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In this paper, a broadband sleeve-conical antenna with arbitrary sleeve shape is studied. The frequency range of the antenna is aimed at 300 MHz to 3 GHz. The reflection coefficients, obtained by using conventional equations, are compared with simulated data obtained by using the CST MW Studio. The validity of the software has been confirmed by analysing many canonical structures. The given structure subsumes the scattering problem that is considered in the existing literature dealing with special cases. The simulated results of this antenna system are obtained for various values of the length and the radius of the sleeve, through which the effect of these parameters on the radiation field behavior is studied.