Design of Circularly Polarized Waveguide Slot Linear Arrays

Transcription

1 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 10, OCTOBER [2] S. Yang and H. Li, Optimization of novel high-power millimeter-wave TM 0 TE mode converters, IEEE Trans. Microw. Theory Tech., vol. 45, no. 4, pp , Apr [3] C. C. Courtney, Design and numerical simulation of coaxial beamrotating antenna lens, Electron. Lett., vol. 38, no. 11, pp , [4] G.-S. Ling and C.-W. Yuan, Design of a Vlasov antenna with reflector, Int. J. Electron., vol. 91, no. 4, pp , Apr [5] E. L. Holzman, A highly compact 60-GHz lens-corrected conical horn antenna, IEEE Antennas Wireless Propag. Lett., vol. 3, no. 1, pp , Dec [6] Y.-W. Fan, C.-W. Yuan, H.-H. Zhong, T. Shu, and L. Luo, Simulation investigation of an improved MILO, IEEE Trans. Plasma Sci., submitted for publication. [7] Y.-W. Fan, T. Shu, Y.-G. Liu, and H.-H. Zhong et al., A compact magnetically insulated line oscillator with new-type beam dump, Chin. Phys. Lett., vol. 22, no. 1, pp , Jan Fig. 10. Measured radiated waveforms of the MILO through the antenna. Design of Circularly Polarized Waveguide Slot Linear Arrays Giorgio Montisci Fig. 11. The radiation patterns in the MILO HPM experiments. Abstract A design procedure for circularly polarized waveguide slot linear arrays is presented. The array element, a circularly polarized radiator, consists of two closely spaced lined radiating slots. Both the characterization of the isolated element and the evaluation of the mutual coupling between the array elements are performed by using a method of moments procedure. A number of traveling wave arrays with equiphase excitations are designed and then analyzed using a finite element method commercial software. A good circular polarization is achieved, the design goals on the far field pattern are fulfilled and high antenna efficiency can be obtained. Index Terms Circular polarization (CP), slot antennas, waveguide arrays. in HPM conditions. Experimental results also show that no breakdown or pulse shortening took place in the antenna. V. CONCLUSION We have investigated a mode-transducing antenna, which makes a good case for the advantages of both the coaxial plate-inserted mode converter and the coaxial conical horn. The mode converter (with a length of 35 cm) in this mode-transducing antenna is shorter than that in [1] (about 50 cm when working at 1.76 GHz). The coaxial conical horn is also more compact than a conventional conical horn due to the effect of the inner cone. Especially, an antenna at 1.76 GHz was designed with a length of 60 cm and an aperture radius of 23.5 cm, whereas, if it was composed of a converter like that in [1] and a conventional conical horn with the same gain, the total length should be about 95 cm, and the aperture radius should be 28.7 cm. In addition, the new antenna can also be used to radiate a high-power TM 01 circular waveguide mode, se the TM 01 mode can be transformed into TEM mode easily [7]. I. INTRODUCTION Waveguide slot arrays are popular antennas used in the whole microwave range both for their low losses in the feeding structure and for the design accuracy achievable by such antennas. Up to now, longitudinal slot arrays have been the most frequently used for their pure linear polarization [1], but other slot geometries have been sometimes proposed as radiating elements for waveguide arrays, e.g., lined slots [2] or transverse slots [3]. All of them share a linearly polarized radiation pattern. On the contrary, circularly polarized (CP) waveguide slot arrays are not so common in the present literature. As a matter of fact, a number of different configurations of CP slot radiators have been proposed in the past [4] [7] but, to the best of the author s knowledge, only [8] [10] investigate the design of a whole CP waveguide slot array. All of them use a crossed-slot configuration as array element. Moreover [8] uses the Bethe s small-aperture theory for the evaluation of the mutual coupling and [9] is based on a semi-empirical design procedure. Only [10] provides a full wave analysis for the evaluation of the mutual coupling. REFERENCES [1] C.-W. Yuan, Q.-X. Liu, H.-H. Zhong, and B.-L. Qian, A novel TEM 0 TE mode converter, IEEE Microw. Wireless Compon. Lett., vol. 15, no. 8, pp , Aug Manuscript received December 26, 2006; revised March 13, The author is with the Dipartimento di Ingegneria Elettrica ed Elettronica, Università di Cagliari, Cagliari, Italy ( giorgiom@diee.unica.it). Digital Object Identifier /TAP X/$ IEEE

