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 unconformities 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 (FD), 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 core: ferrite and Teflon. For this purpose, FDs were induced in an oil-filled transformer. The sensibility 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 sensibility by 50 times. Although the Teflon core showed low sensibility, its frequency band was concentrated between 5 MHz to 10 MHz, while ferrite presents a frequency response from 0 to 1 MHz. Therefore, Teflon-based Rogowski’s coils can be a promising alternative to low-cost monitoring systems.