Accurate Design Method for Pyramidal Horns of Any Desired Gain and Aperture Phase Error

Abstract

An exact solution is presented for the fourth-order polynomial representing the general horn design problem. When the available approximations are used for the gain reduction factors, this leads to closed-form expressions for the aperture, and hence the other, dimensions of the pyramidal horn of any desired gain and aperture phase error.Index Terms-Optimum pyramidal horn design, pyramidal horn design.

Polynomial-Based Evaluation of the Impact of Aperture Phase Taper on the Gain of Rectangular Horns

“…In [5], Schelkunoff's formula was extended by involving an additional term that accounts for the influence of the edge effect on the on-axis gain and included sectoral horns and open-ended rectangular waveguides. In general, the expressions presented in [2,5] give adequate results and are commonly used in the literature [6][7][8][9][10][11]. Comparisons between calculated results and measured data showed an uncertainty ±0.5 dB for frequencies below 2.6 GHz and ±0.3 dB for higher ones [12].…”

“…The subscript j in (12) and (13) denotes that the specific values are calculated at s or t equal to jN (the maximum value of the two aperture phase error parameters is one, see (11) (6) and (7) for n = 1,2…10. The corresponding polynomial coefficients, e n,i and h n,i , are given in Tables 2 and 3.…”

“…Example 3: In [11], Selvan proposed a design method for pyramidal horns of any desired gain and aperture phase error. However, the accuracy of his method is strictly related to the accuracy of the approximations of (6) and (7).…”

“…Table 6 gives the calculated horns dimensions with the method proposed in [11] using (10) (Aurand's app-roximation) and the proposed second-, fourth-, and sixthorder approximations. Next, we used this data and calculated the exact gain values with ORAMA, see Table 7.…”

“…However, approximate but simple closed-form expressions are often required [11,17,18]. In this paper, we extend the analysis in [17] to include a broader range of aperture phase error values.…”