The quantum noise of the internally pumped ring optical parametric oscillator is analyzed theoretically. The fundamental field and subharmonics are assumed to be resonator modes, whereas the second harmonic can have an arbitrary detuning. The threshold for parametric oscillations in this system is derived in aplane-wave approximation. The noise spectra for the fundamental and subharmonics below the threshold are calculated via asemiclassical approach. It is demonstrated that the fundamental beam reflected from this OPO can be perfectly amplitude squeezed around multiples of the free spectrum range frequency. Such acavity is proposed for use as aquantum amplitude noise eater.