The discone antenna is well known as an easy to build multioctave broadband antenna with a omnidirectional radiation pattern in the H-plane, It comprises a plane conductive disc element spaced close to and axially aligned with a conductive cone element. For applications in the UHF and microwave ranges, high performance antennas have been designed to operate from 0.5 to 5 GHz with a VSWR of about 3.5:1 or less. If the length is finite, the impedance still strongly dependent on apex angle as long as the cone is longer than about quarter of wavelength and the apex angle is relatively larger. A problem that is experienced with these antenna designs is the relatively large size required to operate at the low frequencies. In applications where utilization of this antenna. In this work, the analysis and design of these antenna is obtained by employing a rigorous formulation of the electromagnetic scattering problem. As a design tool, we employ Method of Moments for the analysis of rotationally symmetric structures excited by TEM mode. To properly account the variations in driven-point impedance with frequency, the coaxial waveguide used to feed the antenna is also included in the analysis. The excitation is simulated by a distribution of equivalent electric and magnetic currents placed inside the coaxial cable, over a cross-section plane. These currents are defined such that only excite the mode TEM towards the cable-antenna junction. These numerical tool is employed in the shaping the metallic surfaces involved in the discone-type antennas in order to obtain more compact structures. Simple solutions can be easily obtained making the center fed cone and the disc element with radially outer edge portions rolled backwardly and away from each other to form donut-shaped configurations. The ruled edges not only reduce the diameter of the antenna but also permit the current to flow around them smoothly and without reflections that degrade the VSWR at low end of the frequency band.