  Phase-locked loops (PLLs) are now widely used in communication systems and
have been a classic system for more than 60 years. Well-known mathematical
models of such systems are constructed in a number of approximations, so
questions about how they describe the experimental dynamics qualitatively and
quantitatively, and how the accuracy of the model description depends on the
behavior mode, remain open. One of the most direct approaches to the
verification of any model is its reconstruction from the time series obtained
in experiment. If it is possible to fit the model to experimental data and the
resulting parameter values are close to the expected values (calculated from
the first principles), the quantitative correspondence between the model and
the physical object is nearly proved. In this paper, for the first time, the
equations of the PLL model with a bandpass filter are reconstructed from the
experimental signals of the generator in various modes. The reconstruction
showed that the model known in the literature generally describes the
experimental dynamics in regular and chaotic regimes. The relative error of
parameter estimation is between 2% and 50% for different regimes and
parameters. The reconstructed nonlinear function of phase is not harmonic and
highly asymmetric in contrary to the model one.
