bandwidth improvement methods of transmitarray...

2946 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 63, NO. 7, JULY 2015

Bandwidth Improvement Methods of TransmitarrayAntennas

Ahmed H. Abdelrahman, Member, IEEE, Payam Nayeri, Member, IEEE, Atef Z. Elsherbeni, Fellow, IEEE,and Fan Yang, Senior Member, IEEE

Abstract—Despite several advantages of planar transmitarrayantennas compared to conventional lens antennas, they have a nar-row bandwidth. The goal of this paper is to improve the bandwidthof transmitarray antennas through the control of the transmissionphase range and the optimization of the phase distribution on thetransmitarray aperture. To validate the proposed approaches, twoquad-layer transmitarrays using double square loop elements havebeen designed, fabricated, and tested at Ku-band. The transmis-sion phase distribution is optimized for both antennas, while theydiffer only in the transmission phase ranges. It is shown that thetransmitarray antennas designed using the proposed techniquesachieve 1-dB gain bandwidth of 9.8% and 11.7%, respectively. Themeasured gains at 13.5 GHz are 30.22 and 29.95 dB, respectively,leading to aperture efficiencies of 50% and 47%, respectively.

Index Terms—Multilayer, transmission phase range, transmi-tarray antenna, wideband.

I. INTRODUCTION

A PLANAR transmitarray antenna consists of a feed sourceand an array of printed antenna elements. Each element

incorporates a certain transmission phase shift to compensatefor the different path lengths from the feed source and pro-duce a focused beam in the main beam direction. Transmitarrayantennas combine many of the favorable features of opticallens and array antennas, leading to a low profile and low massdesign with high radiation efficiency and versatile radiation per-formance. Nevertheless, transmitarray antennas have a narrowbandwidth due to the narrow band limitation of the transmitar-ray elements and the differential spatial phase delay resultingfrom the different path lengths from the feed to each elementon the transmitarray aperture.

There are different efforts being made to increase thebandwidth of transmitarray antennas. One approach involvesusing multiple identical layers of relatively wideband elements[1]–[3]. A proposed wideband transmitarray antenna usingsix-layers of Jerusalem cross elements at 30 GHz has been

Manuscript received August 03, 2014; revised December 14, 2014; acceptedApril 02, 2015. Date of publication April 17, 2015; date of current version July02, 2015. This work was supported by NSF Award # ECCS-1413863.

A. H. Abdelrahman is with the Millimeter Wave Circuits and AntennasLaboratory, Electrical and Computer Engineering Department, University ofArizona, Tucson, AZ 85721 USA (e-mail: [email protected]).

P. Nayeri and A. Z. Elsherbeni are with the Electrical Engineering andComputer Science Department, Colorado School of Mines, Golden, CO 80401USA (e-mail: [email protected]; [email protected]).

F. Yang is with the Microwave and Antenna Institute, ElectronicEngineering Department, Tsinghua University, Beijing 100084, China (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2015.2423706

presented in [1]. A quad-layer transmitarray antenna usingdual-resonant double square loops achieves 7.5% 1-dB gainbandwidth at 30.25 GHz, with aperture efficiency of 35.6%that is calculated based on maximum gain and aperture dimen-sions available in [2]. In [3], a triple-layer transmitarray antennaachieves a 1-dB gain bandwidth of 9% with 30% apertureefficiency at 11.3 GHz using spiral dipole elements.

Another approach involves using receiver–transmitterdesigns [4]–[6]. A reconfigurable 1-bit transmitarray antennaachieves 15.8% 3-dB gain bandwidth at 9.8 GHz using PINdiodes, with aperture efficiency of 15.4% that is calculatedbased on maximum gain and aperture dimensions availablein [4]. In [5], 7.1% and 7.6% 1-dB gain bandwidths withaperture efficiencies of 17% and 12.9%, respectively, havebeen achieved using 1-bit transmitarrays at 60 GHz. In [6],a stacked patch reconfigurable transmitarray element usingvaractor diodes had been studied, which achieves 10% 3-dBfractional bandwidth with 400◦ phase range and an insertionloss varying between 2 and 5 dB. But this high insertion lossvalues will lead to low aperture efficiency.

There are other types of wideband planar lenses used forfocusing the electromagnetic waves. Periodic subwavelengthmetamaterials [7]–[9], and band-pass frequency selective sur-faces [10], [11] are the most common methods used to designthis type of planar lenses. It is noted that most of the ideasbeing made to increase the bandwidth of transmitarray anten-nas are at the expenses of the aperture efficiency and designcomplexity.

This paper presents a detailed study on the transmission mag-nitude and phase of transmitarray elements as a function offrequency, aiming to improve the transmitarray antenna band-width. We demonstrate a design methodology for improvingthe bandwidth of transmitarray antennas through the controlof the transmission phase range and the optimization of thephase distribution on the transmitarray aperture. The noveltyof this work is in focusing on aperture distribution synthe-sis to enhance the bandwidth that is general for any elementshape, while most of the other designs are focusing on usingwideband elements. It is important to note that the proposedtechniques do not preclude implementation of wideband ele-ments in transmitarray designs, and a combination of multiplebroadband techniques would implicitly yield a better bandwidthperformance.

