Supernova remnants (SNRs) represent a powerful laboratory to study the Cosmic-Ray acceleration processes at the shocks, and their relation to the properties of the circumstellar medium. With the aim of studying the high-frequency radio emission and investigating the energy distribution of accelerated electrons and the magnetic field conditions, we performed single-dish observations of the large and complex Cygnus Loop SNR from 7.0 to 24.8 GHz with the Medicina and the Sardinia Radio Telescope, focusing on the northern filament (NGC 6992) and the southern shell. Both regions show a spectrum well fitted by a power-law function ($Spropto u^{-alpha}$), with spectral index $alpha=0.45pm0.05$ for NGC 6992 and $alpha=0.49pm0.01$ for the southern shell and without any indication of a spectral break. The spectra are significantly flatter than the whole Cygnus Loop spectrum ($alpha=0.54pm0.01$), suggesting a departure from the plain shock acceleration mechanisms, which for NGC 6992 could be related to the ongoing transition towards a radiative shock. We model the integrated spectrum of the whole SNR considering the evolution of the maximum energy and magnetic field amplification. Through the radio spectral parameters, we infer a magnetic field at the shock of 10 $mu$G. This value is compatible with a pure adiabatic compression of the interstellar magnetic field, suggesting that the amplification process is currently inefficient.
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