IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO. 2, FEBRUARY 1997 287

Design of Millimeter Wave Microstrip Reflectarrays David M. Pozar, Fellow, IEEE, Stephen D. Targonski, and H. D. Syrigos, Senior Member, ZEEE

Abstruct- This paper discusses the theoretical modeling and practical design of millimeter wave reflectarrays using microstrip patch elements of variable size. A full-wave treatment of plane wave reflection from a uniform infinite array of microstrip patches is described and used to generate the required patch- design data and to calculate radiation patterns of the reflectarray. The critical parameters of millimeter wave reflectarray design, such as aperture efficiency, phase errors, losses, and bandwidth are also discussed. Several reflectarray feeding techniques are described, and measurements from four reflectarray design ex- amples at 28 and 77 GHz are presented.

Index Terms- Microstrip arrays.

I. INTRODUCTION S its name implies, a reflectarray antenna combines some A of the best features of reflector and array antennas. In

its basic form, a microstrip reflectarray consists of a flat array of microstrip patches or dipoles printed on a thin dielectric substrate. A feed antenna illuminates the array whose individual elements are designed to scatter the incident field with the proper phase required to form a planar phase surface in front of the aperture, as suggested in Fig. 1. This operation is similar in concept to a parabolic reflector that naturally forms a planar phase front when a feed is placed at its focus, thus, the term $ut rejector is sometimes used to describe the reflectarray. Space feeding the reflectarray eliminates the complexity and losses of a microstrip feed network. The reflectarray concept is not new [ 11, but the rapid development of microstrip antenna technology, coupled with the need for low-cost, high-gain, and aesthetically pleasing antennas for commercial applications, has led to the use of microstrip elements in a variety of reflectarray configurations. This approach is especially fruitful for high-gain millimeter wave antennas, because losses in a microstrip feed network in a large array at high frequencies are often unacceptable [2], and the obtrusive profile of a parabolic reflector is perceived as a nuisance in many situations. A microstrip reflectarray can be made to be flat or conformal, at low cost. There is a great deal of flexibility in choosing the feeding method for a reflectarray, as it is possible to use prime-focus feeding, offset feeding, and novel types of cassegrain feeds. It is also possible to scan the main beam, obtain monopulse patterns, and perform phase- synthesized pattern shaping with a microstrip reflectarray. Linear, dual, or circular polarization can be obtained.

Manuscript received May 3, 1995; revised February 6, 1996. D. M. Pozar and S. D. Targonski are with the Electrical and Computer

Engineering Department, University of Massachusetts, Amherst, MA 01003 USA.

H. D. Syrigos is with Alpha Industries, Inc., Wobum, MA 01801 USA. Publisher Item Identifier S 0018-926X(97)01455-5.

reflectarray Fig. 1. Geometry of the microstrip reflectarray

One of the key features of microstrip reflectarray imple- mentation is how the individual elements are made to scatter with the desired phases. One method is to use microstrip patches of the same size, with stubs of variable length to control the reflection phase [3]-[5]. A better approach, and the one used for the present work, is to use printed dipoles or patches of variable size to control the phase [6], [7]. Both methods can be viewed as techniques for introducing a small shift in the resonant frequency of an element which has the effect of changing the phase of the reflected field. Using elements of variable size allows much more freedom in laying out an array for dual or circular polarization, with the additional advantages of improved bandwidth [6] and simpler analysis when compared with stub-tuned elements. Polarization selectivity can be achieved by using rectangular patches for linear polarization, and square patches, circular patches, or crossed dipoles for dual or circular polarization. As with reflectors, feed illumination spillover and amplitude taper reduce the efficiency of the reflectarray, in addition to material losses and phase errors. The bandwidth of a microstrip reflectarray is generally better than that of its planar array counterpart, but much less than the bandwidth that can be achieved with a parabolic reflector. It is important to realize that the electrical performance of a reflectarray will typically be inferior to a traditional reflector antenna so that the primary advantages of the reflectarray are those of size,

0018-926W97$10.00 0 1997 IEEE

288 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO. 2 , FEBRUARY 1997

weight, and cost. One of the few electrical advantages of the reflectarray is improved cross-polarization performance due to the polarization selectivity that can be obtained with rectangular patch elements.

In this paper, we will present a thorough study of the design and performance of millimeter wave microstrip reflec- tarrays, examining issues such as different feed configurations, spillover and taper efficiencies, losses due to materials and phase errors, pattern bandwidth, and beam squint versus fre- quency. We also briefly describe an analysis of the microstrip reflectmay which is based on a full-wave moment method solution for scattering from an infinite array. The results of this work are validated with four millimeter wave reflectmay designs operating at 28 and 77 GHz.