In order to validate this technique, two quad-layer trans-mitarray prototypes using double square loop elements havebeen designed, fabricated, and tested at Ku-band. The trans-mission phase distribution is optimized for both antennas, while

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ABDELRAHMAN et al.: BANDWIDTH IMPROVEMENT METHODS OF TRANSMITARRAY ANTENNAS 2947

Fig. 1. Quad-layer unit-cell configuration of a double square loop element:(a) top view and (b) side view.

they have different transmission phase ranges. The results showwideband performances of 9.8% and 11.7% for 1-dB gain,with aperture efficiencies of 50% and 47%, respectively, at13.5 GHz.

II. BANDWIDTH ANALYSIS OF A TRANSMITARRAY USING

QUAD-LAYER DOUBLE SQUARE LOOP ELEMENTS

A. Unit-Cell Property

In transmitarrays, a full transmission phase range of 360◦

cannot be achieved by using only a single layer of printed ele-ments, and multiple layers are often required to increase theelement phase range [12]. In our study, we select a doublesquare loop element with four identical layers [2] as a ref-erence to analyze the bandwidth characteristics. The unit-cellperiodicity of P ≈ λ0/2 = 11.1mm, where λ0 is the free spacewavelength at 13.5 GHz. The geometrical model of the elementalong with the design parameters are shown in Fig. 1. Thisunit-cell operates in linear vertical or horizontal polarization.The elements are printed on a dielectric substrate with thick-ness T = 0.5mm and permittivity εr = 2.574. The separationbetween layers is equal to H = 5mm, such that the total sep-aration between two layers is close to a quarter wavelength(H+T ≈ λ0/4 = 5.56mm) [12], [13].

The unit-cell simulations were carried out using the commer-cial software CST Microwave Studio [14]. Periodic boundarieswere imposed on the four sides of the unit-cell to simu-late an infinite array of elements. Absorbing boundaries areconsidered on the top and bottom surfaces of the unit-cell,and a normal incidence plane wave is used to illuminatethe unit-cell element. Parametric studies were performed todetermine the separation between the two loops (S) and loopwidth (W) with varying the outer loop length L1. The opti-mum dimensions were determined to be S = 0.22L1 andW = 0.4mm.

Fig. 2(a) and (b) depict the transmission magnitudes andphases of the unit-cell element as a function of the outerloop length L1 and at different frequencies. It is worthwhileto present these results in polar diagrams as a function ofL1, as shown in Fig. 2(c)–(e). The polar plot magnitude rep-resents the transmission magnitude, i.e., |S21|, and the anglerepresents the transmission phase, i.e., ∠S21. By varying theouter loop length L1 from 7.05 to 10.45 mm (correspond-ing to points A and B), a full phase range of 360◦, with atransmission magnitude equal to or better than −1.2 dB at

Fig. 2. Transmission coefficients at different frequencies: (a) magnitudes;(b) phases; (c) polar plot at 13.0 GHz; (d) polar plot at 13.5 GHz; and (e) polarplot at 14 GHz.

Fig. 3. Transmission coefficients versus frequency for different values of L1:(a) magnitudes and (b) phases.

the center frequency of 13.5 GHz can be achieved with thiselement. However, at lower frequencies (such as 13 GHz),the transmission coefficient curve on the polar diagram rotatescounterclockwise and follow the theoretical curve (green curve)[12], as shown in Fig. 2(c). For example, point A rotates fromthe 270◦ location in Fig. 2(d) to the 340-degree location inFig. 2(c). This leads to a decrease in the transmission magnitude[see Fig. 2(a)] and an increase in the slope of the transmis-sion phase [see Fig. 2(b)] at small values of L1. Similarly, athigher frequencies (such as 14 GHz), the transmission coeffi-cient curve rotates clockwise on the polar diagram as shownin Fig. 2(e), which consequently leads to a decrease in thetransmission magnitude [see Fig. 2(a)] and an increase in theslope of the transmission phase [see Fig. 2(b)] at large valuesof L1. In summary, as the frequency changes, the transmis-sion coefficients of the elements change, as shown in Fig. 2(c)and (e), leading to both phase error and magnitude loss, whichultimately results in a reduction of antenna gain at off-centerfrequencies.

For more clarification, the transmission magnitude and phaseversus frequency for different values of L1 are presented inFig. 3. We can notice the magnitude reduction and the changein slope of the phase, which occur simultaneously at low fre-quencies for small values of L1 (e.g., L1 = 7.5mm), and occurat high frequencies for large values of L1 (e.g., L1 = 10mm).


Fig. 4. Geometry of a printed transmitarray antenna.

