire antenna mounted on finite ground plane is proposed andmeasuredtoprovethisdeduction.Parametersforthe10- andstudied.Thismethodfocusesonanalyzingthecaseof monopole array are totally the same as those given in Table 1. monopoleend-firearray.Themonopolearrayandground The size of finite ground plane is 𝐿 = 230 mm, 𝑊=60mm. plane are simplified into two line sources of transverse The photo of the fabricated antenna is shown in Figure 9. and longitudinal current source, respectively. Superposition Simulationandmeasuredresultsfortheelevation(𝑋𝑍- resultsoftwolinesourcessuggestthebeamtiltangleisa plane) and azimuth (𝑋𝑌-plane) radiation patterns at 3 GHz function about the length of ground plane in front of array are shown in Figure 10. This antenna achieves about 11.56 dB 𝐿𝑔, the length of monopole array 𝐿𝑎, and the phase constant gain in practice and the main beam point at tilt angle of about 𝛽𝑎. Evaluating the value of 𝛽𝑎 correctly is demonstrated to be ∘ 21 from end-fire, which is very close to the estimated tilt ∘ the key point of this estimation method. A low beam tilt angle angle 20 at the beginning of this section. This experimental canbeachievedbyamonopolearraysatisfyingHanson- result demonstrates not only the accuracy of the estimation Woodyard condition with only a short-length ground plane. method proposed in this paper, but also the conclusions A 10-element monopole Yagi-Uda antenna is designed and ∘ deduced at the end of Section 3: the beam tilt angle is sensitive measured for the analysis. It produced a tilt angle about 21 , to 𝛽𝑎, and an appropriate 𝛽𝑎 can lower the angle with a short which is close to the estimation value, with a total ground size ground plane. 𝐿 = 230 mm, 𝑊=60mm. 8 International Journal of Antennas and Propagation

Conflict of Interests The authors declare that there is no conflict of interests regarding the publication of this paper.

References

[1] W. Cao, B. Zhang, A. Liu, T. Yu, D. Guo, and Y. Wei, “Gain enhancement for broadband periodic endfire antenna by using split-ring resonator structures,” IEEE Transactions on Antennas and Propagation,vol.60,no.7,pp.3513–3516,2012. [2] X. Ding and B. Z. Wang, “A novel wideband antenna with reconfigurable broadside and endfire patterns,” IEEE Antennas and Wireless Propagation Letters,vol.12,pp.995–998,2013. [3] Y. H. Sun, G. J. Wen, H. Y. Jin, P. Wang, and Y. J. Huang, “Gain enhancement for wide bandwidth endfire antenna with I-shaped resonator (ISR) structures,” Electronics Letters,vol.49, no. 12, pp. 736–737, 2013. [4] J. Liu and Q. Xue, “Microstrip magnetic dipole yagi array antenna with endfire radiation and vertical polarization,” IEEE Transactions on Antennas and Propagation,vol.61,no.3,pp. 1140–1147, 2013. [5] R. Elliott, “On the theory of corrugated plane surfaces,” IRE Transactions on Antennas and Propagation,vol.2,no.2,pp.71– 81, 1954. [6]C.H.Walter,Traveling Wave Antennas, McGraw-Hill, New York, NY, USA, 1965. [7] H. Nakano, Y. Ogino, and J. Yamauchi, “Bent two-leaf antenna radiating a tilted, linearly polarized, wide beam,” IEEE Transac- tions on Antennas and Propagation,vol.58,no.11,pp.3721–3725, 2010. International Journal of

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