A multi-energy soft x-ray diagnostic is planned to operate in the small aspect ratio tokamak (SMART), consisting of five cameras: one for core measurements, two for edge, and two for divertors. Each camera is equipped with four absolute extreme ultra-violet diodes, with three of them filtered by Ti and Al foils for C and O line emissions, respectively, and Be foils for temperature measurements. In addition, two spectrometers will be installed with a vertical line of sight for impurity control. This study introduces a synthetic model designed to characterize radiated power and soft x-ray emissions. The developed code extracts the radiated power and Zeff values by leveraging distributions of electron density, temperatures, and impurity concentrations. The investigation is centered on the predicted scenarios of SMART's first phase of operation (Ip = 100kA; Bt = 0.1T), employing a double-null configuration with positive and negative triangularity. The anticipated impurities encompass C (1%) and Fe (0.01%) from the vessel, as well as O and N (0.1%) from air and water. For simplicity, the distribution is assumed to be homogeneous within the plasma, considering different mixtures with Zeff values ranging between 1 and 2. Finally, the model estimates signal strength for the diagnostic design, proving its feasibility.