Synthesis of an N-way arbitrary power divider

A method for synthesizing an N-way arbitrary split power divider is presented, based on parallel re-proportioning of the output ports of an M-way equal split power divider. The results of this synthesis can be related to those obtained in other analyses of the power divider. Applying the synthesis concept, the general equations for the input and output reflection coefficients and the transmission coefficients of the N-way arbitrary divider are derived. They are shown to be dependent on M and the output power ratio, but not dependent on N. Further, the input reflection coefficient of the N-way arbitrary split power divider is found to be the same as that of the underlying M-way equal split power divider. Examples show how the derived equations can be used to design a divider for optimal bandwidth.