## 2 Theoretical Infrastructure
### An Overview of Crosstalk Reduction Method  
Crosstalk, caused by undesired electromagnetic coupling between transmission lines, is a significant challenge in transmission systems. Effective reduction techniques often involve optimizing physical configurations and employing material solutions to minimize these interactions. One of the most straightforward methods to reduce crosstalk is adjusting the physical layout of transmission lines. Increasing the distance between adjacent lines or cross-positioning parallel lines can help mitigate electromagnetic coupling [29; 30]. Insulation materials with high dielectric properties placed between layers are also commonly used to suppress capacitive coupling, further reducing crosstalk [31]. In UCPW structures, where transmission lines are flanked by ground planes, crosstalk can be further mitigated by creating a localized return current path. Adding capacitors between these ground planes provides a low-impedance path for the return current, reducing the interaction between signal lines. While capacitors primarily affect the return current flow, their presence can influence the overall coupling by stabilizing the electromagnetic environment between the transmission lines [32; 33; 34]. The crosstalk effects are typically evaluated using two key parameters: NEXT (near-end crosstalk, S\({}_{31}\)) and FEXT (far-end crosstalk, S\({}_{41}\)). Among the commonly used formulations for these parameters, Equations (15) and (16) are particularly relevant [35]. \[\mathrm{N}_{\mathrm{ext}}=\frac{1}{4}\bigg{(}\frac{\mathrm{C}_{m}}{\mathrm{C}} +\frac{\mathrm{L}_{m}}{\mathrm{L}}\bigg{)}, \tag{15}\]  
\[\mathrm{F}_{\mathrm{ext}}=\frac{1}{2\mathrm{v}}\bigg{(}\frac{\mathrm{C}_{m}}{ \mathrm{C}}-\frac{\mathrm{L}_{m}}{\mathrm{L}}\bigg{)} \tag{16}\]  
In these equations, \(C_{m}\) and \(L_{m}\) represent the mutual capacitance and inductance between transmission lines, while \(C\) and \(L\) denote the per-unit-length capacitance and inductance of a single line. The signal propagation speed is represented by v. Both equations highlight the crucial role of mutual coupling parameters, where increased mutual capacitance or decreased mutual inductance intensifies crosstalk effects. To mitigate this, capacitors placed between ground planes establish a controlled return current path, effectively confining the current within a localized loop and minimizing interference with the signal lines. This controlled return path reduces overall mutual coupling and stabilizes both NEXT (S\({}_{31}\)) and FEXT (S\({}_{41}\)) parameters, as also modeled in prior studies on coupled RLC interconnects [35]. A comparable analysis of mutual coupling based on electromagnetic field distribution is also provided by [PERSON] [36], who investigates crosstalk suppression in photonic and microwave integrated circuits using field-theoretical models. Although capacitors do not directly reduce mutual capacitance (\(C_{m}\)), they play a fundamental role in modifying the electromagnetic field distribution between transmission lines. By directing the return current through a well-defined path, capacitors minimize unwanted coupling, thereby improving signal integrity in UCPW transmission lines. The experimental observations in this study align with theoretical formulations of mutual coupling behavior, demonstrating that strategic capacitor placement significantly improves crosstalk suppression. This approach not only mitigates coupling effects but also preserves impedance matching, making it a viable solution for high-speed and high-density electronic applications. While capacitors may not directly lower the value of mutual capacitance (\(C_{m}\)), they significantly influence the electromagnetic field distribution between transmission lines. By guiding the return current through a well-defined path, capacitors reduce the potential for interference and enhance the crosstalk performance of UCPW structures.