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A general analysis and design procedure is developed for the asymmetrical multisection power divider with arbitrary power division ratio and arbitrary specifications of input and output impedance matching over any desired frequency bandwidth. The even- and odd-mode analysis, which was previously applied to the design of multisection Gysel power dividers, required that the unequal power division ratios be accompanied with appropriately proportional output impedances. This requirement is relaxed here. The equivalent circuits are first obtained for the divider and then their scattering parameters are determined. Some error functions are then constructed by the method of least squares. Their minimization determines the geometrical dimensions of the optimum divider. An approximate method based on the even and odd modes is developed for its initial design of the divider. Two examples of single- and double-section dividers are designed. Their frequency responses of isolation and transmission coefficients are obtained by the proposed method, HFSS software, fabrication, and measurement. They agree within the approximate assumptions. A two-section and two-way power divider is designed and fabricated by the proposed method for the case of unequal port impedances in the L-band. The measured isolation between the outputs is better than -22 dB in 44% of the band.