2 3026 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 10, OCTOBER 2006 Fig. 1. Isolated element geometry and array geometry. The phase reference of V (for a generic n) is chosen at the center of the element n 0 1. In this paper, as an alternative to the CP slot array configurations available in the existing literature, the two-slot antenna proposed in [7] is used as the radiating element of a CP traveling wave linear array. This element is characterized through a method of moments (MoM) procedure using analytical (sinusoidal) entire domain basis functions [7], unlike the case of the crossed-slot configuration, which requires subdomain basis functions or numerical entire domain basis functions. The use of analytical entire domain basis functions strongly simplifies the analysis of the isolated element, as well as the evaluation of the mutual coupling, and allows an easy manipulation of the array aperture distribution. A design procedure is presented, based the MoM characterization both of the isolated CP radiator and of the mutual coupling between the array elements. As pointed out in [7], the proposed radiating element is designed in order to have the minimum of the AR in the broadside direction. Therefore, this CP element is suitable to be used for the design of an array with an equiphase aperture distribution, i.e., with the main lobe in the broadside direction. The costs of this choice are that: a) a slightly variable array spacing is required to compensate the phase variation of the excitations due to the geometrical differences of each array element; b) a dielectric filled waveguide is required because the array spacing must be near to a guided wavelength, but smaller than the free-space wavelength in order to avoid grating lobes. Of course, the use of a dielectric filled waveguide reduces the antenna efficiency, especially in large arrays. Nevertheless, materials with a high dielectric strength allow to rease the radiated power and can be particularly useful, for example, in antennas for RADAR applications. In Section II, the design curves for the radiating element are derived by using a specialized MoM analysis software [7] and, in Section III, the array design strategy is presented. A number of linear arrays are designed and, in Section IV, the features of an array with a Taylor aperture distribution with 020 db sidelobes, are shown in detail. The proposed design procedure is validated by using a finite element method (FEM) commercial software (Ansoft HFSS 9). The results show a very good agreement with the design goals for both the AR and the efficiency and the radiation pattern requirements. II. ARRAY ELEMENT DESIGN The CP array element (Fig. 1), consists of two closely spaced lined radiating slots cut in the broadwall of a rectangular waveguide [7]. This slot radiator is suitable to be used as the element of a traveling wave CP linear array, provided that it is designed to be reflectionless at one of the two ports. In this paper, the traveling wave is considered in the direction from port 1 to port 2 and the linear array radiates LHCP [7]. The simulations of this section are performed with the MoM procedure presented in [7]. A WR90 waveguide filled with Teflon (" r =2:1) at the operating frequency of 7.5 GHz is considered. Fig. 2. Schematic flow chart of the optimization procedure for the derivation of, x, and s required to comply with the requirements on AR and S. TABLE I SELECTED ELEMENT CONFIGURATIONS Fig. 3. (a) Optimized slot spacing versus slot length and (b) phase of E versus slot length [the phase reference is 0 for a slot length of 12 mm; the slot spacing for each value of the slot length is derived from the curve (a)]. Slots width = 1:5 mm. The isolated radiating element must be designed in order to obtain a CP field (AR < 0:5 db)in the broadside direction, the required input matching at port 1 (S 11 < 035 db) and a given element excitation. As explained in [7], the AR requirement is fulfilled by a proper choice of the spacing s, and the element excitation is controlled by the length of the slots (L). In order to comply with the S 11 requirement, a proper choice of the values of the tilt angles () and of the offsets (x) is also needed. For each L, the optimal values of, x, and s are determined by following the procedure outlined in Fig. 2. It has been found that the optimal tilt angle must be greater than 45 and is an reasing function of L, while the offset is a slightly decreasing one (with 1=(01x) = 3=0:05 1 [deg:=mm]). Therefore, a reasonable starting point for the tilt angle is 47, and the starting point for the slot offset must be chosen in order that, for each L in the range of interest, the slots do not overlap and remain inside the waveguide wall. As a result, four element types (see Table I) are selected and the curve (a) in Fig. 3 is derived. The variation of the element excitation is obtained by varying the slot length, therefore the radiating element must be off-resonance. As will be shown in Section III, in this context, the amplitude and the phase of S 21, and the phase variation of the electric field-peak E (1st=2nd) on the

