Efficient RF energy harvesting is crucial for enabling self-powered wireless devices and Internet of Things (IoT) applications. This work presents a dual-band impedance-matching network with an integrated rectifier configuration operating at 2.45GHz (Wi-Fi and IoT) and 3.5GHz (5G mobile network), addressing the challenge of achieving simultaneous conjugate matching and maximum power transfer from the antenna to the rectifier circuit across multiple frequencies. We propose an inverted L-shaped matching network with series and shorted stubs for 2.45GHz matching, coupled with an additional series stub for 3.5GHz matching. The integrated voltage doubler rectifier, comprising Schottky diodes, filtering capacitors, and optimized load resistance, was simulated using an Advanced Design System (ADS) on an FR4 substrate with a dielectric constant of 4.3. The designed circuit exhibits a high conversion efficiency of 85.96% at -6dBm input power levels, making it suitable for low-power applications. This integrated approach facilitates efficient RF-to-DC power transfer from the antenna to the rectifier circuit across dual bands, paving the way for compact, efficient RF energy harvesting systems that contribute to the development of self-sustainable wireless sensor networks and enable a wide range of IoT applications in various domains, including environmental monitoring, healthcare, and industrial automation.