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A novel method is presented for the design of a multiband power divider. The method employs network theory and even-odd-mode analysis to derive the equivalent input and output port admittances of a three-port junction, which is based on the conditions of reciprocity, isolation, and matching. If an impedance transformer that transforms the equivalent admittance to normalized unit conductance at multiple frequencies is found, then the multiband power divider can be constructed by attaching the transformer to each port of the junction. To verify the proposed design method, three different tri-band power dividers are designed and simulated, of which one is fabricated and measured. The measured results are in good agreement with the simulations. The return loss and isolation are better than 15 dB, simultaneously, the measured bandwidths of three operating bands are over 100 MHz, and the passband ripple is 0.2 dB.