The application of the frequency detector method for measuring the phase noise spectrum of semiconductor lasers has been experimentally demonstrated. The frequency detector is based on an unbalanced Mach-Zehnder interferometer and a photodetector. Analytical relations are obtained that allow one to choose the parameters of the Mach-Zehnder interferometer and perform experimental calibration of the measuring system. A technique is proposed for measuring the spectral components of the phase noise of lasers in the presence of a slow drift of the delay in fiber-optic lines and the frequency of the laser under study. The results of measuring the phase noise of a low-noise DX-1 laser module and high-noise laser diodes LSDLD155 (DFB) and LSFLD155 (FP) are presented. A strong correlation between the amplitude and phase noise levels of these lasers is found. The decisive influence of the noise of LSDLD155 and LSFLD155 lasers on the level of phase noise of optoelectronic (OE) microwave generators built using them is shown. It has been suggested that the low-noise laser module DX-1, which has a phase noise level 20-60 dB lower (in different parts of the spectrum), is not decisive in the level of phase and amplitude noise of an optoelectronic microwave generator. The investigated OE generator was built during the research in this work. The generator has low phase noise: -120 dBc/Hz at a frequency detuning of 10 kHz. Oscillation frequency 6.8 GHz; fiber optic delay line length 200 m.