A new design method is proposed for maximizing the minimum power in the main beam of on-vehicle antenna. This method is useful to design the on-vehicle antenna for the efficient detection of the vehicle on side lane in the highway. For an example, the system of the detection and warning of the detected vehicle coming from the back is considered. Then, the on-vehicle antenna is set in the back bumper, etc. of my vehicle. The gain or radiation power of the on-vehicle antenna is differentiated by the 3 dB beam width in the horizontal plane, and the result equation is put to zero. As the result, the optimum beam width giving maximum value of the gain or radiation power is determined. The optimum antenna aperture size can be determined by using the optimum beam width, thus, the optimum antenna can be determined. It is assumed that the antenna aperture distribution is uniform. The optimum beam widths giving maximum gain for square, rectangular and circular aperture shapes are shown as 101.6 sinθ(deg), 136.9 sinθ(deg) and 99.6 sinθ(deg), respectively. where θ is the angle between the back direction and the direction of the detected vehicle coming from the back on side lane. The simple equation giving the angle of maximum radiation power is also shown. By using these equations, the optimum 3 dB beam width of on-vehicle antenna, that is, the optimum antenna aperture size can be easily determined when the position of the detected vehicle on side lane is given. The variance of radiation power is also shown when the position of the detected vehicle on side lane varies. In this paper, the proposed design method is applied for the vehicle on side lane toward back direction, but, this method can be also applicable for the vehicle on side lane toward front direction. The fundamental optimum design of the on-vehicle antenna can be easily performed by using the method in this paper.
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