11. ANALYSIS OF MICROSTRIP REFLECTARRAYS

Fig. 1 shows the basic geometry of a microstrip reflectarray using patches of variable size. In general, the feed may be positioned at an arbitrary angle and distance from the reflec- tarray, but is assumed to be far enough from the reflectarray so that the incident field can be approximated by a plane wave. The basic design principle requires that the phase 4, of the field reflected from an element in the reflectarray be chosen so the the total phase delay from the feed to a fixed aperture plane in front of the reflectarray is constant for all elements

very good results for more than eight microstrip reflectarray designs have been obtained with this procedure. Fortunately, the computationally impractical analysis of an array with thousands of elements of unequal size is not necessary for a successful reflectarray design.

Here we present a brief summary of the solution used to design and analyze a microstrip reflectarray. We assume an incident plane wave of the form

- E, ~ Eoe3ko(zU%+yv,+z C O S 8 % ) (2)

where 2 0 defines the amplitude and polarization of the inci- dent field and

U, = sin 0, cos 4, v, = sin 8, sin 4,

(3 a) (3b)

are the direction cosines of the wave. The phase reference for this and the following fields is at the origin (bottom of substrate). In the absence of microstrip patches, the specular reflected field from the dielectric substrate and ground plane can be expressed as

where Roe and R44 are the plane wave reflection coefficients given by [XI

( 54

(5b)

k0&~cOS0~COSkld - j k 1 S ink lde2gkodcose ,

dl cos k1 - 3 k0 cos 8% sin kl e 2 J k o d COS 0,

k o ~ , cos 0, cos k1 d + j kl sin kl d Ree =

'" = lcl cos kl d + j k o cos 0, sin kl d

ko(R, - T, . ? o ) - +, = ZTN. (1)

The vectors R,, F , , io are defined in Fig. 1. The overall design procedure for a reflectarray using patches of variable size is outlined below.

1) The reflectarray substrate is selected on the basis of frequency, bandwidth, loss, and cost.

2) A full-wave moment-method solution is used to generate data for the amplitude and phase of the field reflected from an infinite uniform array of microstrip patches versus patch length.

3) The required patch sizes are determined from the phase- delay condition given in (l), with interpolation of the data generated in step 2).

4) The pattern of the reflectarray is calculated using array theory. The amplitude and phase of the excitation at each reflectarray element is found from the feed pattern and geometrical optics. For the best accuracy, the moment- method analysis is again used to find the amplitude and phase of the reflected field from each patch.

5 ) The spillover of the feed pattern is computed, and the directivity and gain of the reflectarray are found.

This procedure assumes that the reflection from an individual patch surrounded by patches of different sizes can be approx- imated by the reflection from an infinite array of patches of equal size. One argument for this approach is that the mutual coupling between elements is very small for thin microstrip substrates so the effect of neighboring patches is negligible. In addition, we have also analyzed several reflectarrays using a model for reflection from a single patch element (no mutual coupling effects) with results in close agreement with the infinite array model. But the ultimate justification is that

where

(6) kl = k o d e r -sin 2 0,.

In these results, E, can be made complex to account for dielectric loss; if no loss is present, IRse) = = 1. Note that the reflected wave given by (4) propagates in the direction O , , 4, + T .

The presence of microstrip elements gives rise to an ad- ditional scattered field component which can be expressed in terms of the incident field using scattering coefficients as

Then the total field reflected from the reflectarray in the specular direction can be written as

The phase $, required in (1) for design can be found from this result.

To calculate the radiation pattern of the reflectarray, we assume that the reflectarray is divided into unit cells according to the element grid spacing, and that each unit cell radiates a spherical wave field proportional to the total field given by (8). The incident field amplitude and phase at the ith unit cell is determined by the feed pattern at that unit cell, including

POZAR et al.: DESIGN OF MILLIMETER WAVE MICROSTIUP REFLECTARRAYS 289

1/Ri amplitude decay and koRi phase-delay factors. The fields radiated from the electrically small unit cells have fairly broad patterns which allows us to write the radiation pattern of an N-element reflectarray as

i=l - (9) , E ~ ( Q ; , 4 i ) e j k o ( z , sin0cos$+y, sinesin$)

where xi, y; are the coordinates of the center of the ith patch, 8;, $i are the angles of incidence from the feed to the ith patch, and Bf is the field pattern of the feed (including the e- jkoRa/Ri dependence). The dyadic 0 accounts for the transformation from a plane wave field to a spherical wave, and is related to the radar cross section of a square plate [9]

where 82, er are unit vectors representing the polarizations of the incident and reflected waves, respectively, and hlz is a unit vector in the direction of the incident magnetic field. The expression in (9) thus includes both co-pol and cross-pol components. One way of interpreting this result is to consider the scattered fields from each patch radiating as in an ordinary array, with a physical optics-like numerical integration of the specular reflection from each unit cell. This technique then accounts for the finite size of the reflectarray ground plane.

