A millimetre-wave bandpass filter – lens array A. Abbaspour-Tamijani, K. Sarabandi and G.M. Rebeiz Abstract: A filter – lens array (FLA) is a planar array of bandpass integrated antenna – filter – antenna (AFA) elements which are stagger-tuned in the vicinity of a centre frequency, so as to provide the phase shift required for transforming spherical and planar wavefronts. Due to the filtering response of the AFA elements, FLA presents a bandpass gain and can act as a combination of a conventional lensarray and a filter. An FLA structure is demonstrated with f/D ¼ 1.25 and 8.2% bandwidth at 35 GHz. This FLA is composed of 137 AFA elements and fabricated on two three-inch glass wafers (e r ¼ 4:45). A gain of 25.6 dBi and a total efficiency of 45% have been measured at 35 GHz. The Ka-band FLA shows a low-loss scanning performance for up to at least +308 in the H-plane and +208 in the E-plane. 1 Introduction Lensarrays have been considered as low-cost planar alternatives to dielectric lens antennas for applications in millimetre-wave radars, electronic beam-forming, imaging, and quasi-optical power combining, see for example [1–4]. In these works, focusing is obtained by using arrays of receive and transmit antennas connected through transmission line sections of appropriate lengths. Due to their discrete and modular nature, lensarrays can be modified to perform additional functions besides focusing. Hollung et al. [5], for instance, have considered integration of amplifiers in the discrete lensarray topology to create an active focusing structure. A different type of dual-function lensarray, which can be useful in applications such as multibeam antennas for satel- lite and wireless communications, combines the filtering and focusing functions in the same aperture [6]. Filter – lens arrays (FLA) of this type can be obtained by the inte- gration of bandpass filters in discrete transmission-line based lens arrays. An alternative approach based on nonuni- form arrays of integrated antenna-filter-antenna (AFA) elements. An AFA is an integrated module composed of two microstrip patch antennas coupled to a sandwiched coplanarwaveguide (CPW) resonant structure, and acts as a bandpass filter with radiative ports. Uniform arrays of AFAs have been demonstrated for realising bandpass frequency-selective surfaces [7]. In this paper we show that in a nonuniform array configuration, AFA elements can be used to form a focusing array with bandpass charac- teristics. Simulated and measured results are presented for a Ka-band design, and the performance of the FLA is studied from different aspects. 2 Wave transformation using array of scaled AFAs 2.1 Basic concept In FLA the transformation between the spherical and planar wave-fronts is achieved through the phase delay of the com- prising cells (Fig.1). The input–output phasedelay for each cell is a function of frequency, and can be written in terms of the S-parameters of the corresponding AFA element F m ðvÞ¼/S m 21 ðvÞ ð1Þ where m is the cell index. To achieve the desired wave transformation at a given frequency v 0 , the AFA modules must be designed to provide the necessary phase delay at that frequency. One way to realise AFA elements with the desired values of phase-delay is to tune the passband through scaling the dimensions of a reference design. This concept is illustrated in Fig.2a, where scaled versions of a typical AFA with three-pole frequency response are used to form an FLA. If S 21 (v) represents the frequency response of the original AFA element, scaling the lateral dimensions of this design by a factor of a (’1) results in a perturbed frequency response S a 21 ðvÞ, which can be approximated by S a 21 ðvÞ ’ S 21 ðavÞ ð2Þ This relationship would be exact if the substrate and metal thicknesses could also be scaled by the same factor. For the three-pole AFA in the example of Fig. 2, it is observed that nearly 1808 of phase-variation(DF) can be achieved at the centre frequency for 0.97  a  1.03. The correspond- ing amplitude variation is less than 1 dB at the centre fre- quency. The maximum possible phase shift DF is limited by the inband variations of the AFA phase delay and equals (N 2 1)  908 for an N-pole filter. One way to increase the achievable phaseshift to the ideally required value of 3608 is using higher-order AFA elements (five- poles or higher), but such elements are lossy and result in low-efficiency structures. The preferred method is to combine two types of three-pole AFA elements in the array, explained in the following Section. # The Institution of Engineering and Technology 2007 doi:10.1049/iet-map:20050295 Paper first received 24th September 2005 and in revised form 21st April 2006 A. Abbaspour-Tamijani is with the Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287 K. Sarabandi is with the Department of Electrical Engineering and Computer Science, The University of Michigan at Ann Arbor, Ann Arbor, MI 48109, USA G.M. Rebeiz is with the Department of Electrical and Computer Engineering, The University of California at San Diego, San Diego, CA 92093 E-mail: abbasa@asu.edu IET Microw. Antennas Propag., 2007, 1, (2), pp. 388–395 388