B. Bandwidth Performance

The transmission phase for each element of the transmitarrayis designed to compensate for the different path lengths fromthe illuminating feed, and achieve a uniform (or progressive)phase on the array aperture. The required phase for a singleelement is not an absolute value, but it is relative to the phasesof all other array elements. For the ith element, the requiredtransmission phase is calculated as

ψi = k (Ri − �ri.r̂o) + ψ0 (1)

where k is the propagation constant in free space, Ri is thedistance from the feed source to the ith element, �ri is the ithelement position vector, and r̂o is the main beam unit vector,as shown in Fig. 4. ψ0 is a phase constant that can be addedto all elements of the array. Once the phase of the ith elementis determined, the corresponding outer loop length L1 can beobtained from Fig. 2(b).

To demonstrate the contribution of both phase error andmagnitude loss on the transmitarray bandwidth, a quad-layertransmitarray antenna using the double square loop elementsof Fig. 1 is designed. The transmitarray has a circular aper-ture with a diameter of 14.5λ0 = 32.19 cm, and an F/D ratio of0.95, where λ0 is the free space wavelength at 13.5 GHz. Thetransmitarray aperture has 621 elements. The feed horn is verti-cally polarized (along y-direction) with a gain equal to 16.3 dBand half-power beamwidths (HPBW) of 30◦ at 13.5 GHz. Thefeed horn pattern is approximately modeled as cosq (θ) withq = 9.25, which is corresponding to an edge taper of −10.2 dB.Moreover, the phase constant ψ0 is selected deliberately foroptimum performances (it will be discussed in details in thenext section).

Using the transmission magnitude and phase propertiesshown in Fig. 2, the array theory [15] is used to calculate theantenna gain as a function of frequency at five different cases,as shown in Fig. 5. In the ideal case, the element magnitude isequal to 1 (0 dB) and the element phase changes with frequencyaccording to equation (1). The case of differential spatial phaseeffect is the phase error that occurs only due to the change ofpath lengths from the feed to each element on the transmitar-ray aperture with the change of frequency. To consider the caseof total phase error effect, the element magnitude is selected tobe equal to 1 (0 dB), while the phase properties of Fig. 2 areconsidered. Similarly, the case of only magnitude loss effectis demonstrated by considering only the magnitude properties

Fig. 5. Effects of element phase error and element loss on the transmitarrayantenna gain.

of Fig. 2, while the element phase changes with frequencyaccording to equation (1). The practical case is to consider bothmagnitude and phase properties of the element.

At the center frequency (13.5 GHz), the phase error is almostzero because the element achieves the full phase range of 360◦

when varying its dimensions as shown in Fig. 2(d). However,the phase error limits the antenna bandwidth due to the differ-ential spatial phase delay and the change in the slope of theelement phase versus element dimensions that occurs at off-center frequencies, as mentioned in Section II-A. The elementmagnitude loss shows less impact on bandwidth limitation com-pared to the phase error effect. However, it reduces the antennagain. This gain reduction increases at off-center frequencies, asdiscussed in Section II-A. For example, at the center frequency13.5 GHz, the gain reduction is 0.47 dB, while at the off-centerfrequencies, the gain reductions are 0.85 dB at 13 GHz and0.77 dB at 14 GHz.

III. BANDWIDTH PERFORMANCE WITH DIFFERENT

REFERENCE PHASES AT THE APERTURE CENTER

In this section, we study the effect of the phase constant ψ0,on the bandwidth of the transmitarray antenna. For this phaseanalysis, we consider the reference point to be the center of theaperture, which has a transmission phase value of ψc. The opti-mum phase constant is then determined by studying all possiblevalues of phase in one full cycle (360◦).

Several quad-layer transmitarray antennas using the samedouble square loop elements of Fig. 1 are studied here. Thetransmitarrays have the same configuration as that presented inthe previous section (such as aperture shape and diameter, num-ber of elements, and feed characteristics). They differ only inthe aperture phase constant ψ0. To illustrate the phase constanteffect, Fig. 6 demonstrates antenna gain for two of these trans-mitarrays as a function of frequency and also compared with theideal case. The corresponding phases at the aperture center ψc

for these two arrays presented here are 10◦ and 270◦, respec-tively. It is observed that different phase constants will lead todifferent bandwidth results.

For better interpretation of these results, it is advantageousto observe the transmission magnitude on the aperture, sincethe impact of each element on the overall performance of thearray also depends on the illumination of that particular ele-ment. In most cases, such as in the study here, the feed antenna


Fig. 6. Calculated gain for different phase values at the aperture center.

Fig. 7. Transmission magnitudes on the transmitarray aperture in dB with twodifferent phase values at the aperture center ψc and at three different frequen-cies. (a) at 13.0 GHz and ψc = 10◦; (b) at 13.5 GHz and ψc = 10◦; (c) at14.0 GHz and ψc = 10◦; (d) at 13.0 GHz and ψc = 270◦; (e) at 13.5 GHzand ψc = 270◦; and (f) at 14.0 GHz and ψc = 270◦.

is pointing to the geometrical center of the array, thus the cen-ter elements have a stronger illumination and contribute moreto the overall performance of the array.

It can be seen from Fig. 7(b) and (e) that at the centerfrequency of 13.5 GHz, the transmission magnitudes of theelements are better than −1.2 dB, corresponding to Fig. 2(d).Thus, the change in the phase constant ψ0 (accordingly the cen-ter phase ψc) does not have much effect on the antenna gain at13.5 GHz, as shown in Fig. 6.

