In this paper, a tri-band impedance transformer (TBIT) using a coupled line and a dual-band to tri-band transformer is proposed, which can transform frequency-dependent complex impedances to a real-value impedance. In order to explain how to determine circuit parameters, closed-form equations are derived in detail. Based on the TBIT, a compact T-junction power divider (TTPD) is designed. This TTPD works at three different frequencies with independent controllable power division ratios. Simple steps to design the TTPD are listed. To demonstrate the validity of the theory, this paper exhibits a prototype operating at 2, 4.4, and 5 GHz with different power division ratios. Moreover, the simulated and measured results prove that this TTPD has the features of tri-band operation, independent controllable power division ratios, enhanced bandwidths, and small size. INDEX TERMS Independent controllable power division ratios, tri-band, impedance transformer, power divider.