Acquisition Time of Tracking Loops Operating in the Frequency-Search Mode

This paper presents a theory for computing the signal acquisition time of a second-order tracing system operating in the frequency-search mode. In particular, a closed-form expression is obtained which relates the acquisition time to the relevant system parameters, to the initial loop detuning, and to the slope of the ramp that sweeps the voltage-controlled oscillator. Although the theory is only approximate and the resulting formula is exact only in the limit when the initial loop detuning ΔF goes to infinity, it has been found that it gives quite accurate results as soon as ΔF is some times greater than the equivalent noise bandwidth of the loop.