Multi-feed single-beam power-combining reflectarray antenna F. Arpin, J. Shaker and D.A. McNamara A design procedure is described for multi-feed single-beam power- combining reflectarray antennas. The method is applied to a two-feed case and is then validated experimentally. Introduction: There is renewed interest in reflectarray antennas (e.g. [1]) because of the availability of inexpensive fabrication techniques, improved electromagnetic analysis tools, and the need for low-profile high-directivity antennas. At the same time there is a need to obtain practical radiating power levels from solid-state sources at microwave and millimetre-wave frequencies. Spatial power combining techniques [2] appear to offer an attractive means for achieving this. Possible methods of using reflectarrays to effectively perform spatial power combining have been discussed in [3]. We are currently undertaking research into a different means of incorporating spatial power combining into a reflectarray. We describe a design procedure of a two-feed reflectarray, and the experimental validation of the proce- dure. Design considerations for multi-feed reflectarray: Following [1], rectangular patches were selected as the cell element of the reflectar- ray. As a first step in the design, a cell size d x by d y is selected, and the nth patch is positioned at the centre (x n , y n ) of the nth cell. The total number of cells used is selected according to the aperture size required. The individual elements are made to scatter the incident field with the correct phase by varying the size of the patches. Although the geometry in Fig. 1 shows the two feeds that are relevant to this Letter, in order to review the single-feed design procedure of [1] consider for the moment that only feed 1 is present. If we assume that a main lobe is required broadside to the reflectarray, the equal phase design equation [1] is then k o r n (1)  f n ¼ 2pN, where r n (1) ¼j r n (1) j is the distance from the feed to the nth patch. The quantity f n is determined by computing the phase of the reflection coefficient of a plane wave from an infinite two-dimensionally periodic array of patches all of the same size as the nth patch, with cell size d x by d y , located on a conductor-backed dielectric substrate of the same thickness and permittivity as that of the intended reflectarray. N is an integer. Fig. 1 Geometry and notation of two-feed reflectarray We next determine the equal phase design equation for the two-feed system using a scalar approach. We write the fields of each feed incident on the nth patch as E 1 ð r ð1Þ n Þ¼jE 1 ð r ð1Þ n Þje jðk o r ð1Þ n f n Þ ð1Þ and E 2 ð r ð2Þ n Þ¼jE 2 ð r ð2Þ n Þje jðk o r ð2Þ n f n Þ ð2Þ Thus the total field at the nth patch is the sum of the fields from each of the feeds, or E T ¼jE 1 ð r ð1Þ n Þje jðk o r ð1Þ n f n Þ þjE 2 ð r ð2Þ n Þje jðk o r ð2Þ n f n Þ ð3Þ The phase of this total field is therefore given by ff E T ¼ tan 1 jE 1 ð r ð1Þ n Þj sinðk o r ð1Þ n  f n Þ jE 2 ð r ð2Þ n Þj sinðk o r ð2Þ n  f n Þ jE 1 ð r ð1Þ n Þj cosðk o r ð1Þ n  f n Þ þjE 2 ð r ð2Þ n Þj cosðk o r ð2Þ n  f n Þ 8 > > > < > > > : 9 > > > = > > > ; ð4Þ We next assume that the radiation patterns of the individual feeds are sufficiently broad that the angular dependence of their patterns can be neglected as far as the illumination of the reflectarray is concerned. However, we retain the ‘distance-to-the-patch’ factor and write jE 1 ( r n (1) )j¼ 1=r n (1) and jE 2 ( r n (2) )j¼ 1=r n (2) , and then use these in (4). To design a two-feed reflectarray we must select the f n for each patch that will make the phase ff E T of the total field constant for all patches. The four-quadrant inverse tangent function (defined over angular range [p, p]) should be used. We have used numerical optimisation to determine the value of f n required to make ff E T ¼ 0 for each of the patches. With the f n known the patch sizes can be selected. Theoretical design of two-feed reflectarray: To test the ‘extreme case’ we considered the situation shown in Fig. 1 where the feeds are on opposite sides of the reflectarray. The design frequency was 30 GHz, with an aperture size 155  155 mm, a cell size d x ¼ d y ¼ 5 mm, and an F=D ¼ 1. Application of (4) results in a reflectarray the patch size distribution of which is shown in Fig. 2. Fig. 2 Distribution of relative patch sizes for two-feed reflectarray Experimental validation: For the purposes of this experimental measurement the feeds were simply excited using a 3 dB power divider and appropriate lengths of semi-rigid coaxial lines between the power divider output and the inputs to the two feeds. The measured insertion loss between the power divider input port and the inputs to each of the feeds (i.e. one path for each feed) was measured as 4.78 and 4.86 dB. The excess loss in the two feed paths is thus 1.78 and 1.86 dB, respectively. The return loss at the input port (with both feeds connected, and in the presence of the reflectarray) was measured as 20.55 dB; the reflection loss due to this return loss is 0.04 dB. The phase imbalance in the above-mentioned paths was measured to be 21.56  . The pattern prediction approach (detailed in the next paragraph) shows that this lowers the level of the pattern peak by 0.14 dB compared to what it would be if there were no such phase imbalance. Thus, to correct for all the above imperfections, we must add 3.82 dB to the measured gain in order to determine the efficiency of the reflectarray. To gain some understanding of the operation of the reflectarray, some pattern prediction capability, albeit approximate, is necessary. We will use array theory, along with the assumptions listed earlier, to compute the radiation patterns. Even though the reflectarray was designed for proper operation with both feeds in use, the performance is first examined with only feed 1 present (and feed 2 removed). Under these conditions the excitation of the nth patch can be approximated as a n (1) ¼ e j(korn (1) fn) =r n (1) , and the reflectarray pattern is then F ðy; fÞ¼ cos q y P N n¼1 a ð1Þ n e jk o ðx n sin y cos f þ y n sin y sin fÞ ð5Þ The raised-cosine element pattern cos q y with q ¼ 1/2 has been used in the computed H-plane patterns to be shown below. ELECTRONICS LETTERS 19th August 2004 Vol. 40 No. 17