New Design Formulas for Impedance-Transforming 3-dB Marchand Baluns

New design formulas for impedance-transforming 3-dB Marchand baluns are proposed. They are about the even- and odd-mode impedances of the coupled transmission-line sections of the Marchand baluns and determined by coupling coefficients together with termination impedances. The particular property proposed in this paper is to choose the coupling coefficient arbitrarily, resulting in infinite sets of design formulas available. This is quite different from the conventional design approach in which only one coupling coefficient is possible. For the perfect isolation of the Marchand balun, an isolation circuit (IC) is needed, being composed of two 90° transmission-line sections and resistance(s). Sufficient area to build such a long IC is, however, inherently not available. For this, ways to reduce the IC size are also suggested. To validate them, a microstrip Marchand balun terminated in 130 and 70 Ω is designed at a design center frequency of 1.5 GHz and tested. The measured results are in good agreement with prediction, showing that power divisions are 3.57 and 3.262 dB, return losses at all ports are better than 21 dB, and the isolation is better than 20 dB around the design center frequency. The measured phase difference between two balanced signals is 180°±2° in about 50% bandwidth.