At the lower frequency of 13.0 GHz and referring to Fig. 2(c)and (d), we can expect the best selection of the aperture centerphase is ψc = 270◦ at the center frequency (equivalent to 340◦

at 13.0 GHz), which is represented by point A in Fig. 2(c) and(d). The selection of this aperture center phase places the ele-ments with smaller transmission magnitudes (which implicitlyinclude phase errors) at the farthest positions away from thegeometrical center of the aperture, as shown in Fig. 7(d). Thus,the aperture phase at the center ψc = 270◦ is considered thebest selection along a range of lower frequencies. This providesa solid explanation on why the antenna achieves a higher gain atthe lower frequencies when ψc is set to 270◦, as shown in Fig. 6.

On the other hand, at the higher frequency of 14.0 GHz andreferring to Fig. 2(d) and (e), we can expect the worst selectionof the aperture center phase is ψc = 270◦ (element resonates at14.0 GHz), which is represented by point A in Fig. 2(d) and (e).

TABLE ICOMPARISON OF TRANSMITARRAY ANTENNAS DIFFER IN THE PHASE

VALUES AT THE CENTER OF THE APERTURE

It leads the elements with smaller transmission magnitudes(which implicitly include phase errors) to start at the aperturecenter, as shown in Fig. 7(f). This clarifies the reason of havinglow antenna gain values at the higher frequencies when ψc =270◦, as shown in Fig. 6. It is important to clarify that usingthe element’s transmission magnitude response to optimize theaperture phase distribution is implicitly led to the decrease ofthe effect of the element’s phase error, which is associated withthe transmission magnitude reduction at off-center frequencies.

Through a parametric study, the case of ψc = 10◦ shows thebest element distributions and widest bandwidth compared tothe other cases. Table I summarizes the performances of fivetransmitarrays, which have different phase values at the centerof the aperture.

IV. PROPER SELECTION OF ELEMENT PHASE RANGE FOR

IMPROVEMENT OF TRANSMITARRAY BANDWIDTH

Based on the results of Fig. 2, it is clear that selecting a rangeof outer loop dimensions L1, which can achieve the full phaserange of 360◦ at a certain frequency, will result in transmissioncoefficient variation at other frequencies. In particular, largevariation (both magnitude reduction and phase slope change)occurs for elements with dimensions that correspond to a trans-mission phase around 270◦ at the center frequency, which canbest be observed in the polar diagrams of Fig. 2. Accordingly,in order to minimize the effect of these elements across the fre-quency band of interest, one could avoid using elements thathave transmission phases around 270◦.

To study the feasibility of this technique, four new quad-layertransmitarray antennas are designed using the double squareloop elements of Fig. 1. The transmitarrays have the same con-figuration as those studied in Sections II-B and III. Also, theaperture phase at the center for all four antennas is set to ψc =10◦. The four transmitarrays differ only in the transmissionphase ranges of their elements at the center frequency, whichare 360◦, 300◦, 240◦, and 180◦, respectively. We note that thesephase ranges have been carefully selected to avoid using spe-cific elements that have transmission phases around 270◦. Forbetter demonstration of the phase range selection, Fig. 8(a) and(b) presents in polar diagrams the phase ranges for two cases ofthese four transmitarrays. The polar diagrams of Fig. 8(c) and(d) present the transmission coefficients for the case of limitedphase range of 240◦ at lower and higher frequencies, respec-tively. The figures demonstrate avoiding of those elements withlow transmission coefficients at off-center frequencies in com-parison with the case of full phase range of Fig. 2(c) and (e),


Fig. 8. Two different transmission phase ranges. (a) 360◦ at 13.5 GHz; (b) 240◦at 13.5 GHz; (c) 240◦ at 13.0 GHz; and (d) 240◦ at 14.0 GHz.

Fig. 9. Transmitarray calculated gain for different transmission phase ranges.

TABLE IICOMPARISON OF FOUR TRANSMITARRAY ANTENNAS DIFFER IN THE

ELEMENT TRANSMISSION PHASE RANGES

respectively. Fig. 9 depicts the calculated gain versus frequencyof these two transmitarrays presented here. A summary of theperformances of the arrays is also given in Table II.

Comparison of the gain bandwidths in Fig. 9 shows thatas expected, limiting the transmission phase range by avoid-ing elements with transmission phases around 270◦, increasesthe antenna gain bandwidth. In particular, since elements withpoor transmission coefficient at extreme frequencies are notused in these arrays, the antenna gain at these extreme frequen-cies increase, which ultimately results in an overall increase ofantenna gain bandwidth.

It is also important to note that exclusion of these elementsand consequently using a phase range less than a full cycleresult in some reduction of antenna gain at the center frequency.

Fig. 10. Aperture efficiency and 1-dB gain bandwidth versus transmissionphase range.

