## 2 Theoretical Infrastructure
### Recommended Transmission Line Structure  
As shown in Figure 2, two ungrounded coplanar transmission lines are routed side by side. Unlike traditional methods that place capacitors directly between signal lines or between signal lines and ground planes, capacitors, designated as C\({}_{\text{first}}\), C\({}_{\text{middle}}\), and C\({}_{\text{end}}\), are positioned exclusively between the ground planes at specified locations. Each capacitor is soldered onto pre-designed pads placed along the ground lines. This configuration ensures that the capacitors influence the return current path rather than directly interacting with the signal traces, which helps maintain signal integrity without introducing unwanted resonance effects. These pads are strategically distributed to enable flexible positioning of capacitors, allowing for the evaluation of various capacitance values and configurations to achieve optimal crosstalk reduction in unique designs.  
The capacitors were soldered manually onto these pads using standard high-frequency PCB assembly techniques. This approach ensures precision and repeatability in capacitor placement. Additionally, the inclusion of these pads during the PCB design phase provides the flexibility to adjust the placement or replace capacitors without requiring a redesign or re-fabrication of the PCB. This post-production adjustability represents a significant advantage over other methods, particularly in iterative design environments or for prototyping purposes.  
In this setup, Transmission Line 1 is defined as the victim line, and Transmission Line 2 is designated as the aggressor. Termination resistors with values of 50 \(\Omega\) are used for impedance matching at high frequencies, ensuring accurate S-parameter measurements.  
Figure 2: Top view of the tested transmission line model.  
The transmission line dimensions used in this study are as follows: \(w\) = 0.14 mm, \(s\) = 0.1 mm, \(t\) = 0.035 mm, \(h\) = 1.5 mm, and \(\epsilon_{r}\) = 4.5 F/m. With these parameters, the designed transmission line achieves an approximate impedance of 50 \(\Omega\), ensuring compatibility with high-frequency applications. The dielectric material for the circuit board is selected as FR4 due to its cost-effectiveness and widespread usage in high-frequency PCB designs.  
By enabling precise placement and post-production adjustments of capacitors, this approach offers an effective, scalable, and practical method for reducing crosstalk in high-frequency transmission lines. Unlike conventional approaches where capacitors can create frequency-dependent resonance effects, the placement of capacitors strictly between the ground planes prevents unwanted filtering artifacts. The flexibility of this design ensures its adaptability to a wide range of applications, addressing both experimental and production-level requirements.  
As depicted in Figure 2, the capacitors are specifically placed between the ground planes rather than between signal traces. This key distinction ensures that the capacitors primarily act on the return current flow, rather than introducing direct reactive effects into the signal path. By carefully optimizing their placement, the capacitors enhance electromagnetic shielding while preserving impedance consistency across the transmission line.