The scattering coefficients defined in (7) are found using a full-wave moment-method solution. The procedure is very similar to the analysis of radar cross section of a microstrip antenna [lo] and the analysis of infinite arrays of microstrip elements [8], [ l l ] , and so we refer the reader to those references for details of the relevant Green's functions and Fourier transforms. The moment-method impedance matrix elements can be computed as

where Ti is the Fourier transform of the ith expansion mode current, and ?? is the dyadic Green's function for the dielectric substrate. The Floquet wavenumbers are defined as

27rm k,, = ~ + lcoui a

2n-n kyn = - + k02.'i b

The voltage vector elements can be expressed using the reciprocity theorem [lo] as

vi = s, pi. (P +E') drc dy = 1 pi .? dx d7J (13)

where 7' is the ith expansion mode current, zi is the electric field radiated by that mode in the presence of the grounded dielectric substrate, and 7; is an equivalent surface current

-. - density that radiates the field Ez++ET in the absence of patches. It can be shown that one choice for this current is

- J ; = J s O e j k o ( z Y , + Y v , + d c o s O ~ ) (14)

where - -2 Jso = ~ [ ~ ( E o Q cos q5z - EO$ cos 19' sin 4,)

+ y(Eoe sin 4L + Eo4 cos OL cos 4,)]. Using this expression in (13) results in delta functions from the space integrations, which allows the voltage vector elements to be simplified to

- v, = Jso . G(-kou,, -ko?J,) . F,(-lcou,, -kO?J,)e3leodcos@*.

(15)

We havc found that very good results can be obtained using just two expansion modes for each current polarization per patch if a mode enforcing the edge condition for the current at the radiating edges of the patch is used.

111. DESIGN CONSIDERATIONS FOR MICROSTRIP REFLECTARRAYS

In this section, we discuss the essential design characteristics and options of microstrip reflectarrays and compare with cor- responding results for parabolic reflectors when appropriate.

A. Feed Conjgurations Fig. 2 compares the geometries of a prime focus parabolic

reflector and a reflectarray. Both antennas have the same subtended (half) angle 00, but different f / D ratios. For the reflectarray, the relation between 80 and f / D is

which differs from the expression for the parabola (2 tan-' D / 4 f ) . Since spillover and amplitude taper efficiency are a direct function of subtended angle, as opposed to f / D ratio, the former offers the best basis for comparison. Thus, for the same subtended angle and aperture size, the reflectarray will be slightly smaller in depth. This can be an advantage in applications where space or appearance is important.

Like the parabolic reflector, many types of feed configura- tions can be used with a reflectarray. In fact, due to the extra degree of freedom offered by a controllable reflection phase, the reflectarray offers possibilities beyond those of the ordinary reflector antenna. As shown in Fig. 1, it is easy to design the reflectarray to produce a main beam scanned off broadside. This allows the antenna to be mounted vertically and still have a main beam pointing above the horizon. The directivity will be reduced by a cos H factor due to the projected aperture. It is also possible to use an offset feed, as shown in Fig. 3(a). This configuration reduces aperture blockage and can also minimize beam squint versus frequency.

Fig. 3(b) shows a reflectarray with a cassegrain feed. The standard hyperbolic subreflector can be used, or a simpler

290 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO 2, FEBRUARY 1997

(3) I

Fig. 2. reflectarray.

Subtended angles of (a) a prime focus parabolic reflector and @) a

flat reflector plate can be used by appropriately designing the reflection phase of the reflectarray. In fact, since the reflectarray elements can provide phase compensation for any subreflector shape, the subreflector can be independently contoured to provide a particular amplitude distribution to maximize directivity or shape the main beam. Another inter- esting possibility is to design a small microstrip feed antenna on the reflectarray substrate. This might be a single element or a small array (possibly a monopulse array), and offers further simplicity and cost savings compared to the use of a separate feed horn antenna.

B. Spillover and Taper EfJiciencies

form For an assumed axisymmetric feed-power pattern of the

G,(%,d) = COS^ % (17)

where n = 2,4,6,8, . . . , we can find closed-form expressions for the spillover and amplitude taper efficiencies for a circular reflectarray. Using the definitions in [12] gives the spillover efficiency as

(18)

where Bo is the subtended half-angle defined in Fig. 2(b). This result is the same as that for a circular parabolic reflector having the same value of 00. Similarly, an expression for the amplitude taper efficiency for a circular reflectarray can be derived as

qs = 1 - COSn+l B O

(19) 2n (1 - COS(^/^)-' 00)’

Ilt = ~ tan2 (; - 1)2(l- cosn B o ) .