3 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 10, OCTOBER Fig. 5. Evaluation of the external mutual coupling between two generic array elements. The phase reference of the unitary ident TE mode is at the center of the element i. and are the slot apertures, in the waveguide/external region, respectively of the first and the second slot of the radiating element. Fig. 4. Amplitude and phase of S as a function of the slot length. The slot spacing s for each value of the slot length is derived from Fig. 3. first/second slot of the radiating element, are fundamental quantities to accomplish the array design procedure. They are shown, respectively, in Figs. 4 and 3 curve (b) and. Se the element radiates circular polarization, the phase variation of E (1st) and E (2nd) is the same. Actually E (2nd) = E (1st) exp(j ) wherein is such to get circular polarization. III. ARRAY DESIGN PROCEDURE Using the design procedure presented in this section together with the curves in Figs. 3 and 4 it is possible to design a traveling wave linear array with a generic equiphase aperture distribution. The design of such an array (Fig. 1) requires the specification of the fraction (i.e., the array nominal efficiency) of the input power that is to be radiated (the rest of the power is dissipated into a matched termination). The following approximations are considered. i) The higher order mode interaction (in the waveguide region) between the array elements is neglected. This approximation is reasonable se the spacing between two adjacent elements is about a guided wavelength [1]. ii) It is assumed that each array element is reflectionless also when interacts with the other elements. The complex amplitude of the TE 10 -mode traveling wave through the waveguide is tapered because each element radiates a fraction of the ident power. If V n in Fig. 1 is the complex amplitude of the TE 10 -mode traveling wave that impinges upon the nth array element and V n+1 is the complex amplitude of the traveling wave after the interaction with the element n, the parameter T (n) = V n+1 = ^V n, wherein ^V n = V n exp(0j 10 d ), can be used in order to take into account the power radiated by the element n. If is the normalized power radiated by the nth element, then the amplitude of its excitation can be written as jc n j = (1) The phase of C n is determined by the phase of the traveling wave through the array and by the phase of E (1st). The first step in the array design procedure is the choice of the (equiphase) excitations C n. Then, from the C n, the required are calculated by using (1). Se, by design hypothesis each element is considered reflectionless, if is the ident power on the nth array element, the radiated power is = [1 0jT (n) j 2 ] and the following recursive equation for jt (n) j is derived wherein = T (1) = 1 0 P (1) ; T (n) = 1 0 n P () jt () j 2 n =2;...;N (2) = P () jt () j 2, V 1 = 1, P (1) 1 is the nominal radiation efficiency. = Pin = 1and The jt (n) j are easily computed by using (2) but, in order to perform the design of the array, the S (n) 21 are needed because the design curves in Fig. 4 involve the S (n) 21, i.e., are derived for the isolated element. If the mutual coupling between the elements is neglected, the S (n) 21 of the nth isolated element is equal to T (n). Therefore, the length L n of the slots is calculated by using the design curve in Fig. 4. Then, starting from the value of L n, the slot spacing s n, for each array element, is determined by using the design curve (a) in Fig. 3. Finally, the phase of S (n) 21 (n) (Fig. 4) and the difference between the phases of E (1st) (L n +1)and E (1st) (L n )(1 n ) (curve (b) in Fig. 3) are used to choose the array spacings d n (Fig. 1) in order to get equiphase excitations of the array elements: d n =(1+ n=2 +1# n=2) g, g being the guided wavelength. Se the evaluation of the mutual coupling is required, the value of S (n) 21 of each isolated element is not equal to T (n). Therefore, one of the key points of the array design procedure is finding a relation to tie T (n) of (2) to S (n) 21 through the mutual coupling. As pointed out in the approximation i), the higher-order mode interaction between the array elements is neglected. On the other hand, the external mutual coupling is evaluated using a spectral domain MoM procedure. In Fig. 5, two arbitrary array elements, i and j, are considered. For the evaluation of the external mutual coupling, only the element j is fed by a unitary TE 10-mode. Then, the TE 10 -mode scattering from the (not fed) element i, due only to the external mutual coupling, is computed. Se both the elements, i and j, are cut in the broadwall of the same waveguide, a dedicated MoM analysis procedure is well suited for the evaluation of the external mutual coupling. Actually, the MoM matrix elements which take into account the internal coupling are set to zero, and no excitation is considered for the rows of the MoM linear system which represent the slot apertures and (i.e., the element i). The details of the MoM procedure are given in [7]. The TE 10 -mode scattering from both the elements is calculated from the solution of the MoM linear system. As shown in Fig. 5, A (i;j)+ and A (i;j)0 are the scattering from the element i, respectively in the positive and negative direction of the z-axis, due to the external coupling between the element j (fed by a TE 10 mode of unitary amplitude) and w1 i w2 i

