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This paper presents the design of an integrated rat-race coupler for balun applications based on high quality factor Slow-wave CoPlanar Waveguides (S-CPW) transmission lines in millimeter wave frequencies. The 28 nm CMOS advanced digital technology by STMicroelectronics is used. The design procedure is detailed. Phase-inverter and optimized criteria for the transmission lines characteristics are used to minimize insertion losses and surface on the die. A 3D full wave EM software coupled to a circuit simulator is used to optimize the various building blocs. The compact and low-loss rat-race coupler shows state-of-art very exciting and promising performances. It occupies a 0.086 mm2 area. From 52 GHz till 67 GHz, return loss is better than 15 dB, while coupling factors are identical, varying between -4.2 and -4.4 dB, that means 1.4 dB maximal insertion loss. Finally between 13 and 85.5 GHz, the phase difference is kept constant, equal to 180°±1° while the isolation is better than 44 dB.