The product of spillover and taper efficiency for a circular reflectarray is plotted in Fig. 4 versus 00 for various values of

feed

Fig. 3. Reflectmay configurations using (a) an offset feed and (b) a cassegrain feed.

n. As in the case of reflectors, there is an optimum value of BO that maximizes aperture efficiency for a given feed pattern. This maximum value is slightly lower than the optimum aperture efficiency for the parabolic case because of a slightly lower taper efficiency.

The reflectarray aperture efficiency will be different if a square or rectangular aperture is used. In this case, the corners of the reflectarray improve the spillover efficiency but degrade the taper efficiency because of the increased edge taper in these areas. Although the above results are useful for general trends, better accuracy can be achieved for a particular feed antenna and reflectarray aperture by numerically integrating the feed-power patteni over the reflectarray elements to find the spillover and taper efficiencies.

C. Phase Errors The phase of the total reflected field from the ith patch

element $% is determined by the patch length and can be com-

POZAR et al.: DESIGN OF MILLIMETER WAVE MICROSTRIP REFLECTARRAYS 29 1

1.0

0.9

0.8

0.7

$' 0.6

2 0.5 i5

0.4 c II b 0.3 a

0.2

0.1

0.0

to occupy most of the unit cell, causing reflection primarily from the patch surface. The difference in path length 2kod represents the range of reflection phase that is unattainable for elements that fill a large fraction of the unit cell. Actually, there is typically only a small percentage of patches with phases that would occur in this range, so the overall effect is not as severe as might be expected. The dipole element does not suffer this problem because of its smaller area, but its bandwidth is significantly less than that of a patch and, as we will discuss below, the losses associated with dipole elements are much greater than the losses of patch elements.

Random phase errors can be introduced by fabrication tolerances in the flatness of the array and etching of the elements. The latter is usually more critical, because of the large slope of the phase versus patch-size curves. Wider bandwidth elements reduce this sensitivity. If the rms error in element size can be measured or estimated, the worst-case phase error can be inferred from curves like those of Fig. 5, and the resulting loss in gain can be predicted as

OJ .- .-

a

Subtended Angle 80

Fig. 4. Aperture efficiency ( v s v t ) for a circular reflectarray versus sub- tended angle.

360

AG = -10 log(1 + g2) dB (20) 300

240

180 z w 120

60

0

where o2 is the variance (in radians squared) of the assumed zero-mean Gaussian distributed phase errors. For a 1-dB loss in gain this result implies a rms phase error of less than 30". For the case of a square patch on a 0.010'' substrate, the data of Fig. 5 gives a worst case (near the resonance region) dimensional tolerance of f0.0007", which is not difficult to achieve with standard processing techniques.

Phase error can also be introduced by the feed antenna if its phase center is not well-defined. In particular, if the phase center of the feed varies between its principle planes,

-O" -O" O'O O" o'2 O 3 0'4 an expression similar to (20) can be used to estimate the loss in directivity.

e, -0 v

c

- 'c

a, cc

Patch Size AL/Lo

Fig. 5. Phase of the total reflected field from an infinite array of microstrip patches versus patch size. f = 28 GHz cr = 2 . 9 5 , ~ = b = 0.536 cm, Bz = q5z = 0. thin dipole: Lo = 0.3237 cm, W = 0.05 cm, square patch (d = 0.010"): Lo = W = 0.2915, square patch (d = 0.020"): Lo = W = 0.2756 cm.

puted using the moment-method procedure described above. Fig. 5 shows typical results for reflectarray elements at 28 GHz. Application of (1) gives values of $; ranging from 0 to 360°, which can be used with this data to determine the required size of each element in the reflectarray. Because of the rapid phase change around resonance, most reflectarray elements have lengths within f5% of the nominal resonant length LO. However, because of the nonlinear shape of the phase versus patch-size curve, phase errors will result for changes in frequency greater than a few percent. This effect limits the bandwidth of the reflectarray, and will be discussed further in Section 11-D.

Deterministic phase errors can also be introduced by several other mechanisms, leading to loss in directivity and degrada- tion of the pattern. As seen from Fig. 5, phase error can arise with patches on thick substrates, since the reflection phase for such cases does not approach zero for large patch length. This occurs because for patches well below resonant size, reflection takes place from the ground plane, while larger patches tend

D. Reflectarray Losses

In addition to losses in directivity due to spillover, amplitude taper, and phase errors, reflectarrays also suffer potentially significant loss due to dielectric loss, copper loss, and surface wave excitation. As discussed in [13], surface wave loss for a single microstrip element on a low-dielectric constant substrate is typically less than 15%. Due to destructive cancellation, however, surface wave loss of a printed array decreases with array size unless the scan angle is close to a scan blindness. Therefore, for reflectarrays designed without grating lobes in visible space, power lost to surface waves should be less than a few percent. Dielectric and conductor loss are typically much more significant, especially at millimeter wave frequencies. Because of high current densities, the reflection loss for an array of thin dipoles can be as high as several dB while wider patches typically have conductor loss in the range of a few tenths of a dB.

