In multi-carrier satellite communication systems, many modulated carriers have to be co-amplified through a TWTA (Traveling Wave Tube Amplifier). In such a case, the intermodulation due to the TWTA nonlinearities i.e., AM/AM and AM/PM conversions degrades that system performance. This paper analyzes the combined effects of the AM/AM and AM/PM conversions on the output properties of the TWTA using a quadrature nonlinear model. A general formula of the output autocorrelation function is derived as a function of the input autocorrelation function with an arbitrary input power spectrum. Based on this formula, the effects of the TWTA nonlinearities (both AM/AM and AM/PM conversions) on the output characteristics such as the output signal and intermodulation power, the intermodulation power spectral distribution, and the output signal-to-intermodulation ratio (SIMR) are theoretically evaluated.