The transmitarray bandwidth can be increased at the expense ofsome compromise in gain and aperture efficiency at the cen-ter frequency. The influence of the element phase range ongain bandwidth and aperture efficiency of the transmitarrays isdepicted in Fig. 10.

Improvement of the transmitarray bandwidth through thecontrol of the transmission phase range does not dispensewith the use of the optimization process that was discussed inSection III. Hence, although the limitation of the transmissionphase range around 270◦ avoids the reduction in transmissionmagnitude of the transmitarray elements along a band of fre-quencies, it increases the transmission phase error due to phasetruncation. This in turn leads to some reduction in the antennagain especially at the center frequency. Therefore, optimizingthe phase distribution in this case aims to keep the region oftruncated phase (around 270◦) away as much as possible fromthe aperture center. This in turn leads to minimize the impact ofthe truncated phase to reduce the antenna gain.

V. COMPARISON BETWEEN DIFFERENT ELEMENT SHAPES

The relation between magnitude and phase of an elementin a multilayer frequency selective surface (M-FSS) is deter-mined by the number of layers, the substrate material, andthe separation between layers regardless of the element shape[12]. However, the performance of one element from anotheris related to the response of its change in transmission phasewith respect to its dimensions. The change in the element trans-mission magnitude is generally a function of the transmissionphase values [12]. Accordingly, the proposed design techniqueto improve the bandwidth of transmitarray antennas is feasiblefor general element shapes. However, the bandwidth values thatcan be obtained differ from one element shape to another.

For further clarification, the bandwidth characteristics of twoother elements are studied. The elements, as shown in Fig. 11,are the double four-legged loaded (DFLL) [16]–[19], and theJerusalem cross. The unit-cell configurations of these elements,such as number of layers, unit-cell periodicity, substrate mate-rial, and layer separation, are the same as that presented inSection II. The two unit-cells were simulated using the CSTMicrowave Studio [14]. Parametric studies were performed todetermine the optimum element dimensions. For the DFLL ele-ment, the separation between loops S = 0.2L, d = 0.2L, andthe width W = 0.3mm. For the Jerusalem cross element, the


Fig. 11. (a) DFLL element and (b) Jerusalem cross element.

Fig. 12. Bandwidth of 1-dB gain versus transmission phase range of threedifferent element shapes.

side length Ls = 0.7L, and the width W = 0.5mm. The fullphase range of 360◦ is achieved by varying the element dimen-sion L, where L varies from 7.25 to 10.45 mm for the DFLLelement, and from 5.35 to 10.25 mm for the Jerusalem crosselement.

For a comprehensive comparison between the three ele-ment shapes, eight new quad-layer transmitarray antennas aredesigned with the same configuration as those presented inSections II-B, III, and IV. The phase at the aperture center forall eight antennas are selected equal to ψc = 10◦. Four of thesetransmitarrays used the DFLL elements of Fig. 11(a) with dif-ferent transmission phase ranges. The other four transmitarraysused the Jerusalem cross elements of Fig. 11(b), which also dif-fer in the transmission phase range. These phase ranges havebeen carefully selected to avoid using specific elements thathave transmission phases around 270◦.

Fig. 12 demonstrates the bandwidth performance of the threeelement shapes with the influence of the element phase range.We can notice that the three curves are almost parallel, whichindicates that the bandwidth improvement using the proposedtechnique is feasible for general element shapes. However, thebandwidth values that can be obtained differ from one elementshape to another. Regarding the three element shapes underconsideration, the double square loop element has the widestbandwidth performance. Meanwhile, the gain and the corre-sponding aperture efficiency values are almost the same for thethree elements at the center frequency.

VI. PROTOTYPE FABRICATION AND MEASUREMENTS

To validate the proposed bandwidth improvement method,two quad-layer transmitarray antennas using double square

TABLE IIIDESIGN CONFIGURATIONS OF THE TWO TRANSMITARRAY PROTOTYPES

Fig. 13. (a) Transmitarray mask with presenting the difference in dimensionsfor some elements of the two antennas. (b) Elements that are different in thetwo antennas, as represented by the “x” symbol.

loop elements have been fabricated and tested. The two pro-totypes are the two cases with phase ranges of 360◦ and 240◦

that were presented in Table II. For both designs, an opti-mum transmission phase distribution is selected for the array,which corresponds to a reference phase at the aperture centerof ψc = 10◦. The design parameters of Antenna 1 that has fullphase range and Antenna 2 that has limited phase range aresummarized in Table III.


Fig. 14. Measurement setup of a transmitarray antenna using the NSI planarnear-field system.

Fig. 15. Measured and simulated radiation patterns and gain at 13.5 GHz.(a) Antenna 1 with full phase range. (b) Antenna 2 with limited phase range.

The two antennas are identical in every parameter except therange of outer loop length L1, which are selected based on thedesignated element phase range. Fig. 13(a) illustrates the trans-mitarray mask with presenting the difference in dimensions forsome elements of the two antennas. Fig. 13(b) shows the ele-ments that are different in the two antennas due to the differencein the range of dimension L1 (the dots represent the elementsthat are same in the two antennas and the “x” symbols representthe elements that are different). The elements that are differentare 140 elements out of 621 total elements. The elements ofeach layer are printed on a dielectric substrate. Plastic screwsand plastic spacers are used to maintain an equal separationbetween layers.

