Abstract-Microwave-to-dc rectification is valuable in many applications including rf energy recovery, dc-dc conversion, and wireless power transfer. In such applications, it is desired for the microwave rectifier system to provide a constant rf input impedance. Consequently, variation in rectifier input impedance over varying incident power levels can hurt system performance. To address this challenge, we introduce multi-way transmissionline resistance compression networks (TLRCNs) for maintaining near-constant input impedance in rf-to-dc rectifier systems. A development of TLRCNs is presented, along with their application to rf-to-dc conversion and wireless power transfer. We derive analytical expressions for the behavior of TLRCNs, and describe two design methodologies applicable to both single and multi-stage implementations. A 2.45-GHz 4-way TLRCN network is implemented and applied to create a 4-Watt resistancecompressed rectifier system that has narrow-range resistive input characteristics over a 10-dB power range. It is demonstrated to improve the impedance match to mostly-resistive but variable input impedance class-E rectifiers over a 10-dB power range. The resulting TLRCN plus rectifier system has >50% rf-to-dc conversion efficiency over a >10-dB input power range at 2.45 GHz (peak efficiency 70%), and SWR <1.1 over a 7.7-dB range, despite a non-negligible reactive component in the rectifier loads.

This work presents a development of multi-way transmission-line resistance compression networks (TLRCNs) and their application to rf-to-dc conversion. We derive analytical expressions for the behavior of TLRCNs, and describe two design methodologies applicable to both single-and multi-stage imple mentations. A 2.45-GHz 4-way TLRCN network is implemented and applied to create a resistance-compressed rectifier system that has narrow-range resistive input characteristics over a 10-dB power range. It is demonstrated to improve the impedance match to mostly-resistive but variable input impedance class-E rectifiers over a 10-dB power range. The resulting TLRCN plus rectifier system has >50% rf-to-dc conversion efficiency over a > 10-dB input power range at 2.45 GHz (peak efficiency 70%), and SWR <1.1 over a 7.7-dB range.Index Terms-transmission lines, impedance matching, match ing networks, resonant rectifiers, rectennas, wireless power trans fer I. INTRODUC TIONIn numerous applications it is desirable to implement mi crowave rectification to capture rf energy and convert it to dc power. Such applications include energy recovery from terminations such as isolation ports [1], dc-dc conversion [2], and wireless power transfer [3]. In many such applications, it is desirable for the rf impedance at the rectifier input to appear constant and resistive across power level (e.g., such that impedance matching or isolation can be maintained, reflected power can be minimized, etc.). In this paper, we focus on a means for maintaining near-constant input impedance in microwave-to-dc rectifier systems. This can be a challenge because at different incident power levels, the input impedance to an rf rectifier typically varies [1], [2], [4].We explore the use of resistance compression networks (RCNs) to interface between an rf input and a plurality of rectifiers, minimizing the effective input impedance variation and acting as an impedance transformation stage. RCNs pro vide reduced impedance variation at the rf input (as com pared to the rectifier inputs), and in discrete implementations have been applied to dc-dc resonant converters [4] and in isolation-port energy recovery in outphasing systems [1]. At microwave frequencies, however, such discrete RCN networks have limitations relating to the component non-idealities and interconnect parasitics. Recently, initial work has explored the use of transmission-line resistance compression networks (TLRCNs) which are based on transmission-line sections and are suitable for microwave frequencies. A two-way TLRCN based on a pair of transmission-line sections (asymmetric about a 90-degree base length) was proposed in [5], [6] for energy recovery in outphasing power amplifiers. transformation : resistance compression : rectifier I I I z· 1 I loads I In, I I � ebase + ll.e 1 1 RL Zin,2 : I L I ebaBe + ll.e2 Zin,3 : L ZT,Aj4 I Z2 Fig. 1. Four-wa y TLRCN with quarter-wave impedance transformation stage. Each pair of transmission line lengths can be expressed in terms of a base line length plus ...