A simulation guided analytical approach to the theory of the Dick effect [frequency standard]

A pulse-mode operated frequency standard is considered, based on the Ramsey double interaction method. Phase noise of the interrogating signal appears as “end-to-end phase difference”, thereby introducing frequency noise in the loop. Pulsed operation of the standard down-converts by aliasing the phase noise around harmonics of the pulse rate. The analysis offered in this paper is based on phase noise power spectral densities Sφ(f). A model of the frequency control servo system is proposed, in which the input signal is the (known) local oscillator (LO) phase noise Sφ(f) and the output signal is the (unknown) phase noise Sφ(f) of the standard in closed loop operation. The level of excess white frequency noise added by aliasing on the stabilized LO through the Dick effect can be related analytically to the characteristics of the free LO phase noise. From this, the stability limitation (with slope τ^-1/2) typical of the Dick effect can then be obtained by the usual conversion formulas based on the power law model