Design and optimization of multi-band Wilkinson power divider

In this paper, a general and easy procedure for designing the symmetrical Wilkinson power divider that achieves equal-power split at N arbitrary frequencies is introduced. Each quarter-wave branch in the conventional Wilkinson divider is replaced by N sections of transmission lines, and the isolation between the output ports is achieved by using N resistors. The design parameters are the characteristic impedances and lengths of the N transmission line sections, and the N isolation resistors. The even-odd modes of analysis are used to derive the design equations. Closed-form expressions, which are suitable for CAD purposes, are derived for the dual-band divider. For N >= 3, closed-form expressions are not available, and therefore, the powerful particle swarm optimization method is used to obtain the design parameters. Examples of the dual-, triple-, and quad-band dividers are presented to validate the proposed design procedure, and the results are compared, wherever possible, with published results using other methods.