4 3028 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 10, OCTOBER 2006 the (not fed) element i. It is worth noting that the scattering from the element j is virtually independent from the (not fed) element i. Therefore, the complex amplitude of the TE 10 -mode traveling wave, after the interaction with the nth array element, i.e., V n+1 in Fig. 1, can be written as the sum of two terms: 1) the contribution of the isolated element n; 2) the contribution of the coupling between the element n and all the other array elements. Then TABLE II MAIN FEATURES AND GEOMETRICAL PARAMETERS OF THE DESIGNED ARRAY V n+1 = S (n) ^V 12 n + A (n;j)+ ^Vj e 0j d + j=1 N j=n+1 A (n;j)+ V j (3) and, dividing by ^V n T (n) = S (n) 12 + (n;j) A (n;j)+ + (n;j) = (n;j) = j01 k=n k=j j=1 T (k) with j > n; 1 N j=n+1 (n;j) A (n;j)+ with j < n: (4) T (k) The following simplifying assumptions are further considered in the design procedure: iii) the A (i;j)0, which virtually contribute to the array return loss, are neglected; iv) the effect of the external mutual coupling on the AR is neglected; v) the phase of T (n) is computed assuming that the relation between the amplitude and the phase of T (n) is the same of the relation between the amplitude and the phase of S 21. This means that, once the amplitude of T (n) is known, its phase is calculated using the curve in Fig. 3; vi) the phase variation of E (1st) (L n ) is considered independent of the mutual coupling; vii) the waveguide dielectric losses are neglected; At this point, the evaluation of the external mutual coupling requires the knowledge of the geometric parameters of all the array elements and of their spacings d n. On the other hand, these quantities depend on the mutual coupling itself and therefore an iterative procedure is needed. At the first step of the iterative procedure, the external mutual coupling is assumed to be zero and the design parameters L nj (0), s nj (0), d n j (0) are computed. At the kth step the mutual coupling coefficients A (i;n)+ j (k) are derived by using the design parameters L nj (k01), s n j (k01), d n j (k01) computed at the previous (k 0 1)th step. Then, the values of S (n) 21 j (k) of the isolated element are obtained by using (4), and the new values of the design parameters L n j (k), s n j (k), d n j (k) are computed through the design curves in Figs. 3 and 4. At each step of the iterative procedure, the amplitude of the T (n) is set by (2) and, according to the approximation v), its phase is calculated by using the curve in Fig. 3. The values of A (i;j)+ (and consequently L n, s n, d n) converge after a few steps (usually 3 4 steps are enough). IV. RESULTS In order to investigate the properties of proposed configuration, a number of linear arrays with different size and aperture distributions are designed. All of them show a good agreement with the design goals on the far field pattern and a very good circular polarization. In this section, the case of a 15-element array with Taylor aperture distribution, 020 db sidelobes, and nominal efficiency equal to 0.99, is described in detail. The design parameters are shown in Table II. The Fig. 6. Array return loss (RL) and amplitude of the traveling wave reaching the dissipative termination (jv j) as a function of the frequency. Dashed line: lossless dielectric. Continuous line: lossy dielectric (tan() =0:001). operating frequency is 7.5 GHz. All the slots have the same width (1.5 mm) and the waveguide wall thickness t (see Fig. 5) is 1 mm. The array length is cm (with d n between 0:974 g and 0:836 g ). In order to validate the presented design procedure, a FEM commercial software is used. All the simulations that follow are performed with Ansoft HFSS 9. Both a lossless and a lossy dielectric inside the waveguide is considered. Teflon (" r =2:1, with dielectric loss tangent tan() =0:001)is chosen for its high dielectric strength. The frequency response of the designed array is plotted in Fig. 6. The normalized far field pattern at the operating frequency is shown in Fig. 7 curve (a). The side lobe level (SLL) is below db. The asymmetry of the far-field pattern is mainly due to the asymmetry of the element factor. The AR at the operating frequency is shown in Fig. 8 curves (a). Its value in the broadside direction is less than 0.6 db and remains below 1 db in the whole 03 db-beamwidth (about 5 ). The radiating features of the designed array, in a 100 MHz bandwidth around the operating frequency, are summarized in Table III. The realized gain and the efficiency take into account the power reflected at the input array port, the power dissipated into the matched termination, as well as the dielectric losses. From Table III it results that, at the operating frequency, the array efficiency perfectly complies with the design goals. The power loss due to the lossy dielectric is about 7% but it only causes a reduction of the array gain. The other array parameters are virtually independent from the dielectric losses.

