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# Directivity of V Antennas

The V antenna is a traveling wave antenna where high directivity can be achieved when the length of each arm of the V is greater than the wavelength. However, the angle between the arms must be chosen so that the fields radiated by both arms constructively add in the forward direction. Several authors have investigated the optimum angle of the V antenna as a function of the length of its arms. For instance, refer to G. A. Thiele and E. P. Ekelman, Jr., “Design Formulas for Vee Dipoles,” IEEE Trans. Antennas Propagat., Vol. AP-28, No. 4, pp. 588–590, July 1980.

Thiele and Ekelman have reported a formula for calculating the angle between the arms that maximizes the directivity of a symmetric V antenna, which depends on the length of the arm measured in wavelengths. This formula is a polynomial fit to the results of various simulations using the Method of Moments (MoM). A linear fit to maximum directivity as a function of arm length has also been reported and it is given by

where L/λ is the arm length in wavelengths.

Details of the segmentation and kernel of the integral equation used have not been provided, but the thin-wire approximation was probably used. Despite these missing data, these formulas serve as a reference to compare with the results obtained from AN-SOF.

Figure 1 shows the AN-SOF model of a V antenna and the calculated radiation pattern for an arm length L/λ = 2 and an angle Θ = 67°. Figure 2 shows maximum directivity as a function of the arm length in wavelengths. We can see that the agreement is quite good. The values obtained from Eq. (1) are somewhat lower than those of AN-SOF, as if the antenna arms were shorter. This displacement of the results obtained by the traditional method of moments with thin-wire kernel with respect to the MoM with exact kernel is well known, so it is expected to be observed in these comparisons.