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This study presents an exact theoretical analysis of performance degradation in OFDM system when the signal including phase noise is passed through a dynamic non-linear circuit such as HPA. The HPA is modelled using a memory polynomial model. The theoretical analysis shows that the detected data symbol at the receiver include common phase error, intersubcarrier interference and intermodulation components. The analytical expressions for intermodulation term are derived using combinatorial methods. Using the derived expressions, a closed form SNR at the output, degradation factor and hence, the probability of error can be evaluated theoretically. The results show that when the OFDM signal with phase noise passes through dynamic non-linear circuit, the phase noise expansion occurs. This expansion is related to the memory length of non-linear device and causes higher degradation in OFDM signal. By use of this exact analysis, designers can choose optimum parameters and operating point of HPA for a desired performance of OFDM transceiver. This reduces energy consumption. To verify the accuracy of the analysis, a comparison between the theoretical and simulated results is presented. The comparison shows that the BER of analytical results closely matches with the simulation results of the OFDM system.