Dielectric loss is strongly dependent on the thickness and loss tangent of the reflectarray substrate. As shown in Fig. 6, dielectric loss can be several dB for thin substrates with high-loss tangents. Note that loss is greatest for elements near resonance which includes most of the elements in a reflectarray. Dielectric loss increases with frequency for a

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO. 2 , FEBRUARY 1997 292

3.0

2.5

2.0 - 88 9

1.5 8 _I

0.5

0.0 (

& d=0.010"

/ \ ta5=0.007

I , I

i -0.06 -0.04 -0 02 0 00 0 02 0 04 0.06 E

Normalized Patch Length AULD

Fig. 6. Dielectric loss for an infinite array of microstrip patches versus patch size. f = 28 GHz, E , = 2.95,a = b = 0.536 cm, 0% = 4% = 0, Lo = W = 0.296 cm for d = 0.010"; Lo = W = 0.279 cm for d = 0.020".

fixed loss tangent, but this trend is compounded by the fact that the loss tangent also increases with frequency. It is hard to find data on the variation of loss tangent with frequency, and most manufacturer's specifications give data only at 10 GHz. Some estimates suggest that the variation of loss tangent is approximately linear with frequency 1141, so the values of 0.002 and 0.007 used in Fig. 6 should be reasonable estimates for the loss tangents of Duroid 5880 and Taconic TLE materials, respectively, at 28 GHz. The data of Fig. 6 suggest that the effect of a lossy material can be largely offset by using a thicker substrate; this also has a beneficial effect on bandwidth.

E. Bandwidth

The bandwidth of a reflectarray is limited primarily by phase errors that increase away from the center frequency. Phase error arises because the reflection phase is not a linear function of the electrical size of the patch element, so the change in phase versus frequency is different for different elements. The slope of the phase versus length curve is a measure of the bandwidth of the reflectarray, as a curve with a smaller slope will lead to less phase error when the electrical size of the elements change with frequency. As with microstrip patch antennas, the bandwidth of reflectmay elements can be improved by using thicker substrates or wider elements. These trends are clearly evident from the data in Fig. 5 which show results for a thin dipole element and square-patch elements for two substrate thicknesses. Other broadbanding techniques, such as stacking patches, can also be used. Another source of phase error occurs because the path lengths from the feed to the aperture plane may differ by multiples of 360" for many of the elements, leading to different phase versus frequency slopes.

A related problem occurs for reflectmays with offset feeds where the main beam can scan with frequency due to a change in phase taper across the reflectmay with a change in frequency. We have found that this beam squint is most severe when the angle of the main beam differs greatly from the natural specular reflection angle. Beam squint is minimized

Fig. 7. Photograph of 28 GHz 6" square reflectmay.

if the angle of the main beam is chosen to be close to the natural specular reflection angle.

IV. DESIGN EXAMPLES

A. iY-Square Offset Beam Reflectarray at 28 GHz We first consider a 6" square microstrip reflectarray with a

broadside feed and a main beam scanned 25" off broadside, as shown in Fig. 7. The subtended angle of the aperture (to the edges of the square) is 2B0 = 72". A circular corrugated horn having a -10 dB beamwidth of about 92" was used for a feed antenna, giving an edge taper of about -7 dB. The patches were square and, thus, capable of handling either linear or circular polarization, but the feed was linearly polarized. The first version of this design used a 0.010'' Taconic TLE substrate ( E ~ = 2.95), but the estimated loss tangent of 0.0074 of this material at 28 GHz led to a loss of almost 2 dB. A second version was, therefore, designed on 0.020" Duroid material ( E ~ = 2.2) having an estimated loss tangent of 0.0028 at 28 GHz. This design demonstrated an increase in gain of about 2.3 dB over the first model. The lower loss was due to the reduced loss tangent and the increased substrate thickness, and also the use of a wider range of patch sizes to reduce reflection phase errors. A detailed loss budget for both versions is given in Table I.

In this table, the maximum directivity is computed as 47rNab/X2. The first version of this reflectarray used 528 elements with a = 0.609 cm and b = 0.667 cm, while the second version used 784 elements with a = b = 0.544 cm. The cos Q loss accounts for the decrease in projected aperture area due to the 25" scan angle. The spillover, taper, dielectric, and conductor losses were calculated numerically as part of the moment method solution for the pattern calculation. The design phase-error loss accounts for the fact that the necessary reflection phases could not be obtained for some patches for the reasons discussed in Section 111-C. The measured gains in

POZAR et al.: DESIGN OF MILLIMETER WAVE MICROSTFUP REFLECTARRAYS

maximum directivity cos 8 loss

spillover loss

293

33.1 dB 34.1 dB -0.4 dB -0.4 dB -0.7 dB -0.7 dB

TABLE I Loss BUDGET FOR Two 28 GHz 6“ SQUARE REFLECTARRAYS

taper loss dielectric loss copper loss

I 0.010” Taconic I 0.020” Duroid

-0.7 dB -0.7 dB -1.8 dB -0.2 dB -0.2 dB -0.1 dB

design phase error loss calculated gain measured gain

aperture efficiency

-1.5 dB -0.7 dB 28.4 dB 31.3 dB 28.7 dB 31.0 dB

35% 54%

- Calculated

Fig. 8. reflectmay.

