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When measuring the phase fluctuation between a pair of low-power microwave signals, the signals must be amplified before detection. In such cases, the phase noise of the amplifier pair is the main cause of 1/f background noise of the instrument. This article proposes a scheme that makes amplification possible while rejecting the close-in 1/f (flicker) noise of the two amplifiers. The noise rejection, which relies upon an understanding of the amplifier noise mechanism, does not require averaging. Therefore, our scheme can also be the detector of a closed-loop noise reduction system. The first prototype, compared to a traditional saturated mixer system under the same conditions, shows a 24 dB noise reduction in the 1/f region.