The present author suggests a new distribution function for the roots of the complex polynomial corresponding to the nulls of the radiation pattern of a linear antenna array on the unit circle in a complex plane which is more general than the one suggested by the same author in a previous paper. The new distribution function is of the form ψK=ψ0{1+ξK((ln(ψm/ψ0-1)-lnξ)/(ln m))}. When ψ0 and ξ are chosen properly, the suggested distribution includes the following distributions or arrays as special cases: (1) the uniform end-fire arrays; (2) the uniform broadside arrays; (3) the Schelkunoff's distribution in the range of ψ; (4) the Dolph-Tchebyscheff's distribution for number of elements not greater then seven. But the suggested distribution has the advantage of improving all of them, especially for the suppression of side-lobes near-by the main beam which is very important in certain practical applications.Moreover, since the primary patterns of many types of radiating elements fall off with increasing angle from the main maximum so that the wide-angle lobes would be at a lower level than those close to the main beam, it is necessary to design an array pattern in such a way so that the side-lobes should increase in magnetude with increase in angle from the position of the main beam in order to achieve an over-all pattern with side-lobes all equal or approximately equal in magnitude which is useful in many practical applications. Neither Schelkunoff's distribution in the range of ψ nor Dolph-Tchebyscheff's distribution meets this requirement but the suggested distribution does.In this paper, explicit expressions for the relative antenna currents have been put in closed forms convenient for calculation and semigraphical method has been used for all the pattern calculations.
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