## 1 Introduction  
With the rapid advancements in user interaction systems and display technologies, integrated touch and display circuits, referred to as Touch and Display Driver ICs (TDDIs) [1, 2, 3], have emerged as a highly popular solution. TDDIs provide both cost and area efficiency by integrating the touch panel and display into an in-cell structure, eliminating the need for separate touch modules and ICs. Figure 1a illustrates the stack-up of an in-cell LCD display panel, where the TSP electrodes are integrated onto the color filter glass. These electrodes, made of transparent indium tin oxide (ITO), maintain optical transmittance while enabling capacitive sensing. They form either fringing field capacitance or self-capacitance (C\({}_{\text{S}}\)) [4, 5, 6, 7] with the LCD's common electrode (V\({}_{\text{COM}}\)) layer, which stabilizes the voltage across the liquid crystal (LC) layer during operation. When a finger touches the cover glass, an additional finger capacitance (C\({}_{\text{F}}\)) is introduced, altering the total capacitance and enabling touch detection. The color filter layer, positioned beneath the TSP electrodes, selectively transmits RGB subpixel data for accurate color representation. Below the LC layer, the thin-film transistor (TFT) array, fabricated on the TFT glass, actively controls pixel switching by modulating the electric field across the liquid crystals. By embedding TSP electrodes within the display stack, this design reduces manufacturing complexity and cost while enabling thinner and lighter panels. Figure 1b shows the illustration of a dot-matrix type in-cell TSP panel, highlighting a disadvantage related to the uniformity of the capacitance (Cs). The dot-matrix  
channels, denoted as CH\({}_{\text{Dot}}\) [N:1], consist of N individual sensing channels, each connected to a dot-matrix capacitance readout IC, where the capacitance values are measured and processed. Since the trace of each dot-matrix TSP electrode is routed within the panel, the width (W\({}_{\text{U}}\)) of the dot-matrix electrodes in the upper area is wider than that (W\({}_{\text{L}}\)) in the lower area. Consequently, the capacitance varies depending on the channel location. Additionally, the V\({}_{\text{COM}}\) layer, serving as the reference potential, is connected through a unity-gain feedback buffer to stabilize the voltage level before being distributed via contact pins (V\({}_{\text{COM1}}\)-V\({}_{\text{COM4}}\)) at the four corners of the rectangular layer in mobile devices. This configuration introduces a loading effect caused by the network of series and parallel resistance (R\({}_{\text{S}}\)) connections within the V\({}_{\text{COM}}\) layer. As a result, the parasitic resistances are particularly pronounced at the center of the layer, leading to variations in the time constant and, consequently, nonuniformity in the measured C\({}_{\text{S}}\). These challenges in accurately measuring the Cs are exacerbated by the small variation introduced when a finger contacts the TSP electrode. The capacitance change caused by finger contact (C\({}_{\text{F}}\)) is only 3-5% of the baseline Cs. This minimal variation is often masked by the significantly larger and nonuniform baseline Cs, emphasizing the necessity of a precise Cs compensation circuit. Another major concern of the TSP readout system is its noise immunity to external disturbances, which is highly influenced by the choice of the TSP driving frequency. Most external noise sources, such as charger-induced noise, fluorescent lamp ramp noise, and electromagnetic interference (EMI) from surrounding components within the compact form factor of mobile devices, typically fall within the range of several tens to hundreds of kHz [8; 9; 10; 11]. Consequently, a higher TSP driving frequency is generally required to effectively mitigate these noise effects. However, this frequency is constrained by the time constant determined by the TSP's Cs and the TSP electrode's series resistance, significantly limiting the available frequency range.