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The microwave signal at the output of a photodiode that detects a modulated optical beam contains the phase noise α(t) and amplitude noise α(t) of the detector. Beside the white noise, which is well understood, the spectral densities Sψ(f) and Sα(f) show flicker noise proportional to 1/f. We report on the measurement of the phase and amplitude noise of high-speed p-i-n photodiodes. The main result is that the flicker coefficient of the samples is ∼10-12 rad2/Hz (-120 dBrad2/Hz) for phase noise, and ∼10-12 Hz-1 (-120 dB) for amplitude noise. These values could be observed only after solving a number of experimental problems and in a protected environment. By contrast, in ordinary conditions, insufficient electromagnetic interference isolation, and also insufficient mechanical isolation, are responsible for additional noise to be taken in. This suggests that if package and electromagnetic compatibility are revisited, applications can take the full benefit from the surprisingly low noise of the p-i-n photodiodes.