Measured and calculated E-plane patterns for the 28 GHz 6‘-square

this table have been corrected by 0.2 dB to account for loss in the waveguide feed transition. The aperture efficiency was computed as the ratio of the measured gain to the maximum directivity reduced by the cos0 loss. The choice of substrate is seen to have a significant impact on the aperture efficiency of the reflectarray. The efficiency of this reflectmay could be improved slightly by using a feed antenna giving an edge taper closer to the optimum value of -10 dB.

Measured and calculated E-plane patterns for the 0.020” Duroid version of this reflectarray are shown in Fig. 8. Note that the beam is scanned to 25”, and the sidelobes are below 20 dB. The H-plane pattern shows similar sidelobe levels. The measured cross-pol level is below 35 dB in both planes; this is much better than the cross-pol level of the typical parabolic reflector due to the reflection properties of the patch elements. The 1-dB gain bandwidth of the reflectarray is about 5%.

B. 9”-Diameter Rejectarray at 28 GHz

This reflectarray was 9” in diameter, with a broadside main beam and a prime-focus backfire feed antenna, as shown in Fig. 9. It used 996 rectangular (linearly polarized) patch elements on a 0.010’’ Taconic TLE substrate with a grid spacing of a = 0.56 cm and b = 0.67 cm. The subtended angle of the aperture was 200 = 114O, which was close to the 10-dB beamwidth of the feed. The feed consisted of a circular waveguide-fed dielectric cap [15], having a backfire-type radiation pattern. The circular aperture of the reflectarray helps to reduce sidelobes, as can be seen from the measured and calculated patterns shown in Fig. 10. The poor loss characteristics of the substrate material resulted in a dielectric loss of approximately 1.3 dB, and a measured gain of 31.2 dB (corrected for 0.2-dB feed transition loss). The dielectric loss for this case was slightly lower than the loss

Fig. 9. Photograph of 28 GHz 9”-diameter reflectmay.

(b)

Fig. 10. (a) E plane. (b) H plane.

for the 6“ square reflectarray on the same material because the average size of the rectangular patches was larger than the average size of the square patches used in the previous case.

The performance of the 9” reflectarray was compared to a parabolic dish antenna of the same diameter and using the same feed antenna. The parabolic dish had f / D = 0.44, and was fabricated from metallized plastic. Results are summarized in Table 11. The maximum directivity is computed from the physical area of the aperture. Because the subtended angle of the reflector is 2B0 = 118”, the spillover for the dish is negligible, but the taper loss is high. Still, the dielectric and phase error losses of the reflectarray serve to reduce its gain by several decibels below that of the parabolic dish. This could be improved by using a less lossy and/or thicker reflectarray substrate.

Measured and calculated patterns for the 9”-diameter reflectmay.

294 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO. 2, FEBRUARY 1997

auerture diameter

TABLE I1 COMPARISON OF 28 GHz CIRCULAR REFLECTARRAY AND PARABOLIC DISH

9" 91'

maximum directivity I 36.1 dB 36.5 dB spillover loss

Fig. 11. Layout mask for the 77-GHz reflectarrays.

The measured reflectarray sidelobe levels were about 23 dB for both principal planes, while the calculated sidelobe levels were about 28 dB for both planes. The difference was probably caused by phase errors due to etching tolerances on the patches, and perhaps by the lack of a well-defined phase center for the feed. We are unable to explain the relatively high sidelobe levels for the reflector antenna, or the slightly low value of measured gain. Finally, note that the cross- polarization level for the reflectarray is significantly better than that of the parabolic reflector. The 1-dB gain bandwidth of the reflectarray is about 2%.

C. 6"Square Prime Focus Rejectarray at 77 GHz This reflectarray was 6" square, and operated at 77 GHz.

It was fabricated on 0.005" Duroid substrate, with 5776 linearly polarized rectangular patch elements. The mask for this antenna is shown in Fig. 11. This reflectarray was fed with a prime focus flared rectangular waveguide "J-feed"; a cassegrain feed for the same reflectarray is discussed in the following section. The loss budget for this model is given in Table 111, where it is compared with results for the cassegrain version.

