Ultimate performances of oscillators in time domain

Abstract

Assuming a noise free resonator the ultimate performances of an oscillator in time domain can be calculated. It shall be demonstrated that the ultimate time flicker level of an oscillator is only limited by two factors: the loaded Q of the resonator and the flicker noise level at 1 Hz of the amplifier phase noise. A chart can be drawn relating the three quantities /spl sigma//sub y/(/spl tau/), Q/sub loaded/ and /spl Lscr//sub ampli/(1 Hz). It is possible to see immediately that to obtain for example in time domain a flicker level of 5/spl times/10/sup -14/ using a resonator which exhibits a loaded Q coefficient of 6.5/spl times/10/sup 5/ we must use an amplifier with a flicker phase noise as low as /spl Lscr//sub amp/ (1 Hz)=-148 dBc/Hz. This performance level is hard to find in current amplifiers. Thus, it is of utmost importance to measure precisely the contributions of the amplifier to the noise in the oscillator loop. We introduce new system based on the injection principle giving an improvement of thirty dB versus the homodyne method and permitting measurements at -165 dB at 1 Hz for flicker noise and -190 dB for thermal noise. The advantages and ultimate performances of this new measurement system are described.