New Design Formulas for Asymmetric Coupled-Section Marchand Balun

Design formulas for the asymmetric coupled-section Marchand balun are derived. The characteristic impedance, port impedance and electrical length of asymmetrical coupled transmission lines across two layers comprise the design formulas for designing the Marchand balun. A Marchand balun is realized based on the deduced design formulas using two identical asymmetrical coupled transmission lines fabricated across two layers. The conventional approach for designing the Marchand balun exploits the coupling coefficients of coupled transmission lines, and then provides ranges for their characteristic impedances which may but lead to inaccurate design. More accurate design method is established using the design formulas derived without using the coupling coefficients of coupled transmission lines. One example to verify the derived design formulas is taken and fabricated, showing measurement results of bandwidth from 0.62 to 1.44 GHz with the return loss of more than 10 dB, where $S_{21}$ and $S_{31}$ show better than $-4~{\rm dB}$ . Over these frequencies the measurement results show the phase and amplitude imbalances of $\pm 2^{\circ}$ and 0.2 dB, respectively.