# Analysis of Multi-Level Simultaneous Driving Technique for Capacitive Touch Sensors
## 2 Capacitive Touch Sensing System
### Random Noise Components for Capacitive Touch Sensors  
Propagation characteristics for TX-to-RX paths and the crosstalk noise for constant driving codes in \(\mathbf{H}\) cause static errors in sensing target capacitances. These static errors can usually be corrected using the delay controls of the driving codes and value compensation on the receiver side due to the  
Figure 1: Example of two-channel simultaneous driving and sensing. static nature that is determined by the touch panel structure and circuit implementation. Conversely, random noise components of sensing values result in touch location jitters and detection failures. These dynamic errors primarily depend on the SNR of the capacitive signal acquired by the analog front end of the receiver. For a large in-band noise, we can change the modulation frequency of the TX [17]. To suppress the remaining dynamic errors, in the software of the touch sensor, the spatial and temporal properties of the TX-to-RX values on the entire touch panel can be utilized at a late processing stage [18; 19; 20]. Figure 2 shows a signal processing flow of a capacitive touch sensor and summarizes the relevant dynamic noise components. A driver generates modulated TX signals with frequency \(f_{c}\). In conjunction with \(f_{c}\) and its harmonic components, several noise sources from drivers, resistances, amplifiers, coupling noise through fingers and display panels can be injected and propagated through the capacitive element \(c\) and the charge amplifier (CA). These noises are attenuated by the frequency responses of CA and an anti-aliasing filter. After de-modulating with \(f_{c}\), the capacitive signal representing \(c\) appears at zero frequency. Let \(z_{ij}\) in \(\mathbf{Z}_{j}\) be the root-mean-square (RMS) value of the total noise at the \(i\)-th spread code and \(j\)-th receiver circuit. Then, \(z_{ij}\) for the number of concurrent driving channels \(n\) can be defined as follows:  
\[ \begin{array}{rcl}z_{ij}^{2}&=&\sum\limits_{k}^{n}z_{drv\_kj}^{2}\cdot\int \left|A_{v}\left(f\right)\right|^{2}\left|A_{LPF}\left(f\right)\right|^{2}df +\sum 4k_{B}TR_{j}\int\left|A_{R_{j}}\left(f\right)\right|^{2}\left|A_{LPF} \left(f\right)\right|^{2}df\\ &&+4k_{B}TR_{f}\int\left|A_{LPF}\left(f\right)\right|^{2}df+\sum z_{ext}^{2}+ z_{amp\_j}^{2}\end{array}  \tag{3}\]  
where \(z_{drv\_kj}\), \(z_{ext}\), and \(z_{amp\_j}\) are the RMS noise level for driver circuit \(k\) appearing at receiver \(j\), the in-band external noise component and the amplifier noise in receiver \(j\), respectively. These are categorized into purely random or correlated sources of electronic noise [21]. \(A_{v}\) which is the closed loop gain of CA [22], adjusts all noise components appearing at the input of the amplifier by feedback components \(R_{f}\) and \(C_{f}\). \(R_{j}\) represents a series resistance on a TX-to-RX path arriving at receiver \(j\). On the other hand, as a feedback resistor of CA, \(R_{f}\) can be changed by a gain configuration. By employing [PERSON]'s constant \(k_{B}\) and the absolute temperature \(T\), we obtain two thermal noise factors that are affected by the gain of the receiver for \(R_{j}\) (\(A_{R_{j}}\)), and the gain of the anti-aliasing filter (\(A_{LPF}\)), as shown in (3). In (3), \(z_{amp\_j}\) can be determined by the input noise voltage of the amplifier [23; 24; 25], as follows:  
\[z_{amp\_j}=\int\left|1+\frac{Z_{in}}{Z_{f}}\right|\cdot\left|e_{nj}(f)\right| \cdot\left|A_{LPF}(f)\right|df \tag{4}\]  
where \(e_{nj}\) is the spectral density of the noise voltage defined in the specification of amplifier \(j\)[25], and \(Z_{in}\) denotes the impedance of the input network of the amplifier including \(c\). \(Z_{f}\) is the impedance of the feedback path, which is composed of \(R_{f}\) and \(C_{f}\).