Synaptic devices that mimic biological neurons have attracted much attention for brain-inspired neuromorphic computing. Especially, synaptic thin-film transistors (TFTs) have emerged with simultaneous signal processing and information storage advantages. However, the analysis of excitatory postsynaptic current (EPSC) relies on an empirical model such as a serial RC circuit, which limits a systematic and in-depth study of synaptic devices in terms of material and electrical properties. Herein, the single-pulse-driven synaptic EPSC (SPSE) model, including capacitive effect and information of the synaptic window, is analytically proposed. The SPSE model can simulate EPSC of synaptic devices at given TFT-operating conditions. EPSC with the SPSE model can be characterized with quantified parameters for the capacitive effects and the synaptic windows, which also depend on the electrical condition applied to TFTs. Various kinds of synaptic-TFTs with different gate insulators (e.g., SiO2 and ion-gel) are used to confirm the performance of the SPSE model. For example, the SPSE model can capture the long-term robustness of ion-gel-based TFTs with specific quantified parameters. In addition, the SPSE model enables the estimation of energy consumption, which can potentially be leveraged to compare the energy cost of EPSC fairly. The SPSE model can provide a guideline to understand the physical properties of synaptic TFTs.