Modeling and Design of Electronically Tunable ... - IEEE Xplore

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 55, NO. 8, AUGUST 2007

Modeling and Design of Electronically Tunable Reflectarrays Sean Victor Hum, Member, IEEE, Michal Okoniewski, Senior Member, IEEE, and Robert J. Davies, Member, IEEE

Abstract—The reflectarray has significant promise in applications requiring high-gain, low-profile reflectors. Recent advances in tuning technology have raised the possibility of realizing electronically tunable reflectarrays, which can dynamically adjust their radiation patterns. This paper presents an electronically tunable reflectarray based on elements tuned using varactor diodes. Modeling approaches based on an equivalent circuit representation and computational electromagnetics simulations are presented. Both techniques accurately predict the scattering characteristics of the unit cell as compared to experimental measurements. The development of a unit cell with over 320 of phase agility at 5.5 GHz is discussed. Finally, a 70-element electronically tunable reflectarray prototype operating at 5.8 GHz is presented. Radiation pattern measurements with the reflectarray demonstrate its dynamic beam-forming characteristics. Measurements of the gain of the reflectarray correlate well with theoretical expectations. Index Terms—Antenna arrays, microstrip arrays, reconfigurable antennas, reflectarrays, reflector antennas.

I. INTRODUCTION

I

N RECENT years, the planar reflectarray antenna [1] has evolved into an attractive candidate for applications requiring high-gain, low-profile reflectors. In traditional reflectarrays, phasing of the scattered field to form the desired radiation pattern is achieved by modifying the printed characteristics of the individual elements composing the array. For linearly polarized (LP) reflectors, the most popular approaches include varying the size of the microstrip dipole [2] or patch elements [3], and loading patches with variable-length stubs [4]. Recently, the bandwidth of the former technique has been extended using stacked-patch topologies [5]. Folded reflectarrays based on variable-size patches have also been proposed [6]. For circularly polarized (CP) arrays, a number of interesting concepts have been presented including varying the rotational angle of stub-loaded microstrip patches [7], slot ring resonators [8], and microstrip ring resonators [9]. Stacking

Manuscript received November 21, 2006; revised April 10, 2007. This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC), in part by the Informatics Circle of Research Excellence (iCORE), Alberta, Canada, in part by TRLabs, and in part by the Alberta Ingenuity Fund (AIF). S. V. Hum is with the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON M5S 3G4, Canada (e-mail: [email protected]). M. Okoniewski is with the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB T2N 1N4, Canada and also with TRLabs, Calgary, AB T2E 8X2, Canada. R. J. Davies is with TRLabs, Calgary, AB T2E 8X2, Canada. Digital Object Identifier 10.1109/TAP.2007.902002

of these elements has also been employed to extend bandwidth [10] and enable dual-frequency operation [11]. All of these approaches have met with much success in the design of fixed reflectarrays, which emulate their reflector antenna counterparts and are also extensible to shaped-beam applications (e.g., [12]). One interesting capability of the reflectarray is the possibility of making the beam pattern dynamic using reconfigurable array elements. This concept holds significant promise as a platform for a reconfigurable antenna array. Spatial feeding of the elements removes the need for a bulky and lossy feed network that characterizes traditional phased arrays, potentially improving gain and allowing greater flexibility in array configurations. The tunable reflectarray also potentially is a very cost-effective platform for beam-forming since the need for transceiver modules for each antenna element is eliminated, and the phase-shifting operation is internalized to the antenna element structure. Reconfigurable reflectarrays require elements whose scattered field phase can be adjusted over a broad range (ideally 360 ). Mechanical approaches based on motors have been proposed for CP systems to rotate the elements [7], though switches have also been proposed to implement electrical rotation of elements [13], [14]. Similarly, approaches for LP antennas have been proposed that use RF/MEMS switches [15], [16], tunable MEMS patches [22], and motors to move dielectric components [18], to achieve the desired effect. Recently, several promising techniques have been experimentally demonstrated. In [19], electronic control of the element was demonstrated by loading the radiating edge of a patch antenna with a varactor diode. Unfortunately only 180 of tunable phase range was achieved, allowing for only limited beam scanning. This problem is potentially alleviated using an active cell topology [20]. It has also been shown that tunable impedance surfaces can also be adapted for use as reconfigurable reflectors [21]. However, only a bulk phase gradient can be programmed into such structures, and the structure periodicity requires dense arrays of elements, necessitating many devices to implement reconfigurability compared to reflectarrays. Most recently, MEMS switches have enabled the phase agility of reflectarray elements to be enhanced through the use of multiple switches positioned along slots in a patch [17]. Finally, interesting approaches based on exotic materials have also been presented, but tend to be somewhat lossy [23], [24]. This paper presents the design, modeling and measurements of an electronically tunable LP reflectarray based on a phase-agile reflectarray element previously introduced in [25]. The paper is organized as follows: Section II presents the basic

