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The paper considers using the method of mode matching in time domain for simulation of a pulse signal propagation in a dielectric circular rod antenna. The mode basis for circular dielectric waveguide and free space are obtained. The systems of integral-differential evolutionary equations for dielectric waveguide and free space are reduced to the system of matrix differential equations by the method of moments. Numerical solution scheme for these systems by FDTD method are proposed. In order to calculate signal radiation by the rod antenna the field matching procedure based on the boundary conditions is proposed.