ITC/USA 2005 Conference Proceedings / The Forty-First Annual International Telemetering Conference and Technical Exhibition / October 24-27, 2005 / Riviera Hotel & Convention Center, Las Vegas, Nevada / The four-quadrant frequency discriminator (FQFD) plays an important role in GPS receivers for carrier synchronization. This paper presents a detailed study of the operating principle of the FQFD, and the acquisition performance degradation due to the gain fluctuation of the FQFD is discussed. A modified FQFD called the enveloped-four-quadrant frequency discriminator (Enveloped-FQFD) is proposed, which introduces an envelope calculator on the basis of the FQFD. Performance comparison of the FQFD and the Enveloped-FQFD is given through theoretical analysis and computer simulation. Simulation results show that by employing the Enveloped-FQFD, a quicker pull-in process and a wider threshold than the FQFD can be achieved, while the additional hardware costs are trivial.