Science and industry have sought to develop systems aiming to avoid total failures in power transformers since these machines can be working under overloads, moisture, mechanical and thermal stresses, among others. These non-conformities can promote the degradation of the insulation system and lead the transformer to total failure. In the incipient stages of these faults, it is common to detect Full Discharges (FDs), which are short circuits between degraded coils. Therefore, several techniques were developed to perform FD diagnosis using UHF, acoustics, and current sensors. In this scenario, this article presents a mathematical model for Rogowski coils and compares two different types of cores: Ferrite and Teflon. For this purpose, FDs were induced in an oil-filled transformer. The sensitivity and frequency response of the Rogowski coils were compared. This analysis was achieved using the Power Spectrum Density (PSD) and the energy of the acquired signals. Additionally, the Short-Time Fourier Transform (STFT) was applied to detect repetitive discharges. The results indicated that the Ferrite core increases the sensitivity by 50 times in the frequency band between 0 and 1 MHz. However, the Teflon core showed higher sensitivity between 5 and 10 MHz.