A Simplified Calculation for Dolph‐Tchebycheff Arrays
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A series is derived for the currents on the radiators of a Dolph‐Tchebycheff array, which is more suitable for numerical calculation than the series given by Barbiere, when the number of radiators becomes large. The series is not alternating in character and is given in terms of a variable α=tanh2[ln(r+(r2−1)12)N−1], where r is the side‐lobe ratio and N is the number of radiators. α is constrained to the interval 0≤α≤1. The important practical case, when α≈ln2(r+(r2−1)12)(N−1)2, is approximated by a Bessel function. The calculations show that the currents on the two end elements of the array play a special role and that their adjustment should have due attention, whenever the inequality ln[r+(r2[minus]1)½]< (N[minus]1)½ is satisfied.
[1] C.L. Dolph,et al. A Current Distribution for Broadside Arrays Which Optimizes the Relationship between Beam Width and Side-Lobe Level , 1946, Proceedings of the IRE.
[2] Domenick Barbiere. A Method for Calculating the Current Distribution of Tschebyscheff Arrays , 1952, Proceedings of the IRE.