The measured gain was 36.0 dB (not including feed losses). This is several dB below the calculated value of 39.5 dB, perhaps due to a combination of effects including feed line

-0.9 dB -0.2 dB

-16 -12 -8 -4 0 4 8 12 16

(4

taper loss dielectric loss

copper loss residual design phase error

calculated gain measured gain

measured sidelobes measured cross-pol

0

-5

-10

-1 5

-20

-0.8 dB -0.8 dB -1 4 dB 0.0 dB -0.2 dB -0 1 dB -1.1 dB 0.0 dB 31.7 dB 35.4 dB 31 2 dB 33.9 dB

23(E), 23(H) dB 18(E), 17(H) dB -34 dB -22 dB

-16 -12 -8 -4 0 4 8 12 16

(b)

Fig. 12. Measured and calculated patterns for the 76-GHz prime focus reflectarray. (a) E plane. (b) H plane.

losses and random phase errors due to both etching of the patches and the flatness of the reflectarray substrate. The measured beamwidths were 1.55" x 1.65", which gives an approximate directivity of 41 dB; the close agreement with the calculated gain implies dissipative losses as the main cause of the low measured gain since random phase errors would lead to larger beamwidths. Measured patterns for this reflectarray are shown in Fig. 12. Peak sidelobes in both planes were about 25 dB. This result and the presence of well-defined pattern nulls lends further support to the conclusion that phase errors were not too severe.

D. B-Square Cussegruin Rejectarray ut 77 GHz This reflectarray used the same patch layout as the preceding

design, but was fed with a conical waveguide horn and a hy- perboloidal subreflector in a cassegrain configuration. Fig. 13 shows a photograph of this antenna. The subreflector was 1.61 cm in diameter, and the feed was a conical horn with an aperture diameter of 1.25 cm; this combination unfortunately results in a high spillover loss. The measured patterns were very similar to those obtained with the prime focus feed with measured beamwidths of 1.5" x 1.7", and peak sidelobe levels of 19 dB. The measured gain was 36.9 dB. Although this reflectarray did not suffer the feed line loss of the feed used in the prime focus model, the gain was reduced by the additional spillover (estimated as 2 dB) and blockage losses associated

POZAR et al.: DESIGN OF MILLIMETER WAVE MICROSTRIP REFLECTARRAYS

maximum directivity

tauer loss spillover loss

295

Prime Focus Cassegrain 42.8 dB 42.8 dB -0.9 dB -2.0 dB -0.9 dB -0.9 dB

Fig. 13. Photograph of the 77-GHz reflectarray with cassegrain feed.

TABLE I11 Loss BUDGET FOR Two 77 GHz ~“-SQUAKE REFLECTARRAVS

dielectric loss copper loss

design phase error loss calculated gain

-1.0 dB -1.0 dB -0.2 dB -0.2 dB -0.3 dB -0.3 dB 39.5 dB 38.4 dB

measured gain 36.0 dB 36.9 dB

with the cassegrain configuration. This is partly due to the fact that the 6” aperture size is too small for optimum aperture efficiency for a cassegrain antenna at this frequency. The 1-dB gain bandwidth of this reflectarray was about 2.5%.

V. CONCLUSION

Microstrip reflectarrays offer a useful design alternative for high-gain antennas, avoiding the high losses associated with microstrip arrays and the bulkiness of reflector anten- nas. Many variations in feeding methods, element geometry, and beam forming are possible with microstrip reflectarray s. Reflectarrays can be succesfully used at millimeter wave frequencies, but attention must be given to issues such as phase errors, substrate selection, and bandwidth. In contrast to ordinary microstrip antennas for which it is possible to design antennas and arrays with little or no CAD support, successful microstrip reflectarray design requires the use of accurate modeling software for both design and analysis. The examples described in this paper demonstrate the results that can be obtained from millimeter wave microstrip reflectarrays, but we feel that the efficiencies resulting from these initial efforts can be improved by careful attention to design details such as substrate materials, feed design, and patch fabrication.

REFERENCES

[l] R. G. Malech, “The reflectarray antenna system,” presented at 12th Ann. Antenna Symp., USAF Antenna Res. Develop. Program, University Illinois, Urbana-Champaign, 1962.

[2] D. M. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. Piscataway, NJ: IEEE Press, 1995.

[3] R. E. Munson, H. Haddad, and J. Hanlen, “Microstrip reflectarray an- tenna for satellite communication and RCS enhancement or reduction,” U.S. Patent 4684952, Aug. 1987.

[4] J. Hnang, “Microstrip reflectarray,” in IEEE Int. Symp. Antennas Prop- q a t . , Ontario, Canada, June 1991, pp. 612-615.

[5] D. C. Chang and M. C. Huang, “Microstrip reflectmay antenna with offset feed,” Electron. Lett., vol. 28, pp. 1489-1491, July 1992.

[6] D. M. Pozar and T. A. Metzler, “Analysis of a reflectarray antenna using microstrip patches of variable size,” Electron. Lett., vol. 29, pp.

