# Meander Line Super-Wideband Radiator for Fifth-Generation (5G) Vehicles
## 2 Meander Line Antenna Formula  
To design a high-quality 5G antenna, it is important to consider the substrate material's impact on the gain, efficiency, and reflection coefficient. The substrate material's permittivity, thickness, and loss tangent all play critical roles in ensuring reliable radio frequency quality, cost-effective hardware, and maximum efficiency. Choosing the right substrate material is crucial to ensure optimal performance. Common dielectric substrates include FR-4: a widely used epoxy-based substrate known for its cost-effectiveness and ease of fabrication. However, it has limitations in terms of high dielectric loss and limited frequency capability. Rogers Corporation produces high-performance laminates, such as the RO4000 series, which offer lower dielectric loss and better stability across a broad frequency range. Ceramic substrates, like alumina (Al\({}_{2}\)O\({}_{3}\)) and aluminum nitride (AlN), exhibit excellent thermal conductivity and are suitable for high-power applications. However, they can be brittle and challenging to process. Polytetrafluoroethylene (PTFE) substrates, such as Rogers RT/Duroid, are known for their low dielectric constant and low loss tangent, making them suitable for high-frequency designs, but they can be more expensive. The selection of a dielectric substrate depends on the specific application requirements, including the frequency range, power handling capability, thermal properties, and cost considerations. Designers must carefully evaluate these factors to choose the most appropriate substrate for achieving optimal performance in electronic circuits. FR4 and RT/Duroid substrates are commonly used in 5G/6G antennas due to their desirable electrical properties. Among these, FR4 is a cost-effective and popular substrate material for printed circuit boards (PCBs) due to its mechanical durability and low cost [32; 33]. However, it is important to note that different 5G antenna designs may require different substrate materials to achieve optimal performance. For instance, for higher frequencies, a low loss higher dielectric constant substrate yields better radiation performance and bandwidth. It is crucial to calculate the meander line element dimensions using mathematical equations that take into account the operating frequency and other design criteria. The dielectric constant (\(\epsilon_{r}\)) and substrate height (\(l_{s}\)) for planar patch antennas made of FR4 are typically 4.4 and 1.6 mm, respectively. However, determining the appropriate length (\(L_{p}\)) and width (\(W_{p}\)) of a meander line antenna for 5G FR1 2.4 GHz and 5G FR2 28 GHz frequencies can be challenging. Fortunately, there are standard formulas available that can assist with calculating these values; these are depicted in Figure 2 and Equations (1)-(16). By verifying these standard equations, engineers can have confidence in using them for their designs [34; 35; 36]. Once the formulas have been applied, the estimated values for meander line structures Ant1 through Ant4 can be determined and presented in a table,  
Figure 1: Dimensions of 5G FR2 (all in mm). such as Table 1. Impedance matching: To match the impedance of the meander line antenna to the feedline, the following expression can be used to calculate the width of the feedline:  
\[W_{feed}=\frac{Z_{0}}{(h*\epsilon_{r}*c)} \tag{1}\]  
where W\({}_{feed}\) is the width of the feedline, and Z\({}_{0}\) is the characteristic impedance of the feedline. The characteristic impedance of an antenna feedline is crucial for minimizing signal reflections and maximizing power transfer efficiency. A proper match between the feedline and antenna impedance reduces the Voltage Standing Wave Ratio (VSWR), resulting in lower signal loss and improved transmission performance. Consistent impedance throughout the feedline ensures resonance at the antenna's operating frequency: optimizing its efficiency and preventing potential damage to associated equipment due to impedance mismatches.