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In general, the gain

of a reflectarray can be expressed as (2)

(3) where is the illumination efficiency of the feed system, is the magnitude of the reflection coefficient of the th reflectarray element (as a function of scan angle and phasing angle), is the gain of single microstrip patch element, and are the number of elements in each of the principal planes of the array. For a well-designed reflectarray element with element , the effective area of the patch antenna is equal to , gain where are the length and width of the unit cell. The maximum gain can also be expressed as

Fig. 1. Geometry of a reflectarray.

theory of reflectarrays. Section III discusses the design considerations and the implementation of an electronically tunable reflectarray element, and presents the proposed element design. Section IV derives two techniques that can be used to model the scattering behavior of reflectarray cells. Section V discusses experimental measurements of the electronically tunable reflectarray cell. Section VI presents the design of the reflectarray as a whole, and provides experimental measurements of the entire integrated reflectarray. Finally, the conclusions are drawn in Section VII. II. BASIC REFLECTARRAY THEORY The geometry of a general reflectarray is shown in Fig. 1. A horn antenna feeds the reflector surface and is assumed to . One example ray have a phase center located at the origin is shown extending from the feed to an arbitrary point on the reflecting surface. The ray is scattered by the reflectarray element such that the reflected energy from the surface as a whole in the far field. Essentially, the is directed at an angle reflectarray collimates spherical waves from the feed horn into plane waves in the far field. To achieve this, the scattered fields from the reflectarray elements are phased such that, at an imaginary aperture plane in front of the reflectarray surface normal to the direction of the outgoing wave, the phase field is uniform across the aperture. Mathematically, this is expressed defining a , and a unit vector representing the direction of vector the scattered beam, , whereby the reflection in direction is achieved by satisfying the relation

(1) is the position vector to the th element shown in where Fig. 1 and . The term represents the phase shift produced between the incident and reflected field by the th reflectarray element. Note that other beam synthesis approaches are possible, but are not discussed here.

(4) where EF is the normalized element factor of the patch, is the free-space wavelength, and is the overall aperture efficiency . The term is the of the reflectarray, given by is the phase error efficiency of the reflection efficiency and reflector. The objectives in designing electronically tunable reflectarray elements are very similar to those of required in the design of elements of fixed reflectarrays: to achieve a wide range of phase over a broad assortment of incident angles while shifts maintaining high reflection efficiency . The design of an electronically tunable reflectarray element that attempts to satisfy this criteria is described in the next section. III. REFLECTARRAY ELEMENT DESIGN For many linearly-polarized reflectarray cells, the fundamental mechanism which provides changes in the phase of the scattered field is the position of the operating frequency on the resonance curve of the microstrip patch element. This is usually implemented by adjusting the shape or loading of the patch element in fixed reflectarrays. The proposed reflectarray cell utilizes concepts developed for frequency agile antennas, where the resonant frequency of a patch is modified electronically using varactor diodes [26], [27]. The basic idea is that by loading the microstrip patch with an electronically-controlled capacitance, its resonant frequency can be changed to increase the usable frequency range of the patch. The resulting frequency agility, when applied to arrays of microstrip patches, can be used to change the scanning characteristics of the array. To maximize the phase agility of the element, it is important to consider both the size of the patch and the range of capacitances produced by the varactor tuning diode. The element must be designed so that for a patch with a given size, the maximum change in resonant frequency is produced over the range of capacitances offered by the varactor diode. This is demonstrated graphically in Fig. 2. Fig. 2(a) illustrates the scattered field phase from a frequency-agile patch antenna as a function

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Fig. 3. Reflectarray cell topology.

Fig. 2. Frequency agile antenna tuning characteristics. (a) Scattered field phase versus frequency. (b) Scattered field phase versus capacitance.

of frequency. A varactor diode is used which has a tuning range to . As the capacitance is increased in uniform of steps, the resonant frequency of the patch is reduced, though the reduction diminishes with increasing capacitance. The operating frequency (or likewise, the patch size) must be selected carefully to maximize the phase agility of the element. Taking various slices of the curves in Fig. 2(a) at different operating frequencies (or patch sizes) produces the curves shown in Fig. 2(b), which shows the scattered field phase as a function of tuning capacitance . From Fig. 2(b), it can be clearly seen that the choice of patch size/operating frequency and diode characteristics affect the overall phase range of the element. For small patches, the phase of the range is constrained by the minimum capacitance diode. Conversely the phase range of a large patch element will if the be limited by the diode’s maximum capacitance patch is chosen to be too large. Optimal pairing of the patch geometry and the diode promotes the greatest frequency and phase agility of the patch. For the present design, a phase-agile reflectarray element was designed using two varactor diodes that serially connect two halves of a microstrip patch [25], as shown in Fig. 3. The patch structure itself is assumed to have a length and width . It is printed on a substrate with a dielectric constant of and height . This is similar to a frequency agile antenna concept presented in [28], which uses multiple diodes along the width of the patch

