Simultaneous wireless information and power transfer (SWIPT) is a promising technique to prolong the lifetime of energy constrained relay-based systems. Most of the existing literature on relaybased SWIPT systems incorporate linear energy harvesting (EH) model. This paper incorporates a nonlinear EH model into the full-duplex (FD) amplify-and-forward (AF) relay-based system for the first time in the literature. We consider a practical non-linear energy harvester model namely constant-linear-constant (CLC) EH model, which takes into account the sensitivity and saturation characteristics of the EH circuit. First, the end-to-end outage probability of the system is derived for the time-switching (TS) based relay protocol. To prevent the outage performance degradation, the outage throughput and energy efficiency (EE) of the system is maximized by optimizing the TS parameter. Since the formulated problems are convex in nature, the golden-section method is used to find the optimal TS solution. Numerical results reveal the significance of employing a non-linear EH model by demonstrating the difference of the proposed model from the traditional linear EH model system and importance of using full-duplex relay by showing large performance gain over half-duplex relay-based (HDR) system, in terms of outage probability, throughput, and EE.INDEX TERMS Amplify-and-forward (AF) relay, energy harvesting (EH), full-duplex (FD) system, outage probability.