An efficient analysis for log-periodic dipole antenna array

This paper presents an efficient semi-analytic solution for log periodic dipole antenna array LPDA with arbitrary feeding. This method is characterized by its fairly less computational time and storage requirements compared to other numerical methods and other commercial software. The analysis employs the electric field integral equation where extended boundary condition is used yielding a non-singular kernel. The integral equation is then formulated in a matrix form applying the method of moments MoM and entire domain odd cosine Fourier expansion for both current distribution and source terms. The basic idea is the expansion of the Green's function in terms of Fourier series. Two types of series are employed for the kernel; infinite Fourier series IFS for the self kernel and finite Fourier series FFS for the mutual kernel based on the kernel function behavior in each. The resultant integration is obtained analytically in a closed form in terms of Bessel and Hankel functions combined with sine and cosine integrals. The results are compared with the formal LPDA having an independent frequency behavior over a wide band of frequencies of operation with nearly constant VSWR. Results agree with those obtained using piecewise sinusoidal MoM and with the previously published results.