[7] S . D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” in IEEE Int. Symp. Antennas Propagat., Seattle, WA, June 1994, pp. 1820-1823.

[8] F. J. Harackiewicz, “Electromagnetic radiation and scattering from microstrip antennas on anisotropic substrates,” Ph.D. thesis, Univ. Massachusetts, Amherst, 1990.

[9] E. F. Knott, J. F. Shaeffer, and M. T. Tuley, Radar Cross Section. Dedham, MA: Artech House, 1985.

IO] D. M. Pozar, “Radiation and scattering from a microstrip patch on a uniaxial substrate,” IEEE Trans. Antennas Propagat., vol. 35, pp. 613-621, June 1987.

111 -, “Analysis and design considerations for printed phased array antennas,” Microstrip Antenna Handbook. London, U.K.: Peter Pere- grinus, 1989, ch. 12.

121 C. A. Balanis, Antenna Theory. New York Wiley, 1982. 131 D. M. Pozar, “Analysis of finite arrays of printed dipoles,” IEEE Trans.

Antennas Propagat., vol. AP-33, pp. 1045-1053, Oct. 1985. [14] E. Levine, G. Malamud, S. Shtrikman, and D. Treves, “A study of

microstrip array antennas with the feed network,” IEEE Trans. Antennas Propagat., vol. 37, pp. 426-433, Apr. 1989.

[15] H. D. Syrigos, “Backfire feed antenna beats cassegrain design,” Mi- crowave Syst. News, Oct. 1983.

657-658, 1993.

David M. Pozar (S’74M’80-SM’88-F’90) received the B.S.E.E. and M.S.E.E. degrees, in 1975 and 1976, respectively, from the University of Akron, OH, and the Ph.D. degree from Ohio State University, Columbus, in 1980.

During the course of his undergraduate studies he spent one year as an Engineering Co-op Assistant at the National Security Agency, Fort Meade, MD. He was a Graduate Research Assistant at the ElectroScience Lab of Ohio State University, Columbus, while pursuing the Ph.D. degree, and

became a Research Assistant upon its completion. -He joined the faculty at the University of Massachusetts, Amherst in 1980, and in 1989 became a Professor of electrical and 5omputer engineering. In 1988, he spent a six- month sabbatical leave at Ecole Polytechnique Federale de Lausanne, in Lausanne, Switzerland. He has served as an Associate Editor of the IEEE

and as an Associate Editor of the IEEE AP-S Newsletter (1982-1984). He has published over 100 papers on printed antennas and phased arrays, and is the author of Antenna Design Using Personal Computers (Norwood, MA: Artech House, 1985), Microwave Engineering (Reading, MA: Addison- Wesley, 1990), and Microstrip Antennas (Piscataway, NJ: IEEE Press). He is also the author of PCAAD, a software package for personal computer-aided antenna design.

Dr. Pozar belongs to the Antennas and Propagation Society and the Microwave Theory and Techniques Society. He served as a member of the IEEE AP-S AdCom (1989-1991). In 1981 he received the Outstanding Professor Award from Eta Kappa Nu, the student honor society. In 1984 he received an NSF Presidential Young Investigator Award, and the Keys to the Future Award from the IEEE Antennas and Propagation Society. In 1985 he received the University of Massachusetts Engineering Alumni Association Outstanding Junior Faculty Award. In 1986 he received the R.W.P. King Best Paper Award from the IEEE Antennas and Propagation Society, and in 1987 he received the URSI Issac Koga Gold Medal for his work on printed antennas and phased arrays. He again received the R.W.P. King Best Paper Award in 1988. In 1989 he received the United Technologies Corporation Outstanding Teaching Award. Since 1993 he has served as a Distinguished Lecturer for the IEEE Antennas and Propagation Society. In 1995 he received the College of Engineering Outstanding Senior Faculty Award.

TRANSACTIONS ON ANTENNAS AND PROPAGATION (1983-1986 and 1989-1992)

296 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 45, NO. 2, FEBRUARY 1997

Stephen D. Targonski was born in Springfield, MA, on December 31, 1968 He received the B.S.E.E., M.S.E.E, and the PhD. degrees, in 1991, 1993, and 1995, respectively, all from the University of Massachusetts, Amherst

During his graduate studies at the University of Massachusetts, Amherst, he was a Fellow of the Air Force Office of Scientific Research In October 1995, he joined the Department of Communication and Electronic Engineenng at the Royal Melboume Institute of Technoloev. Melboume. Australia, as

H. D. Syrigos (M’72-SM’85), photograph and biography not available at the time of publication.

-, a Postdoctoral Research Fellow. His research interests are in the area of microstrip antennas, with particular interest in microstrip reflectmays and wideband microstrip antennas.

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