Fig. 4. Infinite array scattering scenario.

to bridge the gap. This design only uses two varactor diodes at the edge of the antenna to reduce component count, but in general more could be used if desired. Using a serial connection has a significant advantage over a parallel connection in that for a given frequency, the tuning capacitances are about an order of magnitude higher than those required for a shunt connection to produce the same change in scattered field phase. This is because for the design considered, the fringing capacitance across the gap is much larger than fringing capacitance at the radiating edge of the patch. Since the required tuning capacitances decrease with frequency, for the smallest commercially available packaged varactor diodes, this design enables operation at a higher frequency. A DC bias network is co-located with each diode to isolate RF currents on the patch from the biasing circuitry. A symmetrical biasing structure is used to reduce cross-polarization effects, as suggested by previous symmetrical element designs [4]. The optimal pairing of the diode to the patch structure is facilitated through the use of electromagnetic simulations and an equivalent circuit model, both of which will now be discussed. IV. CELL MODELING We will consider modeling the cell using two techniques: an equivalent circuit model, and numerical electromagnetic simulations. Two assumptions will be made. First, it is assumed that

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Fig. 5. Equivalent circuit for predicting reflectarray cell scattering. (a) Standard microstrip patch, (b) Microstrip patch with varactor diode and discontinuities.

the cell is embedded in an infinite array, surrounded by identical cells in the transverse plane. For large reflectarrays, this is a good assumption as edge effects are not significant, especially when the edge taper of the feed is included. Second, it is assumed that the patch is illuminated at broadside. While other illumination angles can be modeled (see Section IV), this approach facilitates comparisons of the two models. Furthermore, although not all elements will be receiving signals at this angle, it has been shown that the scattered field broadside to the cell closely approximates the scattered field of a microstrip within about 40 of broadside [29]. Hence, broadside illumination will be used in the analysis. The analysis scenario is illustrated in Fig. 4. The scattering behavior can be analyzed by computing the reflection coefficient in an infinite array, as shown of a unit cell of dimensions is in Fig. 4. An incident plane wave with electric field launched toward the patch and the TEM reflection coefficient computed from the scattered field. This reflection coefficient represents the amplitude and phase of the scattered signal with respect to the incoming plane wave polarized in the -direction. A. Equivalent Circuit Model The situation in Fig. 4 can be conveniently represented in circuit form, derived from the basic transmission line model of a microstrip patch [30] shown in Fig. 5(a). The transmission line can effective impedance and effective dielectric constant be computed using standard microstrip quasi-static calculations. represents the fringing capacitance asThe circuit element sociated with each radiating edge of the patch. The patch operates in a scattering mode, whereby electric fields are established in the radiating slots of the patch antenna by the incident wave. These fields excite the patch circuit, and are subsequently re-radiated when radiation fields are re-established in the slots. This is modeled by two voltage sources that drive the patch through associated with each radiating the two radiation resistances slot in an anti-symmetric manner as shown. Computing the reflection coefficient as seen from one of the sources (with acting as the source resistance) amounts to computing the reflection coefficient shown in Fig. 4.

Fig. 6. Simplified equivalent circuit.

The basic circuit model can be adapted to account for the effect of the varactor diode as shown in Fig. 5(b). The patch is , where is the partitioned into two halves of length gap width indicated in Fig. 3. The gap discontinuity can be represented using a equivalent circuit as shown [31]. Using an approximate model of the varactor diode based on a series RLC circuit, two diodes are inserted as shown which yields a parallel arrangement of the diodes. An additional inductance, , is included in series with the varactor diode to account for current crowding effects around the varactor diode. This inductance is separated into two equal series inductances to maintain symmetry. Capitalizing on the symmetry of the circuit and its odd-mode excitation, the circuit of Fig. 5 can be simplified as shown in Fig. 6. The input reflection coefficient is then readily computed as a function of varactor diode capacitance . Before the circuit model can be evaluated, the parameters , and must be determined for the patch geometry discussed. While closed-form approximations derived from the microstrip transmission line model of the patch antenna and , they do not account for the proximity of exist for other nearby array elements, and effects of the discontinuities. Additionally, closed-form expressions for the gap discontinuity for wide microstrip widths, typical of patch antennas, are not must be de-embedded using elecreadily available. Finally, tromagnetic simulations of the discontinuity due to its unique geometry. Numerical electromagnetic computations of microstrip discontinuities were performed and the parameters de-embedded