Fig. 16. Gain versus frequency of the two antennas: (a) theoretical and(b) measurement.

The fabricated prototypes are tested using the NSI planarnear-field measurement system. A photo of the test setup isshown in Fig. 14. Fig. 15(a) and (b) shows the measured gainpatterns of Antennas 1 and 2, respectively, at the center fre-quency of 13.5 GHz. The simulated co-polarized gain patterns,calculated using array theory [15], are also shown for compar-ison. At 13.5 GHz, the measured gain of Antennas 1 and 2is 30.22 and 29.95 dB, respectively. This corresponds to aper-ture efficiencies of 50% and 47%, respectively. The half-powerbeamwidths (HPBWs) for both antennas are same and equal to4.9◦ and 5◦ in the E- and H-planes, respectively. The measuredside-lobe level (SLL) of Antennas 1 and 2 is −22 and −20 dB,respectively. The cross-polarized levels of both antennas areequal to −30 dB.

Fig. 16 demonstrates the calculated and measured gains ver-sus frequency of the two antennas, which confirms the proposedmethodology to increase the bandwidth of the transmitarrayantennas. Optimization of the reference phase at the aper-ture center ψc for both antennas improves the transmitarraybandwidth. Moreover, it can be noticed that reducing the trans-mission phase range by avoiding elements with phases around270◦ in Antenna 2, leads to the increase of antenna gain athigher and lower frequencies compared to the case of havingfull phase range in Antenna 1, but with a slight decrease inantenna gain at the center frequency. This in turn increasesthe transmitarray bandwidth. We also noticed that the mea-surements show slow decline in the gain at low frequenciescompared to the theoretical results, leading to wider bandsthan expectations. Furthermore, the measured gains are about1.2 dB lower than simulation results. We consider these discrep-ancies are due to the fabrication errors, feed alignments, and


TABLE IVMEASUREMENT RESULTS OF THE TWO TRANSMITARRAY PROTOTYPES

approximations of the simulation model. In summary, the mea-surements show wideband performances of 9.8% and 11.7%for 1 dB gain for Antennas 1 and 2, respectively. Table IVsummarizes the measurement results.

VII. CONCLUSION

A new design approach is proposed to improve the band-width of transmitarray antennas. Variation in the transmissioncoefficient of transmitarray elements as a function of frequencyis first studied. This study clarifies that for quad-layer transmi-tarrays, elements with transmission phases around 270◦ sufferfrom the deterioration in both transmission magnitude andphase with the change of frequency. This in turn limits the trans-mitarray bandwidth. Accordingly, to increase the bandwidthof a transmitarray antenna, a phase truncation is performed inthe element selection routine, which avoids certain elementsaround this frequency-sensitive phase region. Moreover, anoptimization of the phase distribution of transmitarray elementsis carried out. It aims to keep the elements, which have eitherlow transmission magnitude at off-center frequencies or havephase truncation at the center frequency, away as much as pos-sible from the aperture center. This in turn minimizes the impactof these elements in reducing the gain along a band of fre-quencies, and hence increases the antenna gain bandwidth. Theproposed design methodology has been validated through thefabrication and testing of two quad-layer transmitarray anten-nas at Ku-band. The phase distribution is optimized for bothantennas to enhance bandwidth, while they have different trans-mission phase ranges of 360◦ and 240◦. The measurementsshow high gains of 30.22 and 29.95 dB at 13.5 GHz, leading toaperture efficiencies of 50% and 47%, respectively, and wide-band performances of 9.8% and 11.7%, respectively, for 1 dBgain bandwidth.

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[11] M. Li and N. Behdad, “Wideband true-time-delay microwave lensesbased on metallo-dielectric and all-dielectric lowpass frequency selectivesurfaces,” IEEE Trans. Antennas Propag., vol. 61, no. 8, pp. 4109–4119,Aug. 2013.

[12] A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmissionphase limit of multilayer frequency selective surfaces for transmitarraydesigns,” IEEE Trans. Antennas Propag., vol. 62, no. 2, pp. 690–697,Feb. 2014.

[13] A. H. Abdelrahman, A. Z. Elsherbeni, and F. Yang, “Transmitarrayantenna design using cross slot elements with no dielectric substrate,”IEEE Antennas Wireless Propag. Lett., vol. 13, pp. 177–180, Feb. 2014.

[14] Simulation Software. CST Microwave Studio, version 2012.01. Feb. 24,2012.

[15] P. Nayeri, A. Z. Elsherbeni, and F. Yang, “Radiation analysis approachesfor reflectarray antennas,” IEEE Antennas Propag. Mag., vol. 55, no. 1,pp. 127–134, Feb. 2013.

[16] B. A. Munk, Frequency Selective Surfaces, Theory and Design. Hoboken,NJ, USA: Wiley, 2000.

