The delay-lock loop (DLL) is a statistically optimum device for tracking the delay difference between two correlated waveforms. In this thesis an extended n-$\triangle$(n=1,2,3,...) DLL is proposed, and its baseband performance including the frequence of skipping cycles is analyzed. The present DLL system employs a correlator and pseudo-noise sequence synthesizer that have been improved from the previously used ones. The shape of the correlator charateristic has the form of expanded S-curve. Despite of increased noise, this extended DLL has desirable characteristics in tracking range and initial synchronization time. Comparing a 3-$\triangle$ DLL with a 1-$\triangle$ DLL, the former gives three times faster initial synchronization time with the serial synchronization method, and gives two times immunity against doppler shift.