A linear antenna array is synthesized for the generation of desired shaped beams using a phase expression. The range of synthesis is fixed the equation for the phase remains the same for the generation of any shape of radiation pattern. Continuous line sources and discrete antenna array elements are synthesized. This technique is suitable to implement in arrays of extremely large dimensions [1].
Synthesis of unequally-spaced arrays to generate desired radiation pattern using poisson's sum formula to calculate the source position function is reported. The synthesis also extended for equally spaced arrays to obtain reduced side lobe levels with applications [2]. Separation between elements of nonuniformly spaced array to give reduced sides lobes is determined by perturbation method [3].
Side lobe level estimation by Diophantine equation and Triangular function are presented and compared for nonuniformly spaced arrays [4]. Methods of synthesis for equal side lobes and minimum error between desired and synthesized patterns by controlling excitation amplitudes and separation between elements of non uniformly spaced array is reported [5].
Synthesis of shaped beam patterns with equal percentage ripple of the main beam by controlling the position of the zeros of the respective pattern function is presented in this paper. Magnitude of the ripple is determined by the amount of displacement of the zeros from the axis. Shaped beams generated shows that the realized patterns are not very close to the desired patterns hence this technique is an approximate method [6].
A design procedure for nonuniformly spaced arrays with particular side lobe level and excitation amplitude levels suitable for pre defined separations between the elements is reported [7]. Earlier dynamic programming technique has been applied to the synthesis of unequally spaced arrays of nine elements and it is extended to twenty five element array in this paper and shows improvement in results than earlier applications and other techniques. Odd number of elements in the array is used. Large array for this technique gives optimum results [8]. A shaped pattern is generated by the perturbation of the roots out side the Schelkunoff's unit circle. Cosecant shaped pattern for two different angular regions have been generated. Desired radiation pattern and generated pattern are in good agreement [9]. Power pattern synthesis of linear antenna arrays without any phase constraint on the far field is presented. The desired pattern is approximated by a harmonic sum with required ripple properties and is then approximated to a realizable power pattern. In this method pattern side lobe levels are easily controlled [10]. Both line source and linear arrays can be synthesized using iterative sampling technique for the generation of shaped radiation patterns. Generated patterns exhibit low side lobes, less ripple of the main beam and sharp cutoff for the main beam [11]. Synthesis of discrete linear antenna arrays for the generation of antenna patterns using steepest descent method of numerical iterative technique is presented. The steepest descent technique is an efficient method of pattern synthesis and uses parameters of the array for synthesis[12]. Legendre - Gaussian quadrate method is implemented for the synthesis of nonuniformly spaced linear antenna arrays to generate shaped beams. A comparison is made with methods of uniformly spaced antenna arrays and these beams have been synthesized with less number of antenna elements in the array than those of uniform antenna arrays for the same radiation pattern [13]. Iterative sampling method is used in line sources and linear array to control side lobe levels or to generate desired beam shapes over specified regions. Equally or unequally spaced linear arrays, arbitrary rectangular arrays and circular apertures are synthesized using this method [14]. Minimax optimization method can be used to solve nonlinear synthesis problems of wide range for which exact analytical solutions don't exist. Minimax optimization is a nonlinear method with definite convergence properties and can be used to synthesize antenna radiation patterns, with low side lobe levels and this method don't require any derivatives hence may be implemented to design complex antenna systems. [15]. Radiation characteristics of uniform array are compared with those of position modulated uniformly excited array with reduced number of elements [16]. Shaped beams such as sector and cosecant beams are generated from circular aperture using phase functions. Phase functions are derived for desired pattern function using the method of stationary phase [17]. An array of discrete antennas is used for the generation of desired shaped beams using particular amplitude distribution and changing phase distribution. A finite series of array factor is expressed into an infinite series and each term is expressed in integral form that contains the envelope of the amplitude and phase functions over the entire aperture [18]. A group of weighted Inagaki modes are defined and applied to the synthesis of shaped beams and compared with the conventional methods of synthesis [19]. Computationally simple technique of synthesis of antenna arrays is presented by Elliott. It is demonstrated in this paper that the synthesis of shaped beams with controlled ripple and predefined side lobe levels over a specified angular region [20]. Additional parameters are introduced in to the pattern function that gives control over the main beam ripple and its side lobe levels. A shaping function is defined that gives the ideal behavior of power pattern in the beam region [21]. Excitation phase control technique is used to minimize the side lobe levels in antenna arrays of equispaced linear and planar geometry. In planar circular array excitation phases drops linearly as the logarithm of the diameter of the array[22]. Uniform antenna array is synthesized using an iterative process with constrained and unconstrained excitation. This paper presents the general synthesis of the shaped beams with and without constraints on the excitation amplitude [23]. Alan R.Cherrette et. al reported design of shaped reflector to generate contour shaped beams replacing corporate feed driving a group of antennas by single feed. A single reflector is shaped to produce desired shaped far field [24]. Synthesis of non uniform array by varying separation between the elements with excitation amplitudes of the elements fixed and equal is reported [25]. An antenna array is proposed to generate beams of different shapes with change in the excitation phase of the individual elements [26].
