An analytical threshold criterion in approximation has been developed for the basic phase-locked loop demodulator utilizing quasi-linearization technique. The analysis is based on assumptions that the loop is excited by an input FM signal and additive white Gaussian noise. This paper defines the threshold criterion by the characteristics of maximum demodulating sensitivity limit. Finally, the effects of the modulation indeces and loop parameters on the threshold characteristics are discussed from a theoretical and practical point of view. / Master of Science