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The finite-difference time-domain (FDTD) method is routinely used to calculate the input admittance/impedance of simple antennas. The value of the input admittance/impedance depends on the level of discretization used in the method, and should converge to a final value as the discretization becomes finer. In this paper, the level of discretization necessary for convergence is studied using two common feed models: the hard-source feed and the transmission-line feed. First, the simplest and most naive methods for introducing the voltage and the current in these models are considered, and the results for the admittance are shown not to converge. Next, improved methods for introducing the voltage and current in these models are constructed. The results for the admittance are then shown to converge, and guidelines are offered for the level of discretization needed for convergence. In addition, two general problems associated with the computation of the admittance are discussed: the agreement between admittances computed with different simple feed models, and the agreement between these admittances and measurements.