1 Introduction
The fundamental architecture of a radio frequency identification (RFID) system comprises two main components: the reader and the electronic tag. RFID systems are categorized into passive, semi-passive, and active types based on how the tags are powered during operation. A passive electronic tag does not have its own power source and relies entirely on the energy from the reader’s electromagnetic field. Typically, such tags consist of a chip, an antenna, and a substrate. These tags are often affixed to the surface of objects or embedded within them, depending on the application needs. To meet various functional demands, miniaturization and shape adaptation have become key aspects in the design of passive RFID tags. Since the form of the tag is largely determined by the antenna structure, the performance of the tag chip is heavily influenced by the antenna's design.
For a passive tag to function properly, the power received by the chip must exceed its minimum operational threshold, known as sensitivity. Therefore, optimizing the antenna to achieve maximum power transfer to the chip under a given reader field strength is crucial. Literature [1] has extensively reviewed such techniques, emphasizing impedance matching between the antenna and the chip. This can be achieved through various methods, such as using lumped elements, dielectric materials, short-circuiting, or modifying the antenna’s geometry. In fact, these techniques share similarities with fractal-based designs, which leverage self-similarity and space-filling properties to enhance performance while reducing size.
Fractal theory was introduced by Mandelbrot in 1975. Fractal structures exhibit self-similarity and space-filling characteristics, making them ideal for antenna design. By applying these properties, it is possible to achieve smaller antennas with broader bandwidths. Based on this concept, this paper presents a passive RFID tag antenna designed using a Hilbert fractal structure, and investigates the effects of the substrate’s dielectric constant and thickness on the antenna’s performance.
2 Hilbert Fractal Iteration Principle
The Hilbert fractal exhibits a form of self-similarity where each iteration increases complexity while maintaining proportional scaling. The 0th-order Hilbert curve is a square-shaped "half-ring" with side length b. In the first iteration, each edge is replaced with a 0th-order structure, forming a new "half-ring" with side length a, where a/6 represents the scale factor. As shown in Figure 1, the contour area remains constant across iterations, and the number of endpoints always stays at two.
The total length of the nth-order Hilbert curve can be calculated using the formula: L = 3b × 2^n - 1. For example, when n=0, L=3b; n=1, L=5b; n=2, L=9b; n=3, L=17b. Studies by Vinoy et al. [2,3] explored the use of Hilbert curves in compact resonant antennas, showing that their performance can reach λ/10, similar to a λ/2 dipole. Zhu [4] examined the impact of feed point location on the input impedance of Hilbert fractal antennas, finding that eccentric feeding allows for better 50 Ω matching.
3 Study on the Influence of Dielectric Constant and Thickness of Antenna Substrate on Antenna Performance
In real-world applications, RFID tags are typically encapsulated, and factors such as the antenna’s dimensions, the dielectric constant and thickness of the substrate, and the surrounding packaging material significantly affect the antenna’s performance. Thus, these factors must be carefully considered during the design process.
Figure 2 shows a 2nd-order Hilbert fractal antenna design with a scale factor of a/b = 4/11, dimensions of 50 mm × 24 mm, and a line width of 1 mm. The layout follows a symmetric dipole configuration. The tag chip used operates at 915 MHz, with an external impedance of ZL = 18.1 - j149 Ω. Without considering the dielectric effect, the simulation results are presented in Figure 3.
As seen in Figure 3, the antenna resonates at 0.93 GHz and 1.87 GHz. The radiation patterns (E-plane) at both frequencies are analyzed, yielding the results in Figures 4 and 5. At the first resonance frequency, the pattern resembles that of a dipole, with omnidirectional radiation. At the second frequency, the pattern shows a 90° twist. Considering the size at the first resonance, the antenna measures 100 mm, compared to approximately 160 mm for a standard dipole, indicating a 37.5% reduction in size.
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