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Logarithmicpotential TheoryAuthor: Edmund A. Laport
Logarithmic potentials have been mentioned frequently in the previous chapters of this book and have been used to obtain essential design information for antennas and transmission lines. The logarithmicpotential method of calculating various antenna and transmissionline parameters is an invaluable tool for the antenna engineer. With it, he can calculate quickly, and with sufficient accuracy, problems that would otherwise cost him enormous amounts of time and labor.
Another dynamic relationship that is employed directly is that which exists between the charge and current. This relationship is as follows: The current I flowing in a wire is related to the charge per unit length Q on the wire by Therefore in any system where v is constant, the current is directly proportional to the charge per unit length. This permits one to interpret charge ratios directly as current ratios. The meterkilogramsecond system of units and common logarithms are used, which accounts for the numerical coefficients that appear in all equations. The charge per unit length Q is in coulombs per meter on each conductor, identified by subscript for the conductor of that number and by double subscript for its image charge, which is always of the opposite sign of the charge on the conductor. In order to apply to each logarithmic term the sign of the real or image charge under consideration, reciprocal distances are used for all linear distances from the axes of the conductors. This avoids the problem of signs, because the sign of the logarithm of a reciprocal of a distance will then always be the same as that of the charge from which this distance is measured  otherwise, it would always have the opposite sign. Furthermore, we shall take advantage of the fact that a transmission line of low loss, which includes almost all practical radiofrequency lines, has a characteristic impedance Z_{0} = , and since v = 1/, Z_{0} = 1/vC. The velocity of propagation v for airdielectric systems has the value 3·10^{8} meters per second. The capacitance per unit length is defined in the usual way as the charge per unit length divided by the potential difference, Q/V.
All crosssectional dimensions must be in the same units (inches or centimeters), and the ground is assumed to be perfectly conducting.


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