[17] C. Guo, H. Sun, and X. Lu, “Dual band frequency selective surface withdouble-four-legged loaded slots elements,” in Proc. Int. Conf. Microw.Millimeter Wave Technol. (ICMMT), Nanjing, China, Apr. 2008, pp. 297–300.

[18] L. Epp, C. Chan, and R. Mittra, “The study of FSS surfaces with vary-ing surface impedance and lumped elements,” in Proc. IEEE AntennasPropag. Soc. Symp., California, USA, Jun. 1989, pp. 1056–1059.

[19] S. M. Choudhury, M. A. Zaman, M. Gaffar, and M. A. Matin, “A novelapproach for changing bandwidth of FSS filter using gradual circumfer-ential variation of loaded elements,” in Proc. Prog. Electromagn. Res.Symp., Cambridge, MA, USA, Jul. 2010, pp. 1132–1134.

Ahmed H. Abdelrahman (S’13–M’15) received theB.S. and M.S. degrees in electrical engineering,electronics and communications from Ain ShamsUniversity, Cairo, Egypt, in 2001 and 2010, respec-tively, and the Ph.D. degree in engineering sciencesfrom The University of Mississippi, University, MS,USA, in 2014.

He is currently a Postdoctoral Research Associatewith the Department of Electrical and ComputerEngineering, University of Arizona, Tucson, AZ,USA. He also possesses over 8 years of experience in

the satellite communications industry. He worked as an RF Design Engineerand Communication System Engineer building the low earth orbit satelliteEgyptsat-1. His research interests include transmitarray/reflectarray antennas,mobile antennas, 3-D printed antennas, and thermoacoustic imaging.

Dr. Abdelrahman was the recipient of several prestigious awards, includingthe third place winner Student Paper Competition Award at the 2013 ACESAnnual Conference, and the Honorable Mention Student Paper CompetitionAward at the 2014 IEEE AP-S International Symposium on Antennas andPropagation.


Payam Nayeri (S’09–M’12) received the B.S. degreein applied physics from Shahid Beheshti University,Tehran, Iran, in 2004, the M.S. degree in electri-cal engineering from Iran University of Science andTechnology, Tehran, Iran, in 2007, and the Ph.D.degree in electrical engineering from The Universityof Mississippi, Oxford, MS, USA, in 2012.

From 2008 to 2012, he was a GraduateStudent Researcher with the Center for AppliedElectromagnetic Systems Research (CAESR), TheUniversity of Mississippi. From August 2012 to

December 2013, he was a Postdoctoral Research Associate and Instructorwith the Department of Electrical Engineering, The University of Mississippi.He joined the Department of Electrical Engineering and Computer Science,Colorado School of Mines, Golden, CO, USA, as a Postdoctoral Fellowin January 2014, where he is currently an Adjunct Professor and ResearchAssociate. His research interests include array/reflectarray antennas, multi-beam and beam-scanning arrays and reflectors, computational methods andoptimization techniques in electromagnetics, and antenna measurements.

Dr. Nayeri is a member of Sigma Xi, Phi Kappa Phi, and the AppliedComputational Electromagnetic Society (ACES). He was the recipient ofseveral prestigious awards, including the IEEE Antennas and PropagationSociety Doctoral Research Award in 2010, The University of MississippiGraduate Achievement Award in Electrical Engineering in 2011, and the BestStudent Paper Award of the 29th International Review of Progress in AppliedComputational Electromagnetics (ACES 2013).

Atef Z. Elsherbeni (S’84–M’86–SM’91–F’07)received the B.Sc. degree (Hons.) in electronicsand communications, the B.Sc. degree (Hons.) inapplied physics, and the M.Eng. degree in electricalengineering from Cairo University, Cairo, Egypt, in1976, 1979, and 1982, respectively, and the Ph.D.degree in electrical engineering from ManitobaUniversity, Winnipeg, MB, Canada, in 1987.

He joined the Faculty of The University ofMississippi, MS, USA, in August 1987 as anAssistant Professor of Electrical Engineering. He