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from these simulations. An in-house finite-difference time-domain (FDTD) electromagnetic simulator was used for the analysis. A microstrip transmission line with a gap discontinuity was and . An open-end microstrip transmission used to obtain line was simulated to obtain . An electric wall normal to the from direction of propagation, located a distance the end of the microstrip line, was included in the simulation to produce a boundary condition approximating the infinite array scenario since fringing off the end of the patch interacts most strongly in the E-plane of the array. was computed by adding two shorting strips to the gap discontinuity simulation in place of the varactor diodes. This forces conduction currents through the regions where the diodes would normally be and allowed the current crowding effect to be characterized and the value of to be computed. Finally, the computation of required simulations of the patch inside the PPWG or periodic waveguide. The patch can either be driven by a suitable feed or excited with an incoming in the radiated field, plane wave. Using the measured power the radiation resistance of the slot can be readily computed if the magnitude of the voltage established in the patch slots is known. This observation is readily available in FDTD simulations of the unit cell. The radiation resistance can then be calculated as

(5) B. Computational Electromagnetics Model The scattering characteristics of the unit cell can also be computed using a computational electromagnetics approach. For this analysis, the FDTD technique was employed. Perfect electrical conductors (PECs) were used in the simulation for all metallic surfaces. For dielectrics, dispersionless, lossless materials were used. To implement the varactor diode, the same series RLC equivalent circuit model discussed previously was used. Lumped element modeling was achieved using standard lumped-element extensions in the FDTD code. The simulation very closely followed the setup shown in Fig. 4. The reflectarray cell was placed at the end of a waveg. A uniform uiding structure of transverse dimensions plane wave, launched at the end of the waveguide, was scattered from the structure and the reflection characteristics analyzed by evaluating the TEM reflection coefficient of the structure. For broadside illumination, periodic boundary conditions reduce to a parallel-plate waveguide (PPWG) as the waveguiding structure, with electric walls bounding the simulation in the -direction and magnetic walls bounding the simulation in the -direction. This technique is an established technique for determining broadside scattering characteristics as well as approximating off-broadside scattering [32]. Periodic boundary conditions can also be used, especially if accurate simulation of off-broadside scattering is desired. C. Model Validation Both models were compared against each other and against the experimental results measured for a reflectarray element de-

TABLE I EQUIVALENT CIRCUIT PARAMETERS FOR VARIOUS SUBSTRATE HEIGHTS

signed to operate at 5.5 GHz. The element was designed for a mm substrate with dielectric constant and . For the circuit model and FDTD loss tangent simulations, a lossless substrate was assumed. The cell spacing mm which corresponds to just over half was chosen as a wavelength at 5.5 GHz ( . The cell was designed around a commercial varactor tuning diode available from MCE Metelics (now Aeroflex). A MGV100-20 gallium arsenide (GaAs) varactor diode was chosen for the design, since it offered the lowest loss in commercially available tuning diodes. It develops a capacitance of 1.80-0.12 pF between 0–20 V of reverse bias voltage. Good scattering charmm acteristics were obtained with patch dimensions of and mm. A gap of mm was used to accommodate the varactor diode. Although the cell was designed on a 1.5 mm substrate, several substrate heights were simulated to test the equivalent circuit model since changing the substrate height is known to cause significant changes in the scattering characteristics of reflectarray elements. The results of equivalent circuit parameter de-embedding are summarized in Table I. The scattering of the cell predicted by the circuit model is compared to direct FDTD scattering simulations at 5.5 GHz in nH and Fig. 7. Varactor diode parameters of were initially used in both models. A unit cell size of mm was used in the FDTD simulation. The results in Fig. 7(a) demonstrate that it is indeed possible to extend the phase agility of a reflectarray cell to close to 360 . mm case, of phase range was In fact, for the achieved assuming the capacitor could be tuned from 0–1 pF. A more realistic range of 326.1 is achieved assuming a 5:1 capacitance change (0.2–1 pF), achievable with most GaAs tuning diodes. As the height of the substrate is changed, the phase slope and range change. As expected, thinner substrates normally lead to more narrowband patch performance, which manifests itself as a high-slope transition in the phase characteristic with a large overall phase range. The opposite is true of a thicker substrate. Again, behavior at various patch heights is shown to demonstrate the accuracy of the model, but the best overall compromise between phase range, slope, and reflection loss is achieved mm substrate in this case. with the Examining Fig. 7(b), we notice that there is a change in the scattered field amplitude as the varactor capacitance is changed. When the structure is at resonance, or at the center of the phase tuning characteristic, there is a pronounced dip in the reflected cell amplitude. This is caused by the resistance in the varactor diode. The effect is more severe the closer the frequency is to the resonant frequency of the patch without diode loading, sug-

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discussed in Section IV was used to measure the scattering response of the cells, since a high-quality air-filled PPWG with the dimensions shown could not be practically realized. Instead, the element was placed at the end of a section of rectangular waveguide (RWG). The TE mode traveling in the waveguide simulates illumination at an off-broadside angle [33]. The exact angle of illumination is given by

(6)

