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We use a density-based topology optimization approach to design dualband planar metallic antennas. The design problem is formulated based on the time-domain Maxwell's equations, solved using the finite-difference timedomain (FDTD) method. The antenna design is formulated as an optimization problem where the received and reflected energy by the antenna in two frequency bands, centered around 2.5 GHz and 5.5 GHz, are optimized. Two design examples that exhibit outstanding performance are presented. In one design case, we employ a nonlinear filtering scheme to impose size control on the optimized design and ensure manufacturability.