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