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The concurrent complementary operators method (C-COM) is extended to simulate microwave planar circuits with the finite-difference time-domain (FDTD) method for the first time. The dispersive boundary condition (DBC) and its complementary operator are used to truncate the FDTD lattices and the fields in the boundary layers are calculated, respectively. Then these two simulations are averaged to annihilate the first-order reflections. Numerical error analysis shows that the performance of the DBC is improved greatly due to the implementation of complementary operators, and the setup of its parameters becomes easier and more robust. A flexible and high-performance absorbing boundary condition is thus obtained through the combination of the DBC and C-COM. This method has been successfully used to simulate a variety of planar circuit structures. Simulations of a microstrip low-pass filter, coupled-line bandpass filter, modified microstrip transmission lines, and dielectric resonator antenna, are presented in this paper.