A miniaturized rat-race coupler with arbitrary power division ratio is proposed in this paper. The design formulas of the rat-race coupler with arbitrary power division ratio are derived using the even-odd decomposition analysis. The proposed structure demonstrates miniaturized size and perfect isolation due to adding phase inverter to the branch. For demonstration, a 20 dB rat-race coupler operating at 1 GHz with 81.34% size reduction is designed and fabricated. There is good agreement between measured and simulated results.
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