5 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 54, NO. 10, OCTOBER last element rather than with an absorber (Fig. 1), the power reflected back into the waveguide is about 1%. In this case, the value of H can be optimized in order to minimize the AR and the optimal value of H is 35.1 mm. As shown in Fig. 8 curves (b), this solution provides a very good AR in the broadside direction (about 0.4 db) and the side lobe level is db [Fig. 7, curve (b)]. V. CONCLUSION Fig. 7. (a) radiation pattern (yz-plane) of the 020 db-taylor array with an absorber at the array termination and (b) radiation pattern of the 020 db-taylor array with a short circuit termination at a distance H=35:1 mmfrom the last array element. In both cases the curves, for the lossless dielectric and for the lossy (tan() =0:001) dielectric, overlap. A procedure for the design of a CP traveling wave linear array has been presented. It takes into account the mutual coupling between the elements through a full wave MoM analysis. A number of linear arrays have been designed to assess the presented procedure. All of them show a good circular polarization in the 03 db beamwidth and in quite large bandwidth around the operating frequency. It is worth noting that the absorber at the array termination can be replaced by a short-circuit without degrading the far field pattern and at the only cost of a slight rease of the average AR in the 03 db beamwidth. The proposed linear array can be a promising starting point for the design of planar arrays for both broadcast and RADAR applications. ACKNOWLEDGMENT The Author thanks Prof. G. Mazzarella and Dr. G. A. Casula for helpful discussions and suggestions. Fig. 8. (a) AR (yz-plane) of the 020 db-taylor array with an absorber at the array termination. (b) AR of the 020 db-taylor array with a short circuit termination at a distance H=35:1mmfrom the last array element. Dashed line: lossless dielectric. Continuous line: lossy dielectric (tan() =0:001). TABLE III RADIATING FEATURES OF THE DESIGNED ARRAY Another factor that contributes to reduce the array efficiency is the use of the absorber at the array termination. Moreover, the dissipative termination could generate thermal noise. These problems can be solved by using a terminal matching element [11] or by short-circuiting the waveguide termination. This latter solution is reasonable when the power reaching the termination is a small fraction of the radiated power. Actually, the power reflected back into the waveguide by the short circuit termination modifies the far field pattern and the AR. The use of a matching element is advantageous because allows to radiate all the residual power without degrading the AR but it can modify the far field pattern because all the residual power is radiated by the last array element. As a matter of fact, when the residual power reaching the termination is less than 2% the matching element solution is virtually equivalent to the terminal short circuit solution. Actually if, for example, the Taylor array designed in this section is terminated with a short circuit at a distance H from the center of the REFERENCES [1] R. S. Elliot, Antenna Theory and Design. Englewood Cliffs, NJ: Prentice- Hall, [2] S. R. Rengarajan, Compound radiating slot in a broad wall of a rectangular waveguide, IEEE Trans. Antennas Propag., vol. 37, pp , Sep [3] X. Shan and Z. Shen, Transverse slot antenna array in the broad wall of a rectangular waveguide partially filled with a dielectric slab, IEEE Trans. Antennas Propag., vol. 52, pp , Apr [4] A. J. Simmons, Circularly polarized slot radiators, IRE Trans. Antennas Propag., vol. 5, pp , Jan [5] K.-S. Min, J. Hirokawa, M. Ando, and N. Goto, U-shaped slots for circularly polarized slotted waveguide array, in Proc. AP-S Int. Symp., 1995, vol. 3, pp , AP-S. Digest. [6] N. Kuga, Y. Tsuneyama, H. Arai, and N. Goto, A H-plane slottedwaveguide array for circular polarization using lined-slot pairs, in Proc USNC/URSI, San Antonio, TX, 2003, p [7] G. Montisci, M. Musa, and G. Mazzarella, Waveguide slot antennas for circularly polarized radiated field, IEEE Trans. Antennas Propag., vol. 52, pp , Feb [8] W. J. Getsinger, Elliptically polarized leaky-wave array, IRE Trans. Antennas Propag., pp , [9] N. E. Armstrong and N. G. Alexopoulos, On the design of circularly polarized narrow wall linear array, IEEE Trans. Antennas Propag., vol. 23, pp , Mar [10] J. Hirokawa, M. Ando, N. Goto, N. Takahashi, T. Ojima, and M. Uematsu, A single layer slotted leaky waveguide array antenna for mobile reception of direct broadcast from satellite, IEEE Trans. Veh.Technol., vol. 44, pp , Nov [11] J. Hirokawa, K. Sakurai, M. Ando, and N. Goto, Matching slot pair for a circularly-polarized slotted waveguide array, in Proc. Inst. Elect. Eng., Pt. H, Dec. 1990, vol. 137, no. 6, pp