# Numerical Modeling, Analysis, and Optimization of RFID Tags Functioning at Low Frequencies
## 1 Introduction  
RFID tags are increasingly present in everyday applications, operating at frequencies ranging from low frequencies, like 125 kHz, to high values in the GHz range. RFID (radio frequency identification) systems have been massively developed in recent years due to their multiple applications in various fields. This form of wireless communication, data collection, and monitoring is used in all aspects of life, from animal tracking, access control, payments, and smart cards, e-health, to personal tracking, IoT, supply chains and logistics, smart cities, and data processing [1, 2]. This study is primarily focused on RFID in the low-frequency domain, aiming to determine more reliable and smaller structures that meet the need for integration.  
By analyzing the specialized literature in the field for the frequencies under consideration, it was determined that planar coil structures are the most widely used and suitable structures for low frequencies [3, 4, 5, 6, 7, 8], but these RFID structures are also used at high-frequency applications for frequency values such as 960 MHz [9], 2.4 GHz [10, 11], and even 5 GHz [11].  
Additionally, by reviewing the studies, it was concluded that these structures come in various sizes and shapes; therefore, the goal was to determine how geometric parametersinfluence the operation of the tags. The main shapes of the spiral coils of planar structures are square [12; 13; 14; 15], circular [14; 15; 16; 17], hexagonal [12; 18; 19], and octagonal [5].  
Planar structures are structures with lower dimensions and can be easily integrated into smaller devices, unlike structures such as the ones in [20; 21], thus leading to decreased dimensions of the devices in which they are used.  
A lot of studies have been conducted only to determine the inductance of planar inductors [22; 23; 24; 25]. In these studies, different methods to increase the inductivity and decrease the dimensions of the structures have been used, like differently shaped structures while keeping the width of the turns the same [4; 13; 14; 15; 16; 17; 23], creating a new square inductor where the thickness of the turn decreases when reaching the interior of the turn [24], and creating interleaving windings for the inductor [25]. All of the research has compared experimental results with analytical results or those obtained through numerical modeling. Starting from this, we created and implemented in MATLAB R2023b (Corporate Headquarters: Natick, Apple Hill Campus 1 Apple Hill Drive Natick, MA 01760-2098, USA) an algorithm, which, based on analytical calculations, determines the structures for certain types of applications, considering the space available and the results expected. The structures are then verified through experimental and numerical modeling.  
Lastly, knowing how a dielectric influences the operation of antennas at high frequencies, the aim was to observe the influence of different types of dielectrics at low frequencies as well. We considered using some of the dielectrics from [26; 27], but also some new dielectrics with different characteristics.