We report on a low-noise diode laser oscillator at 972 nm actively stabilized to an ultrastable vibrationally and thermally compensated reference cavity. To increase the fraction of laser power in the carrier we designed a 20 cm long external cavity diode laser with an intracavity electro-optical modulator. The fractional power in the carrier reaches 99.9%, which corresponds to an rms phase noise of φ(rms)2=1 mrad2 in 10 MHz bandwidth. Using this oscillator, we recorded 1S-2S spectra in atomic hydrogen and have not observed any significant loss of the excitation efficiency due to phase noise multiplication in the three consecutive two-photon processes.