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This paper proposes a new balun that is composed of three coupled quarter-wavelength lines. The proposed balun is optimized by using design of experiments to achieve a maximum bandwidth. After the optimization, it is transformed into the balun consisting of a pair of coupled quarter-wavelength lines in connection with an uncoupled quarter-wavelength line. The design method and its implemented results using a multilayer configuration are presented. It is shown that this new balun can be made more compact, providing good performances over the wide frequency range. Therefore, the balun developed here is applicable to many wireless and mobile communication systems. The design equation for a given set of balun impedances at unbalanced and balanced ports is derived from an equivalent circuit of the proposed balun. To demonstrate the feasibility and validity of the design equation, the size 2012 multilayer ceramic chip baluns with three different balun impedances, which operated in the 2.4-GHz industrial-scientific-medical band frequency, are designed and fabricated by the use of low-temperature co-fired ceramic technology. According to the measured results, the maximum insertion loss is 0.81 dB, the maximum in-band phase imbalance is within 7°, and the maximum in-band amplitude imbalance is less than 0.7 dB.