3-dB Power Dividers With Equal Complex Termination Impedances and Design Methods for Controlling Isolation Circuits

A 3-dB power divider (PD) terminated in equal complex impedances is presented. It consists of two identical 90
$^{\circ}$
transmission-line sections and an isolation circuit, being composed of resistance and capacitance, or resistance and inductance, depending on the termination impedances. If the termination impedance has capacitance, the isolation impedance should consist of inductance, and therefore, the isolation circuit should be implemented with a chip inductor. However, the chip inductor contains additional stray capacitance and resistance, which lead to undesired frequency performance. To avoid the usage of the chip inductors, even with arbitrary termination impedances, three design methods by adding transmission-line sections, adding open stubs, and adding short stubs are introduced. The PDs designed by the three methods can have not only desired isolation impedances, but also the total size of the PDs can be reduced. To verify the suggested theory, three PDs are measured. For one PD with adding transmission-line sections, the measured reflection coefficients at all ports are
$-$
43.29,
$-$
41.55, and
$-$
51.69 dB, the isolation is 56.7 dB, and the power division is
$-$
3.042 dB at a design center frequency of 1 GHz, which agree quite well with those predicted.