Fig. 7. Comparison of equivalent circuit model to FDTD simulations. (a) Phase response. (b) Magnitude response.

gesting that significant power dissipation in the varactor diode is occurring at this point. Part of the design process is to ensure that this loss is not too great, since power lost in the diode will ultimately reduce the reflector efficiency of the reflectarray. In both the phase and magnitude plots, we notice excellent correlation between the equivalent circuit model and the computational electromagnetics model. The circuit model has an advantage of being simpler and faster to evaluate, provided that circuit parameters for the discontinuities are known. However, even with rough estimates of these parameters, the circuit model can be used to produce a basic design of a unit cell, and then the cell can be further optimized through the use of electromagnetic simulations. The circuit model can also be used to predict important tuning parameters such as phase range, phase slope, reflection loss, and bandwidth. V. EXPERIMENTAL MEASUREMENTS OF THE CELL The circuit and computational models were compared to experimental measurements of the reflectarray cell. As discussed in [25], a slightly different setup from the PPWG arrangement

where is the wavenumber in the waveguide; alternatively the can be used in the calcutoff wavelength in the waveguide culation. Additionally, the waveguide approximates an infinite array scenario where the elements are separated by a free-space distance of in the H-plane, and in the E-plane, due to image theory. Fig. 8 shows the computed and measured phase and amplitude of the scattered field from the unit cell at 5.5 GHz, where fixed capacitors were used in the experimental cell for direct comparison to model results. Computed results include an evaluation of the circuit model, as well as FDTD computations inside PPWG and RWG. There is good correlation between both simulated models and the experimental measurements. Differences between the PPWG FDTD model and the RWG FDTD model are attributable to the much closer element spacing simulated by the WR-187 waveguide used as the RWG. Overall, the phase characteristics are similar to those presented earlier. The measured cell achieved a phase range of 335.2 over the range of capacitances tested, which is excellent. A small dip in the amplitude response, as explained earlier, is attributable to loss in the fixed capacitors. The peak drop in amplitude response, however, is only 1.5 dB which corresponds to a reflection efficiency of 70.8%. Experimental measurements of the scattering response of a reflectarray cell employing an actual varactor diode are shown in Fig. 9. An excellent tuning range of 320.3 was observed for of the unit cell at 5.5 GHz. The phase remained within the center of the tuning range over a 72.5 MHz (1.3%) bandwidth which is consistent with the bandwidth of a microstrip patch of this size. As discussed, the bulk of the loss originates from power losses in the diode. For the design frequency of 5.5 GHz, 3.5 dB of reflection loss is observable, which closely matches the reflection loss predicted by the circuit and FDTD models using published Q-values of the actual varactor diode . This loss corresponds to 44.7% reflection efficiency. Though this loss is considerable, it was deemed acceptable for the first prototype of a tunable reflectarray, which is discussed next. VI. ELECTRONICALLY TUNABLE REFLECTARRAY DESIGN The varactor diode-tuned elements were assembled into a element array to test the performance of the reflectarray in a prototype implementation. The reflectarray was designed for use in additional experiment at 5.8 GHz. As such, the remm, yielding flectarray cells were modified so that scattering characteristics at 5.8 GHz virtually identical to the GHz case shown in Fig. 9 (and hence are not repeated

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Fig. 9. Measured unit cell scattering from the varactor-diode based cell. (a) Phase response. (b) Magnitude response. Fig. 8. Comparison of measured and FDTD-simulated unit cell scattering results. (a) Phase response. (b) Magnitude response.

here). A control board (essentially an array of digital-to-analog converters) was placed behind the array and supplied control voltages to each reflectarray element independently through vias on the reflectarray board. A microcontroller was used to interface the system with an external computer which was used to synthesize and download configurations to the array. The physical setup of the reflectarray is shown in Fig. 10 along with the associated coordinate system. The reflectarray surface was integrated with a feeding antenna as shown in Fig. 10. The experimental reflectarray surface was relatively small, and was meant to represent a portion of a much larger reconfigurable reflectarray surface. As such, feed efficiency was not considered paramount in the design of the feeding system. The active reflectarray area, which measures 300 210 mm, was scanned using a pyramidal feed horn. The feed in a prime-focus configuration was designed with an ratio in the E-plane of 2.46. In the actual implementation, an offset feed configuration was used where a feed angle 20 off broadside was used. This was used to reduced feed blockage. The feed configuration produced approximately a 3 dB edge taper in both the E-plane and H-plane at the array surface. The

Fig. 10. Setup of reflectarray system.

resulting illumination efficiency of the feed system was approximately 43%.

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TABLE II REFLECTARRAY LOSS BUDGET ( = 83:5

Fig. 11. Pattern measurements of the several reflectarray configurations measured at  = 83:5 .

