  Rigorous nonlinear analysis of the physical model of Costas loop --- a
classic phase-locked loop (PLL) based circuit for carrier recovery, is a
challenging task. Thus for its analysis, simplified mathematical models and
numerical simulation are widely used. In this work a short survey on nonlinear
models of the BPSK Costas loop, used for pre-design and post-design analysis,
is presented. Their rigorous derivation and limitations of classic analysis are
discussed. It is shown that the use of simplified mathematical models, and the
application of non rigorous methods of analysis (e.g., simulation and
linearization) may lead to wrong conclusions concerning the performance of the
Costas loop physical model.
