Frequency Characterization of a Thin Linear Antenna Using Diakoptic Antenna Theory

A frequency-dependent analytical expression for the input impedance of a thin wire antenna is obtained using diakoptic theory. The linear antenna is diakopted into electrically short segments where each segment is treated as a component with two terminals (except for end pieces, which have only one terminal). An impedance matrix is found which characterizes coupling between all segments. By expanding the free space Green’s function in a power series in wavenumber k, each entry in the resultant impedance matrix is obtained as an explicit function of frequency. Enforcement of the continuity of currents and equality of scalar potentials at the nodes of the diakopted antenna reduces the impedance representation into a system of linear equations for the node currents of the assembled structure. By solving for the feed current the input admittance is found as a ratio of two polynomials in wavenumber k. A more systematic approach for the solution of the input admittance is achieved by expanding both the unknown current vector and the Green’s function in power series in k. Equating coefficients of like powers in k leads to a numerically efficient algorithm which is used to determine the input admittance as a function of frequency. Numerical results are compared with the input impedance obtained from a conventional integral equation solution; good agreement is observed, up to and somewhat beyond the first resonance.