General design equations for arbitrary odd-way filtering Bagley polygon power divider with notch band

The general design equations are derived for arbitrary odd-way Bagley polygon power divider (BPPD) with filtering response and notch band. Firstly, conditions are derived to achieve a perfect input port impedance matching at centre frequency. Then, the formulas of introduced transmission zeros (TZs) are obtained for high-frequency selectivity, wide upper stopband and notch band. Based on the deduced equations, wideband BPPD (WBPPD), filtering BPPD (FBPPD) and FBPPD integrating notch band (FBPPD-N) with arbitrary odd-way power splitting are designed. Finally, a FBPPD-N with a wide passband bandwidth is fabricated and measured to verify the presented ideal. The experimental results indicate that the proposed FBPPD-N has compact size, high-frequency selectivity, wide upper stopband and required notch band. Consequently, the presented general design equations can provide effective guidance for the design of arbitrary odd-way power splitting FBPPD-N.