The whole system was placed on the turntable in the anechoic chamber for radiation pattern measurements at a fixed elevation angle . Due to the size of the reflectarray support structure, only pattern measurements as a function of azimuth angle could be performed. The probe antenna was placed in the chamber such that the reflectarray would have to produce a . beam in the elevation plane at Multiple beam configurations in the azimuth plane were downloaded to the array controller and used to synthesize test cases for the array. The direction of these beams is designated . Initially, an open-loop control technique was used as based on a lookup table implementation of the voltage/phase mapping curve at 5.8 GHz, similar to that shown in Fig. 9. The beams were created by collimating the feed illumination and phasing the array according to the desired beam direction using array theory. The phase of the feed illumination pattern used by the array controller was determined using near-field measurements of the horn in FEKO. The radiation pattern of the array for 21 beam configurations is shown in Fig. 11. The beams were designed to scan from to in steps. Note that not all beams appear in the legend due to space constraints. In terms of beam of the desired beam pointing error, most beams are within pointing direction. Beam-pointing errors are caused by phase errors produced by the open-loop control scheme used to control the array. The measurements in Fig. 11 are normalized with respect to an uniformly excited aperture of the same size, having a directivity of 24.7 dBi which was calculated using . An expected scanning loss curve was also included which was computed using the product of the element factor and subtended aperture loss. Overall correlation with the scanning loss curve was good. Deviations are, most likely, caused by suboptimal phasing of the array because of open-loop control effects, discussed shortly. The normalization in Fig. 11 allows a comparison to be made to the expected losses for this antenna. As indicated in (3) and (4), numerous factors can contribute to reducing the overall gain/efficiency of the reflectarray surface, including the following.

;

= 20 )

1) Aperture phase errors resulting from discretization of the phase characteristics using DACs, and limited overall , accounted for by phase range of the cell (errors in ); 2) Absorption caused by diode loss, metal loss, and dielectric , or ); loss (accounted for by 3) Natural rolloff in the patch antenna’s response as it is ]; scanned off broadside [element factor loss, or loss; 4) Subtended aperture 5) Tapered feed illumination/spillover (illumination effi). ciency, These losses are readily computed and assembled in a loss budget for comparison to theoretical expectations. The effect of element phase error and absorption can be computed using experimental measurements of the scattering characteristics of the reflectarray cell and incorporating them into the array factor expression for the reflectarray. The factor by which the gain is reduced due to these effects is then given by

(7) The effect of element absorption can be isolated directly evaluated knowing the array configuration and the amplitude response of the reflectarray cells as a function of phasing angle . The gain reduction factor due to element absorption is

(8) As a reflectarray is scanned off broadside, the response of the array diminishes due to the reduced subtended aperture of the reflector, and rolloff in the element factor of the patch antennas composing the reflectarray. The reduction in gain caused by element factor loss can be computed using the well-known radiation pattern expressions for microstrip patches [30]. The total scanning loss can be plotted as a function of angle and is shown as a curve in Fig. 11. The peaks of the individual beam configurations correlate well with this curve. To quantify losses, a single beam configuration was considbeam had a measured gain ered as a test case. The of 11.5 dBi, which is 13.2 dB below the expected directivity of a reflectarray this size. While this is significant (amounting to about 5% total system efficiency), it correlates reasonably well with the computed loss budget, which is summarized in Table II. There is a 5.8 dB deficit in the expected and measured gain of the reflectarray. Some of this additional loss is hypothesized to

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Fig. 12. Comparison of measured radiation of the = 20 reflectarray configuration at  = 83:5 . Co-polarized (C) and cross-polarized (X) components are included.

originate from phase errors in the aperture over and above those listed in Table II. These phase errors result from the differences between the programmed and actual phase shift produced by the reflectarray elements. If there is significant variance in the phase tuning characteristic from element to element, then the lookup table used by the controller may not be sufficiently accurate to phase the array without producing significant phase errors in the aperture. In particular, cell-to-cell variances can be caused by a number of factors. • Variation of the manufactured patch dimensions. Analysis of the accuracy of the technology used to manufacture the array (a printed circuit board milling machine), revealed a % variation in patch dimensions; • Variation of the varactor diode parameters from diode to % varidiode. According to the manufacturer, up to a ation in varactor diode junction capacitance was possible from the lot of diodes used; • A slight but known deviation between the phasing characteristic measured in a rectangular waveguide and an actual cell because of the short height of the WR-187 waveguide used in the measurement. To investigate this hypothesis, a closed-loop control scheme was employed to fine-tune the reflectarray bias voltages to see if the gain could be increased. The results of applying the closedconfiguration are shown loop control scheme to the graphically in Fig. 12. The resulting beam has no discernible beam pointing error, unlike the open-loop case which points at . Also, the peak gain of the reflectarray has increased by 1.4 dB. Despite the optimization, there is still 4.4 dB of unaccounted power loss. Further optimization may yield slightly improved performance, but the more likely cause of the remaining power deficit is a combination of feed blockage, measurement error in the anechoic chamber, and a lower-than-expected illumination efficiency. Shadowing produced by the feed horn is visshow a ible in Fig. 11, since configurations with pronounced improvement in relative gain compared to beam configurations closer to broadside. Part of the remaining power

