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This paper presents a radiofrequency (RF) energy harvesting system based on an ultrawideband Archimedean spiral antenna and a half-wave Cockcroft-Walton multiplier circuit. The antenna was proved to operate from 350 MHz to 16 GHz with an outstanding performance. With its use, radio spectrum measurements were carried out at the Telecommunication Engineering School (Universidad Politécnica de Madrid) to determine the power level of the ambient signals in two different scenarios: indoors and outdoors. Based on these measurements, a Cockcroft-Walton multiplier and a lumped element matching network are designed to operate at 800 MHz and 900 MHz frequency bands. To correct the frequency displacement in the circuit, a circuit model is presented that takes into account the different parasitic elements of the components and the PCB. With an input power of 0 dBm, the manufactured circuit shows a rectifying efficiency of 30%. Finally, a test is carried out with the full RF energy harvesting system to check its correct operation. Thus, the RF system is placed in front of a transmitting Vivaldi antenna at a distance of 50 cm. The storage capacitor has a charge of over 1.25 V, which is enough to run a temperature sensor placed as the load to be supplied. This demonstrates the validity of the RF energy harvesting system for low-power practical applications., This research was funded in part by the project TIN2016-75097-P of the Spanish Research and Development National Program, and in part by the project TEC2017-85529-C3-1-R of the Ministerio de Economía y Empresa.