Design Equations for Lumped Element Balun With Inherent Complex Impedance Transformation

This paper demonstrates a novel lumped design approach for complex impedance transformation, based on symmetry relaxation in the out-of-phase-compensated power splitter. In the modified topology, a total of four component values are used, of which two values analytically depend upon the other two, keeping the balance parameter maximally flat and independent of the source and load impedance, as well as of the balun internal components. From the condition of zero input reflection loss, the two other component values are also determined analytically, hence specifying all component values uniquely. A Monte Carlo sensitivity analysis predicts an amplitude imbalance, which in practice defines the limit in balance operational bandwidth, of better than ±1 dB, over a 20% bandwidth at 925 MHz operating frequency. Based on the design equations, demonstrators for four different design cases are fabricated, verifying the simulated performance.