# High-Efficiency Triple-Band RF-to-DC Rectifier Primary Design for RF Energy-Harvesting Systems
## 2 Radio Frequency Energy-Harvesting Design
### Triple-Band Rectifier Design  
[PERSON] et al. [30] realized dual- and triple-band circuits by using one or more parallel shunt stubs. They proved that when impedance matching is required on more than one frequency bands, more circuit freedoms are necessary for the design. They obtained the extra triple- and quad-frequency bands from a dual-band design by applying a parallel combination of two stubs to provide the needed susceptances. Figure 6 illustrates the three basic topologies of two shunt combinations, open-open (Figure 6a), open-shorted (Figure 6b), and shorted-shorted (Figure 6c). Furthermore, [PERSON] et al. [31] designed a six-band rectifier with only three voltage-doubler circuits connected in series. The presented system had an excellent performance in various conditions, such as multiple frequency bands and a wide range of input power levels.  
The main idea of the proposed design is to add a tuning frequency to the dual-band impedance-matching network illustrated in Figure 5a without increasing the complexity of the derived triple-band system by adding an extra branch. Therefore, we proposed the triple-band impedance-matching network topology of Figure 5b, where a combination of shunt stubs is introduced to achieve the third resonating frequency. To design the triple-band rectifier, we utilized the genetic optimizer in the  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Width/Length** & **Parameter** & **Width/Length** \\ \hline TL1 & 3/35 & TL6 & 3/35 \\ TL2 & 3/4 & TL7 & 3/6 \\ TL3 & 3/29 & TL8 & 3/17 \\ TL4 & 1/3 & TL9 & 1/13 \\ TL5 & 48/21 & TL10 & 39/24 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical dimensions of the microstrip lines for the impedance-matching network of Figure 5a: dual-band circuit (width/length values are expressed in mm).  
Figure 5: Proposed impedance-matching circuits of the dual- and triple-band rectifying circuits at: (a) 869 MHz and 940 MHz (dual-band); (b) 866 MHz, 948 MHz, and 2.423 GHz (triple-band).  
software (ADS-C Keysight Technologies 2000-2021) by obtaining a feasible solution of the corresponding parameters, including the sizes (length, width) of the shunt stubs. It is worth mentioning that there is no unique winning strategy for the optimization due to the complexity of the system design. The application of these optimization techniques requires many tuning parameters. Genetic optimization techniques have proven to be effective for many complex optimization problems. The Genetic Algorithm (GA) optimization method is a procedure where a set of parameters, the chromosomes, can evolve to a new set of parameters [32]. The basic idea is that with each change in the parameter population, the performance improves, so the survival of the fittest is achieved. It is a five-step process: (1) representation, (2) evaluation, (3) reproduction, (4) breeding and crossover, and (5) mutation. Figure 7 demonstrates the genetic optimization algorithm. Having the previous dual-band design as a starting point, we applied the shunt stubs technique along with the genetic algorithm optimizer to obtain a feasible geometry for the impedance-matching network of the triple-band rectifier (Figure 5b). The stopping criterion was set to 1000 iterations, whereas the average computational time for each iteration was about 3 min. Table 2 lists the optimized physical parameters of the transmission lines for the triple-band rectifier design of Figure 5b.