Finding the resonate length of low frequency helical dipoles

An efficient recursive procedure to find the resonant length of a normal mode uniformly winding helical dipole antenna, has been developed. In the procedure, starting with two (or an arbitrary even number) turns, the moment method impedance elements are found and the Toeplitz equations are solved. If the imaginary part of the input impedance is capacitive, the antenna does not resonate. So we add one turn on each end of the dipole. Two more impedances are computed for the new dipole. These two impedances, the previous antenna current and impedance elements are used to find the new input impedance with very simple calculations. This process continues until the input impedance is real.