When Bessel Meets Fourier in the Power Representation of Energy Harvesting Rectennas

In this contribution, we develop a closed-form representation for the output DC power of a typical energy harvesting rectenna in terms of the input waveform. Taking into account the non-linearity of the rectifier, with operation in a spectrum band composed of $N$ channels, we present a compact general formula which relates the output DC power to the magnitude of the exponential Fourier-series coefficients of the periodic input signal, through summation of products of modified Bessel functions with different orders. In this way, one can easily compute the output power of the harvesting circuit by looking at the spectrum of the input signal. A tractable lower-bound for the output DC power is also proposed, and comparative results are provided.