Fig. 13. Measured co-polarized (C) and cross-polarized (X) components for 3 reflectarray configurations at  = 83:5 .

deficit could be accounted for by feed blockage. In fact, if the loss budget of a beam configuration further from broadside is considered, the resulting power deficit is less. For example, for configuration, the power deficit using open-loop the control is 2.3 dB. Given that closed-loop optimizer has generally yielded an improvement of 1 dB or better, it is anticipated that the unaccounted power loss approaches 1 dB, which is considered experimentally acceptable. A plot of the measured co- and cross-polarization characteristics for three open-loop array configurations ( , and ) is shown in Fig. 13. The plot has been configuration. normalized to the peak gain for the Cross-polarization components are also shown in Fig. 11. Generally, at the beam pointing angle the cross-polarized component is suppressed by 30 dB or more, which is excellent. The worst-case cross-polarization measured is about 25 dB down from the main beam of the reflectarray, which is still quite good, considering a shaped reflector with the same focal length would probably have much poorer cross-polarization performance. VII. CONCLUSION This paper has presented the design of an electronically tunable reflectarray and associated unit cell. The unit cell design was facilitated and characterized by the use of equivalent circuit and computational models that accurately predict the scattered process of the cell. Both models provide insight into the cell, especially with regards to the impact of cell geometry and tuning device parameters. Experimental measurements of the reflectarray operating at 5.8 GHz demonstrate excellent beam-forming characteristics. A detailed loss budget of the reflectarray surface reveals that a significant source of loss in the electronically tunable reflectarray is power absorption by the tuning elements—varactor diodes in the case of this design. Such losses can be reduced by utilizing tuning components with a higher Q. Efforts are already underway to address the loss and linearity issues of semiconductor tuning devices by using MEMS elements [34]. Additional factors contributing to reduced reflector efficiency included low illumination efficiency, feed blockage, and phase

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errors. The first two factors are easily addressable through the use of a large reflecting surface; as noted in the paper, a relatively small reflectarray design was used to validate concepts and keep implementation costs down. Phase errors can be addressed through employing closed-loop control schemes to manage beams created by the reflectarray, though other solutions include pursuing cell designs with less pronounced phase slopes and in general, reduced sensitivity to manufacturing issues. In summary, the proposed architecture hold significant promise as a dynamic beam-forming platform. It has the potential to significant reduce the cost of traditional systems, such as phased arrays, while simultaneously addressing problems with feed networks by doing away with them completely. Future development in this area will improve the attractiveness of this unique platform even further.

