Frequency Measurement Errors of Passive Resonators Caused by Frequency-Modulated Exciting Signals

Abstract
The condition of resonance for a signal with FM is defined in this paper as the condition of maximum power transfer by the resonant device. It is shown that if the width of the signal spectrum is small compared to the resonator's linewidth, then the frequency error is proportional to the third moment of the instantaneous signal frequency about its mean. One expects that this treatment should, at least, give the leading term for a precise treatment of atomic resonances. Experimental results with a cesium beam frequency standard confirm this expectation and add caution to the idea that higher Q atomic resonances make better absolute frequency standards.