Synthesis of shaped antenna beams with independent control of the amplitudes of the ripples in the main beam region and control of the heights of the side lobes in the unshaped region by introduction of complex roots in to the Taylor line source distribution of far field space factor is presented [27]. Antenna array pattern nulls are synthesized using two iterative methods which are based on analytical and numerical-analytical minimization either by one phase or two phases of element excitation and is also called phase only null synthesis in root mean square approximation [28]. Real radiation pattern and power synthesis are compared to determine merits of each method using linear array of equispaced elements. Three parameters such as side lobe level, envelope and cut off rate of the radiated beam are compared for both synthesis techniques with different number of equispaced linear antenna arrays [29]. Orchard-Elliott method is extended to reduce ripple in the shaped beam patterns by null filling in the side lobe region of the shaped pattern. For the same power pattern null filling gives less mutual coupling effects and multiple aperture distributions [30]. A technique is presented to synthesize antenna arrays using Chebyshev polynomial to approximate the desired radiation pattern with equal side lobe levels. Synthesis of planar array is proposed by applying Chebyshev polynomial to generate the desired radiation pattern with equal side lobes [31]. This paper presents synthesis of fixed patterns by specifying field patterns in amplitude and phase and also specifying field patterns in amplitude alone. The pattern is synthesized from a dipole array with half wave length, quarter wave length and one wave length separation between the elements [32]. Synthesis based on adaptive array theory and minimization of noise and there by maximizing signal to noise ratio is presented by Duford in this paper [33].
Linear and circular apertures are synthesized by phase only control method to generate shaped radiation patterns with low side lobes and reduced ripples in the main beam region [34]. Generation of desired far field antenna pattern from continuous line source and an expression for the field is obtained by relating Fourier Transform to Legendre polynomials and spherical Bessel functions. Efficiency of the synthesis process is computed [35]. Synthesis of linear arrays for power patterns using time modulation method is presented. It is established on comparison that the differential evolution method exhibits very less amplitude dynamic-range ratio than that of Woodward Lawson technique [36]. Traveling wave and center fed antenna elements are synthesized to generate shaped-beam pattern with very less variations of the currents between the elements which reduces mutual coupling effects. In the implicit constrained current method the zeros of the pattern function are not constrained [37].
Radiation characteristics of wide-angle biconical antenna terminated by spherical cap are analyzed. In this paper the spherically capped wide-angle biconical antenna has been investigated and demonstrated the suitability of this antenna for dipole like radiation patterns or for UWB antenna with radiation confined to a particular angular area [40]. Radiation properties of biconical antenna with dissimilar cone angles have been investigated for transmission and reception of electromagnetic waves [41]. An antenna with vertical polarization, omnidirectional radiation pattern, that exhibits broadband characteristics is designed and presented. An accurate mathematical relationship between cone angle, height of the cone and radius of the cone is developed for a broad band compact wide angle conical antenna terminated by spherical cap [42]. Orthogonal properties of the Legendre's functions and their derivatives have been used for calculating the admittance of wide angle biconical antenna terminated by spherical cap [43]. Expression for the terminal admittance is derived by considering more number of higher order complementary waves for biconical antennas with small and wide cone angles. An improved expression for the terminal admittance in wide angle biconical antennas is obtained by considering additional complementary waves [44]. Input impedance of a biconical antenna is determined by using E.M.F method and by using Poynting theorem expression for the complex conjugate power has been derived [45]. The impedance of a biconical antenna is determined by using Schwinger method for analyzing discontinuity in a wave guide. Along the boundary sphere which is enclosing the antenna the tangential electric and magnetic fields are matched. Input impedance and terminating admittance are determined by considering cones of specific cone angles [46]. The input impedance expression for biconical antenna with wide cone angles fed by coaxial line mounted on infinite plane is obtained. Variation of input resistance and reactance's for various cone lengths and cone angles have been plotted and functions are derived [47]. Spherical Hankel functions of the second kind along with the suitable Legendre polynomials have been used and their odd integers have been summed to obtain the expression for the radiation from wide angle biconical antenna terminated by truncated spherical section [48]. Analysis of a wide angle biconical antenna connected with a matched source excited by dc pulse and terminated by matched load is presented in transmission and reception modes[49]. Antennas of arbitrary shape and size have been studied extensively in this paper. Biconical antenna is particularly selected for analysis since it is symmetrical with spherical geometry and also its boundaries lie along the coordinate surfaces in the spherical coordinate system [50]. Conical antenna terminated at the ends by spherical cap is analyzed as a transmission line terminated by appropriate impedance. Radiation by biconical antennas for transverse electromagnetic waves which is considered as principal wave is presented [51]. Cylindrical and nonconical antennas have been analyzed with mathematically. The fields around cylindrical antennas have been analyzed by showing Maxwell's equations for antennas of several shapes but conical antennas have been analyzed in detail [52].
