The electron optical properties of magnetic deflection systems are generally described in terms of the parameters H0, H2 and H4. In this paper, basing on the Biot-Savart's law, we derive the analytical formulas for the flaring saddle coil with a single turn. And then using the method of Fourier harmonic anlysis we obtain the field-para-meters experssions for the different winding distributions. So the relations between the field-parameters and the harmonics and some useful results are obtained. These formulae are useful for designers of deflection systems in television tubes, kinescopes, radars, scanning electron microscopes and electron beam exposure equipments.