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In this paper, a novel L network (LN) is presented, which is composed of a frequency-selected section (FSS) and a middle stub (MS). Based on the proposed LN, a tri-band T-junction power divider (TTPD) with impedance transformation and independent power division ratios is designed. Moreover, the closed-form design theory of the TTPD is derived based on the transmission line theory and circuit theory. Finally, a microstrip prototype of the TTPD is simulated, fabricated, and measured. The design is for three arbitrarily chosen frequencies, 1 GHz, 1.6 GHz, and 2.35 GHz with the independent power division ratios of 0.5, 0.7, and 0.9. The measured results show that the fabricated prototype is consistent with the simulation, which demonstrates the effectiveness of this proposed design.