Reconfigurable Intelligent Surface (RIS) is a promising technology that may effectively improve the quality of signals in wireless communications. In practice, however, the ``double fading'' effect undermines the application of RIS and constitutes a significant challenge to its commercialization. To address this problem, we present a novel 2-bit programmable amplifying transmissive RIS with a power amplification function to enhance the transmission of electromagnetic signals. The transmissive function is achieved through a pair of radiation patches located on the upper and lower surfaces, respectively, while a microstrip line connects two patches. A power amplifier, SP4T switch, and directional coupler provide signal amplification and a 2-bit phase shift. To characterize the signal enhancement of active transmissive RIS, we propose a dual radar cross section (RCS)-based path loss model to predict the power of the received signal for active transmissive RIS-aided wireless communication systems. Simulation and experimental results verify the reliability of the RIS design, and the proposed path loss model is validated by measurements. Compared with the traditional passive RIS, the signal power gain in this design achieves 11.9 dB.