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New isolation circuits and design equations of compact impedance-transforming 3-dB baluns are suggested for theoretically perfect isolation and perfect matching at all ports. Any balun consists of two impedance transformers, being 180° out of phase, and an isolation circuit. For compactness, the impedance transformers need to be reduced and the isolation circuits should depend on phase delay of the compact impedance transformers. The compact balun with -90° phase delay of the compact impedance transformer is called the compact II-type balun and the one with non -90° phase delay is called the constant voltage-standing-wave-ratio type transmission-line impedance transformer (CVT) balun. Three isolation circuits are derived for the compact II-type baluns and five for the CVT baluns. Using the isolation circuits derived, the two types of compact baluns are fabricated and measured at a design center frequency of 1.5 GHz. The measured results have good agreement with prediction, showing power divisions of -2.9 and -3.3 dB (- 2.8 and -3.25 dB ), phase difference between two output signals of 181.8°(178.5°) , matching performance of -21.8, -31.8, and -33.8 dB ( -24, -22, and - 28 dB), and isolation of better than 40 dB (27 dB) for the compact II-type (CVT) balun.