On the eigenmodes of small conducting objects

A mathematical model is of importance to understand the characteristics of an antenna or scatterer. However, a direct model of surface currents has some difficulties handling different feeding positions and analysis frequencies. Instead, we can model the eigencurrents and eigenvalues of a small conducting object, which shows some unique merits. In this letter, we try to solve an important issue for the new model methodology, i.e., the changing rules of eigencurrents and eigenvalues with different frequencies. We start with the impedance matrix obtained by the method of moments and analyze separately its real and imaginary parts. Based on the results, the changing rules of eigencurrents and eigenvalues are obtained. It is revealed that the eigencurrents are almost unchanged with the frequency for small conducting objects, and the eigenvalues decrease approximately cubically with the frequency. As a result, it is possible to model the eigencurrents and eigenvalues with one mathematical expression for a wide bandwidth.