Conventional Costas Loop for QPSK

Abstract

The operating principle of the conventional Costas loop for QPSK is explained (other types of Costas loops for QPSK are discussed in Chaps. 6 and 9). Dynamic behavior of the loop is described using a novel mathematical model developed by the author. This new model allows the designer of a Costas loop to explicitly compute important key parameters (lock range, lock time, pull-in range, pull-in time) as a function of block parameters such as corner frequencies (of filters), gain parameters like phase detector gain and VCO gain. Using these equations the designer of a Costas loop can taylor his system in order to meet desired key parameters, e.g., pull-in range. A case study is presented thereafter for the design of a digital Costas loop for QPSK. This case study guides a designer step by step through the entire design process. Finally a Simulink model for this type of Costas loop is presented. This model allows the designer to simulate a given Costas loop design with user-specified parameters such as carrier frequency, symbol rate, frequency error. All relevant signals within the loop can be viewed on scopes.