## 4 Results
#### 4.1.3 Influence of Substrate Materials on Antenna Behavior
* Efficiency vs. antenna substrate  
This subsection analyzes the relationship between antenna efficiency and substrate material type used in construction. Substrate properties--such as dielectric constant, loss tangent, and thickness--play a decisive role in determining the electromagnetic performance of antenna structures, directly impacting radiation efficiency. Through boxplot-based statistical analysis, the efficiency distributions associated with various substrate types are compared, allowing the identification of trends, material-dependent advantages, and potential trade-offs relevant to rectenna system design for energy harvesting. Comparison of radiation efficiency across different substrate materials, as shows in Figure 11, reveals distinct performance patterns that are critical to antenna design decisions in energy harvesting systems. FR4 substrates exhibit a median efficiency close to 60%, with a relatively wide distribution and noticeable low outliers. This suggests significant variability and the potential for suboptimal performance in certain configurations. However, FR4 remains a widely used and cost-effective material, making it suitable for general-purpose applications where affordability outweighs efficiency constraints. In contrast, RT Duroid demonstrates superior performance, with a median efficiency near 70% and minimal dispersion, reflecting high consistency and reduced energy losses. These properties make it particularly well suited for high-performance applications that demand stable operation and minimal power dissipation. Rogers substrates show a slightly lower median efficiency around 50%, combined with moderate variability. This balance positions Rogers as a viable option in scenarios where moderate performance and cost-effectiveness are equally valued. Non-conventional substrates display a wide efficiency range centered around 60%, highlighting their versatility but also indicating less predictable behavior. Such charac  
Figure 10: Boxplot showing area distribution of different substrates for energy harvesting. teristics make them attractive for exploratory or custom-tailored designs where design freedom is prioritized over performance uniformity. Textile substrates, on the other hand, exhibit the lowest median efficiency, approximately 40%, with a narrow distribution. While their performance is limited, their intrinsic properties--flexibility, light weight, and ease of integration--make them ideal for wearable applications where mechanical adaptability is more critical than high electromagnetic efficiency. Overall, findings emphasize how substrate selection directly influences antenna efficiency and, by extension, suitability for specific energy harvesting contexts. * Operation frequency vs. antenna substrate  
This subsection examines the relationship between operating frequency and the substrate materials used in antenna fabrication. Substrate dielectric properties--particularly relative permittivity and loss tangent--directly impact antenna resonant behavior, influencing achievable frequency range and operational stability. Through statistical analysis of frequency distributions across different substrate types, this section identifies how material selection affects the spectral characteristics of energy harvesting antennas, providing insight into trade-offs between electrical performance, material constraints, and application-specific frequency requirements. Analysis of operational frequency across different substrate materials, as shown in Figure 12, reveals clear behavioral patterns that influence the suitability of antennas for specific energy harvesting applications. FR4 substrates exhibit a median operating frequency of approximately 2 GHz, with a relatively narrow distribution and several high-frequency outliers exceeding 10 GHz. This suggests potential challenges in maintaining consistent performance at higher frequencies, despite the material's widespread use and accessibility.