The imperfectly conducting cylindrical transmitting antenna

The properties of a cylindrical antenna with a continuous ohmic resistance along its length are of interest in the design of certain types of directive broadband antennas and in the determination of the efficiency of dipole antennas. Conventionally, the contribution by ohmic resistance to the distribution of current and the impedance is contained in a particular integral that is either ignored or treated as a higher-order correction to formulas derived for perfectly conducting antennas. An alternative and more useful form has been developed in which the integral equation for the current is rearranged to permit the introduction of a complex wave number
k
. An approximate solution of this equation is then obtained in terms of the three trigonometric functions,
\sin k(h-|z|)
,
\cos kz-\cos kh
, and
\cos \frac{1}{2}k_{0}z - \cos \frac{1}{2}k_{0}h
, where
k_{0}
is the free-space wave number. Expressions are derived for the coefficients of these functions and for
k
. Explicit formulas are given for the distribution of current and the admittance.