advanced to the rank of Associate Professor in 1991, and to the rank ofProfessor in 1997. He was appointed as an Associate Dean of Engineeringfor Research and Graduate Programs in 2009. He became the DobelmanDistinguished Chair and Professor of Electrical Engineering with ColoradoSchool of Mines, Golden, CO, USA, in August 2013. He was appointed as anAdjunct Professor with the Department of Electrical Engineering and ComputerScience, Syracuse University, Syracuse, NY, USA, in 2004. He spent a sabbat-ical term in 1996 with the Department of Electrical Engineering, Universityof California at Los Angeles (UCLA), Los Angeles, CA, USA, and was aVisiting Professor at Magdeburg University, Magdeburg, Germany, during sum-mer of 2005 and at Tampere University of Technology, Tampere, Finland,during summer of 2007. From 2009 to 2011, he was a Finland DistinguishedProfessor selected by the Academy of Finland and TEKES. He is the co-author of the books Antenna Analysis and Design using FEKO ElectromagneticSimulation Software, ACES Series on Computational Electromagnetics andEngineering (SciTech, 2014), Double-Grid Finite-Difference Frequency-Domain (DG-FDFD) Method for Scattering from Chiral Objects, (Morgan &Claypool, 2013), Scattering Analysis of Periodic Structures Using Finite-Difference Time-Domain Method (Morgan & Claypool, 2012), MultiresolutionFrequency Domain Technique for Electromagnetics (Morgan & Claypool,2012), The Finite Difference Time Domain Method for Electromagneticswith Matlab Simulations, (SciTech, 2009), Antenna Design and VisualizationUsing MATLAB (SciTech, 2006), MATLAB Simulations for Radar SystemsDesign (CRC Press, 2003), Electromagnetic Scattering Using the IterativeMultiregion Technique (Morgan & Claypool, 2007), Electromagnetics andAntenna Optimization using Taguchi’s Method (Morgan & Claypool, 2007),Scattering Analysis of Periodic Structures Using Finite-Difference Time-Domain Method (Morgan & Claypool, 2012), Multiresolution FrequencyDomain Technique for Electromagnetics (Morgan & Claypool, 2012), and themain author of the chapters “Handheld Antennas” and “The Finite DifferenceTime Domain Technique for Microstrip Antennas” in Handbook of Antennas inWireless Communications (CRC Press, 2001). He was the advisor/co-advisorfor 33 M.S. and 20 Ph.D. students.

Dr. Elsherbeni is a Fellow of ACES. He is the Editor-in-Chief for ACESJournal, and a past Associate Editor to the Radio Science Journal. He wasthe Chair of the Engineering and Physics Division, Mississippi Academyof Science and was the Chair of the Educational Activity Committee forthe IEEE Region 3 Section. He was the General Chair for the APS-URSI2014 Symposium. He held the president position of ACES Society from2013 to 2015. He was the recipient of the 2013 Applied ComputationalElectromagnetics Society (ACES) Technical Achievements award, 2012University of Mississippi Distinguished Research and Creative AchievementAward, 2006 and 2011 School of Engineering Senior Faculty ResearchAward for Outstanding Performance in research, 2005 School of EngineeringFaculty Service Award for Outstanding Performance in Service, 2004 ACESValued Service Award for Outstanding Service as 2003 ACES SymposiumChair, Mississippi Academy of Science 2003 Outstanding Contribution toScience Award, 2002 IEEE Region 3 Outstanding Engineering EducatorAward, 2002 School of Engineering Outstanding Engineering Faculty Memberof the Year Award, 2001 ACES Exemplary Service Award for leadershipand contributions as Electronic Publishing Managing Editor 1999–2001,2001 Researcher/Scholar of the Year Award in the Department of ElectricalEngineering, The University of Mississippi, and 1996 Outstanding EngineeringEducator of the IEEE Memphis Section.

Fan Yang (S’96–M’03–SM’08) received the B.S.and M.S. degrees from Tsinghua University, Beijing,China, in 1997 and 1999, respectively, and the Ph.D.degree from the University of California at LosAngeles (UCLA), Los Angeles, CA, USA, in 2002,all in electrical engineering.

From 1994 to 1999, he was a Research Assistantwith the State Key Laboratory of Microwaveand Digital Communications, Tsinghua University,Beijing, China. From 1999 to 2002, he was aGraduate Student Researcher with the Antenna

Laboratory, UCLA. From 2002 to 2004, he was a Post-Doctoral ResearchEngineer and Instructor with the Electrical Engineering Department, UCLA.In 2004, he joined the Department of Electrical Engineering, The Universityof Mississippi, MS, USA, as an Assistant Professor, and was promoted toan Associate Professor. In 2011, he joined the Department of ElectronicEngineering, Tsinghua University as a Professor, and has served as the Directorof the Microwave and Antenna Institute since then. He has authored over 200journal articles and conference papers, five book chapters, and three booksentitled Scattering Analysis of Periodic Structures Using Finite-DifferenceTime-Domain Method (Morgan & Claypool, 2012), Electromagnetic BandGap Structures in Antenna Engineering (Cambridge Univ. Press, 2009), andElectromagnetics and Antenna Optimization Using Taguchi’s Method (Morgan& Claypool, 2007). His research interests include antennas, periodic structures,computational electromagnetics, and applied electromagnetic systems.

Dr. Yang served as an Associate Editor of the IEEE TRANSACTIONS ON

ANTENNAS AND PROPAGATION (2010–2013) and an Associate Editor-in-Chief of Applied Computational Electromagnetics Society (ACES) Journal(2008–2014). He was the Technical Program Committee (TPC) Chair of 2014IEEE International Symposium on Antennas and Propagation and USNC-URSIRadio Science Meeting. He was the recipient of several prestigious awards andrecognitions, including the Young Scientist Award of the 2005 URSI GeneralAssembly and of the 2007 International Symposium on ElectromagneticTheory, the 2008 Junior Faculty Research Award of The University ofMississippi, the 2009 inaugural IEEE Donald G. Dudley Jr. UndergraduateTeaching Award, and the 2011 Recipient of Global Experts Program of China.

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