# Analysis of Multi-Level Simultaneous Driving Technique for Capacitive Touch Sensors
## 4 Results and Discussion
### Implementation
However, the conventional \(W\)-\(H\) matrices with \(n=4\) and \(n=8\) as well as \(M\)-\(H\) matrices with \(n\geq 9\) should lower down \(\alpha_{r}\) to satisfy \(M\). Their configuration increases \(z_{x}/\alpha_{r}\) due to the term of the amplifier noise related to \(C\) in (17). This also indicates that the SNRs for regular \(B\)-\(H\) matrices are superior than the ones for \(W\)-\(H\) matrices with small \(\alpha_{r}\) as reported in [1]. Therefore, we can expect that the inherent regularity of the proposed \(M\)-\(H\) matrices can keep \(\alpha_{r}\) high so that the resulting SNR can be improved within the signal capacity \(M\). Figure 11 shows the variations in the SNRs of touch events with respect to the scan rates and their level of interference on the display panel for different \(H\) matrices. The multiplexed driving of TXs in which only a single TX was active at any time yielded the lowest SNR because it had the shortest sensing time per sensor node. For different time constraints due to the scan rates, small fluctuations were found, but \(M\)-\(H\) matrices with \(m=2\) exhibited almost the same SNRs as expected in (13). They also showed similar interference levels. RMS noise voltages observed in the display \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Code**} & **SNR for** & **SNR for** & **Normalized** & **Observed** & **Model for \(\mathbf{z_{x}^{2}}\)** & **Model Error** \\  & \(\mathbf{r_{ij}}\) **[dB]** & \(|\Delta r_{ij}|\) **[dB]** & \(\alpha\) (\(\alpha_{r}\)) & \(z_{x}\) **[mV]** & **Model for \(\mathbf{z_{x}^{2}}\)** & **for \(\mathbf{z_{x}^{2}}\)** **[\%]** \\ \hline \(n=1\), Fully-mixed & 54.5 & 40.3 & 1.0 & 0.191 & \(A+B+C\) & 2.3 \\ \(n=2\), \(W\)-\(H\) & 57.2 & 43.0 & 1.0 & 0.199 & \(2A+B+C\) & 2.1 \\ \(n=3\), \(m=2\) & 60.9 & 47.7 & 1.0 & 0.210 & \(3A+B+C\) & 4.0 \\ \(n=4\), \(m=2\) & 59.6 & 47.2 & 1.0 & 0.213 & \(4A+B+C\) & 2.1 \\ \(n=4\), \(W\)-\(H\) & 58.7 & 44.7 & 0.5 & 0.116 & \(A+0.25B+4C\) & 0.2 \\ \(n=5\), \(m=3\) & 62.7 & 49.2 & 1.0 & 0.222 & \(5A+B+C\) & 3.1 \\ \(n=6\), \(m=2\) & 58.8 & 45.9 & 1.0 & 0.220 & \(6A+B+C\) & 0.6 \\ \(n=6\), \(m=3\) & 60.7 & 49.2 & 1.0 & 0.236 & \(6A+B+C\) & 6.5 \\ \(n=8\), \(W\)-\(H\) & 56.7 & 42.4 & 0.25 & 0.122 & \(0.5A+0.0625B+16C\) & 0.7 \\ \(n=9\), \(m=4\)1  & 63.8 & 51.7 & 0.5 & 0.133 & \(2.25A+0.25B+4C\) & 1.6 \\ \(n=10\), \(m=4\)1  & 63.7 & 50.9 & 0.5 & 0.137 & \(2.5A+0.25B+4C\) & 2.6 \\ \(n=15\), \(m=6.3\)1  & 67.8 & 54.0 & 0.5 & 0.139 & \(3.75A+0.25B+4C\) & 5.0 \\ \(n=15\), \(m=6.6\)1  & 5.0 \\ \(n=15\), \(m=6.6\)1  & 69.3 & 54.8 & 0.5 & 0.141 & \(3.75A+0.25B+4C\) & 3.5 \\ \hline \hline \end{tabular}  
* \(A\)-\(H\) matrix expanded using the Kronecker product; \({}^{b}\) Errors were extracted by applying \(A=0.05\) mV\({}^{2}\), \(B=0.18\) mV\({}^{2}\), \(C=0.03\) mV\({}^{2}\).  
\end{table} 
Table 1: Observed SNRs for \(r_{ij}\) and \(|\Delta r_{ij}|\) in \(W\)-\(H\)s [1; 10; 12; 13; 14] and proposed \(M\)-\(H\)s where \(\Delta V_{TX}\simeq 101\) mV. common electrode (VCOM) plane depended on \(m\). This comes from that the incident driving noise on VCOM is determined by the column sum of the \(H\) matrix and the parasitic capacitance. Figure 12 shows four display noise patterns on capacitive sensors when a two-dot inversion display panel was used [3]. The display driver noise mainly exists in the full-length and the half-length of a horizontal sync (Hsync) period. According to the transfer characteristics shown in Figure 7a, after the de-modulation at the receiver, these noises remained as in-band components. Figure 11: Changes in the SNR according to the scan rate and the interference level. Figure 12: Display noise patterns in eight rows and two adjacent pixel columns induced by four different images; a white blank means “off state”, and all colored squares denote “on state” in RGB sub-pixels. Figure 13 provides the SNR comparison results for the remaining display noise when the worst noise patterns (Y-C-B-R and C-B-R-Y) were displayed below the touch panel.