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[17] H. Legay, G. Caille, E. Girard, P. Pons, H. Aubert, E. Perret, P. Calmon, J. P. Polizzi, J.-P. Ghesquiers, D. Cadoret, and R. Gillard, “MEMS controlled linearly polarised reflectarray elements,” in Proc. ANTEM 2006, Jul. 2007, pp. 359–362. [18] M. E. Cooley, J. F. Walker, D. G. Gonzalez, and G. E. Pollon, “Novel reflectarray element with variable phase characteristics,” in Proc. Inst. Elect. Eng. Microwaves, Antennas and Propagation, May 1997, vol. 144, no. 2, pp. 149–151. [19] L. Boccia, F. Venneri, G. Amendola, and G. D. Massa, “Application of varactor diodes for reflectarray phase control,” in Proc. Antennas and Propagation Society Int. Symp., Jun. 2002, vol. 3, pp. 132–135. [20] L. Boccia, G. Amendola, and G. D. Massa, “A microstrip patch antenna oscillator for reflectarray applications,” in Proc. IEEE Int. Symp. on Antennas and Propagation, Jun. 2004, vol. 4, pp. 3927–3930. [21] D. Sievenpiper, J. Schaffner, H. J. Song, R. Loo, and G. Tangonan, “Two-dimensional beam steering using an electrically tunable impedance surface,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2713–2722, Oct. 2003. [22] J. P. Gianvittorio and Y. Rahmat-Samii, “Reconfigurable reflectarray with variable height patch elements: Design and fabrication,” in Proc. IEEE Antennas and Propagation Society Int. Symp., Jun. 2004, vol. 2, pp. 1800–1803. [23] A. Mössinger, R. Marin, S. Mueller, J. Freese, and R. Jakoby, “Electronically reconfigurable reflectarrays with nematic liquid crystals,” Electron. Lett., vol. 42, no. 16, pp. 899–900, Aug. 2006. [24] R. R. Romanofsky, J. T. Bernhard, F. W. van Keuls, F. A. Miranda, G. Washington, and C. Canedy, “K-band phased array antennas based on Ba Sr TiO thin-film phase shifters,” IEEE Trans. Microw. Theory Tech., vol. 48, no. 12, pp. 2504–2510, Dec. 2000. [25] S. V. Hum, M. Okoniewski, and R. J. Davies, “Realizing an electronically tunable reflectarray using varactor diode-tuned elements,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 6, Jun. 2005. [26] P. Bhartia and I. J. Bahl, “Frequency agile microstrip antennas,” Microw. J., pp. 67–70, Oct. 1982. [27] R. B. Waterhouse and N. V. Shuley, “Full characterisation of varactorloaded, probe-fed, rectangular, microstrip patch antennas,” in Proc. Inst. Elect. Eng. Microwaves, Antennas and Propagation, Oct. 1994, vol. 141, no. 5, pp. 367–373. [28] N. Fayyaz, S. Safavi-Naeini, E. Shin, and N. Hodjat, “A novel electronically tunable rectangular patch antenna with one octave bandwidth,” in Proc. IEEE Canadian Conf. on Electrical and Computer Engineering, May 1998, vol. 1, pp. 29–31. [29] S. D. Targonski and D. M. Pozar, “Analysis and design of a microstrip reflectarray using patches of variable size,” in Antennas and Propagation Society Int. Symp. Digest, Jun. 1994, vol. 3, pp. 1820–1823. [30] C. A. Balanis, Antenna Theory: Analysis and Design. New York: Wiley, 1987. [31] N. H. L. Koster and R. H. Jansen, “The equivalent circuit of the asymmetrical series gap in microstrip and suspended substrate lines,” IEEE Trans. Microw. Theory Tech., vol. 82, no. 8, pp. 1273–1279, Aug. 1982. [32] F.-C. E. Tsai and M. E. Bialkowski, “Designing a 161-element Ku-band microstrip reflectarray of variable size patches using an equivalent unit cell waveguide approach,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2953–2962, Oct. 2003. [33] P. Hannan and M. Balfour, “Simulation of a phased-array antenna in waveguide,” IEEE Trans. Antennas Propag., vol. 13, no. 3, pp. 342–353, May 1965. [34] S. V. Hum, G. McFeetors, and M. Okoniewski, “Integrated MEMS reflectarray elements,” in Proc. Eur. Conf. Antennas and Propagation (EuCAP 2006), Nov. 2006, ESA SP-626. Sean Victor Hum (S’95–M’03) was born in Calgary, AB, Canada. He received the B.Sc., M.Sc., and Ph.D. degrees from the University of Calgary, in 1999, 2001, and 2006 respectively. From 1997 to 2006, he was also a Research Associate with TRLabs, Calgary. In 2006, he joined the Edward S. Rogers Sr. Department of Electrical and Computer Engineering, University of Toronto, Toronto, ON, Canada, where he currently serves as an Assistant Professor. His research interests lie in the area of reconfigurable RF antennas and systems, spacecraft antennas, and microwave photonics. Prof. Hum received the Governor General’s Gold Medal for his master’s degree work on radio-on-fiber systems in 2001. In 2004, he received a IEEE Antennas and Propagation Society Student Paper award for his work on tunable reflectarrays. Most recently, he received an ASTech Leaders of Tomorrow Award.

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Michal Okoniewski (S’88–M’89–SM’97) is a Professor in the Department of Electrical and Computer Engineering, University of Calgary, Calgary, AB, Canada, where he heads the Applied Electromagnetics Group. He holds an endowed Alvin Libin Ingenuity Chair in Biomedical Engineering and a Canada Research Chair in Applied Electromagnetics. He is also affiliated with TRLabs, Calgary. In 2004, he co-founded Acceleware Corp., Alberta, a public company developing acceleration hardware for simulation software. He is interested in many aspects of applied electromagnetics, ranging from computational electrodynamics, to reflectarrays, RF MEMS, and RF micromachined devices, as well as development of computational hardware for electromagnetics applications. He is also actively involved in bioelectromagnetics, where he works on tissue spectroscopy, cancer detection, and novel, cell level micro-imaging methods. Dr. Okoniewski is an Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION.

Robert J. Davies (M’90) received the B.Sc. and M.Sc. degrees in electrical engineering from the University of Calgary, Calgary, AB, Canada, in 1988 and 1990, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Alberta, Edmonton, AB, Canada, in 1999. Currently, he is the Senior Scientist for the Home Technologies (HT) Research Program at TRLabs, Calgary. In addition to performing research in his own areas of specialization, he manages the HT Program throughout TRLabs five sites in western Canada. He has been with TRLabs as a Research Scientist since 1997. Previously, he was a Senior Researcher with Telus Communications and was assigned to TRLabs as an industry seconded researcher. He has authored numerous publications and has six U.S. and four Canadian patents in the areas of hybrid optical/wireless systems and high speed electronics.