# Analysis of Multi-Level Simultaneous Driving Technique for Capacitive Touch Sensors
## 4 Results and Discussion
### \(z_{x}\) Variation with Respect to \(n\)  
By observing the inequality in (7), the converted noise \(z_{ij}\) in (3) can practically decrease in higher simultaneous TX channels under the assumption with small \(z_{drv\_kj}\) and small \(z_{amp\_j}\). The increase in the number of simultaneous TX channels should consider the maximum capacity (\(M\)) of the receiver so that \(\alpha\) should be scaled down not to exceed \(M\) in (7). The column sum \(m\) in an \(H\) matrix determines the maximum capacitive signal level and increases as the number of concurrent driving channels \(n\) increases. Therefore, \(A_{v}(f)\) must be reduced to satisfy (7). In this regard, \(C_{f}\) should be increased in order to decrease \(\alpha\) and eventually, to not exceed \(M\). To maintain the same bandwidth in \(R_{f}\cdot C_{f}\), \(R_{f}\) must be reduced accordingly [1]. For example, when \(R_{f}=500\) k\(\Omega\) and \(C_{f}=4\) pF are initially chosen to detect \(c=2\) pF, for the half gain to this initial set, \(R_{f}=250\) k\(\Omega\) and \(C_{f}=8\) pF should be configured. As shown in Figure 7a, there can be different \(R_{f}\) and \(C_{f}\) configurations to support \(n\) and corresponding magnitude responses. For simplicity, the pair of \((R_{f},C_{f})\) is represented by \(\alpha_{n}=(500\) k\(\Omega/n,4\) pF \(\times n)\)  
Figure 6: Comparison of signal acquisition properties for the identical \(m\) between \(B\)-\(H\)[1; 10; 12; 13; 14] and proposed \(M\)-\(H\) matrices where \(\alpha V_{TX}=350\) mV and \(z_{x}=7.7\) mV. The difference in the gain magnitude between any distinct sets of \((R_{f},C_{f})\) are maintained for all frequency samples. Figure 7b shows RMS plots of the noise components with respect to \(n\) except for the external noise and amplifier noise. Assume that the individual driver noise \(z_{drv\_kj}\) varies from 10 nV to 100 nV. Each resistance value around \(c\) in the touch panel is set to 1 k\(\Omega\). For \(n=3\), 5 to 8, 9 to 12 and 13 to 15, we configured the closed loop gain as \(\alpha_{4}\), \(\alpha_{8}\), \(\alpha_{12}\) and \(\alpha_{16}\), respectively. All noises that occur prior to CA including \(z_{drv\_kj}\) and thermal noise from \(R_{j}\) are directly attenuated by \(A_{v}(f)\) and \(A_{R_{j}}(f)\). As \(R_{f}\) is scaled down at a higher \(n\), the thermal noise component for \(R_{f}\) in (3) must also be reduced. In cases with \(n=2\), 3, 5, 9 and 13, \(z_{ij}\) is instantly suppressed by this property. For \(z_{drv\_kj}^{2}\) with same gain configuration in (3), the aggregated driving noise power increases by \(n\) times. Thus, \(z_{ij}\) is slightly increased when \(n=4\), 6 to 8, 10 to 12 and 14 to 15. The increase in \(z_{ij}\) is clearer in \(z_{drv\_kj}=100\) nV than in \(z_{drv\_kj}=10\) nV. This effect also indicates that a large driving noise can degrade the theoretical SNRs defined in (13) and (15). In contrast, \(z_{ext}\) depends on the amount of noise-induced charges that pass through the capacitive elements from a touching object and from the display panel. In (5), these noises are further modulated  
Figure 7: (**a**) \(A_{v}(f)\) for different gain sets of CA, (**b**) Variation of \(z_{ij}\) with respect to \(n\) without considering \(z_{ext}\). by \(f_{c}\). Therefore, with the low-pass filter in the succeeding process, a larger difference between the fundamental frequencies of the noises and \(f_{c}\) yields less in-band noise \(z_{ext}\). For incident noise through fingers, more noisy charges are injected, as a larger conducting object overlays the TX and RX channels. In practice, \(z_{ext}\) is often significantly distorted by the difference between the sensor ground and the real ground for noise sources (i.e., earth level). On the other hand, display noises are induced by display drivers and their common electrode (VCOM) regardless of touch events [3]. Different display images, vertical structures and driving methods result in various negative effects to the over-layered and embedded capacitive sensors in display modules.