Orthogonal Frequency Division Multiplexing (OFDM) systems are extremely sensitive to nonlinear distortions brought by the Power Amplifier (PA) because of the inherent high peak-to-average power ratio (PAPR) of the signal. In this paper, we analyze the impact of the non-linearities on the output signal, assuming that the transmitter is equipped with a linearization stage before the PA. Therefore, the expression of the Error Vector Magnitude (EVM) of the output signal is analytically derived with or without the use of the linearization process. We provide analytical expressions of the EVM in the form of a series expansion that depends on the transition factors of the PA and predistortion characteristics. Simulations results confirm the accuracy of our analytical expressions, even when limiting the series expansion to an order of 4.