<p>Interdigitated photoconductive antennas (IPCAs) have emerged as advantageous structures for terahertz (THz) radiations. While equivalent circuit models (ECM) are widely used for performances analysis, existing models often overlook critical physical parameters such as displacement current and antenna reactance, and often assume frequency-independent impedance. In this work, we propose a comprehensive and physically consistent modeling approach that considers complex frequency-dependent antenna impedance through full-wave simulation, and involves the displacement current. These inclusions yield a second-order differential equation with complex solutions for the gap voltage. The developed model is validated through simulations under various impedance cases, providing insight into the IPCAs physical behavior. We also demonstrate the evaluation of key antenna parameters such as THz power and conversion efficiency as functions of laser power and operating frequency, offering a more accurate optimization framework tailored to specific THz applications. Finally, a comparative analysis between the proposed and traditional models is carried out on a designed IPCA with 20 fingers, revealing considerable discrepancies, especially for the frequencies where the antenna impedance is predominantly reactive, and the results illustrate an over estimation of the radiated mean power, and the optical-to-THz conversion efficiency by more than 3 mW, and 0.1% respectively, corresponding to a ratio of 3.5, and 4.3 to the estimated values based on the proposed model, which justifies the need for the enhanced model presented in this study.</p>