In RF broadcasting systems, analogue circuit non-idealities are sources of serious performance degradation. In this talk, we focus on systems that employ Orthogonal Frequency Division Multiplexing (OFDM) modulation. We discuss the use of advanced engineering mathematics to address two important issues. Firstly, the behaviour of such systems in memoryless nonlinearities and secondly, the near-carrier spectrum of RF oscillators. The latter is essential in estimating inter-carrier interference in OFDM. Nonlinearities generate a large number of intermodulation products in multi-carrier systems such as OFDM. The issue of their calculation is tackled with combinatorial analysis, leading to accurate closed form SNR expressions in the case of single or multiple OFDM channels. Although the methodology is presented only for third order nonlinearities, it can easily be extended to cover higher order nonlinear phenomena. An important gain in following this approach is that a straightforward mapping between circuit characteristics and OFDM performance is obtained. Next, we apply correlation theory methods to predict the near-carrier power spectral density (PSD) of an RF oscillator with phase noise. Based on the measurement-driven representation of phase noise as a sum of power-law processes, we evaluate closed form expressions for the relevant oscillator autocorrelation functions. These expressions form the basis of an enhanced oscillator spectral model that has a Gaussian PSD at near-carrier frequencies followed by a sequence of power-law regions.