# Analysis of Multi-Level Simultaneous Driving Technique for Capacitive Touch Sensors
## 4 Results and Discussion
### Implementation  
To verify the theoretical noise immunity of the proposed \(M\)-\(H\) sequences, multi-level drivers that support simultaneous TXs were implemented. A transparent touch-screen panel embedded display module with 15 TX channels was tested using the drivers, receiver circuits, and a controller in a field-programmable gate-array (FPGA) device. Figure 10 shows the block diagram and the implemented hardware for the experimental setup. The driver circuits implemented by eight 2-channel 16-bit digital-to-analog converters (DACs) generate simultaneous multi-level waves to stimulate the capacitive touch panel and were controlled by logic circuits that were configured in the FPGA device. Ten parallel CAs, a channel multiplexer, and a 12-bit analog-to-digital converter (ADC) were implemented in a time-shared receiver, effectively establishing 10 RXs. The charges crossing the capacitive elements were first converted to the voltage signal by CA. After passing through an anti-aliasing filter and ADC, a digitized signal was sent to the FPGA and then de-modulated and de-spread by \(\mathbf{H}^{\top}\), as defined in (1). The 2-D 15 \(\times\) 10 capacitance matrix can be monitored by the host machine through either of a universal serial bus or an I\({}^{2}\)C interface. This test setup can be re-configured for different codes and panel structures by changing only \(R_{f}\), C\({}_{f}\), and the embedded memory elements located in the FPGA. Multi-level concurrent driving signals can be finely adjusted by 16-bit DACs configurable at the host PC. Different display images could also be tested via the commercial Android platform and its debug interface. Figure 10: Experimental setup. Figure 9: Frequency response for \(z_{amp\_j}\). Table 1 summarizes the SNRs obtained by a single acquisition for several \(M\)-\(H\) matrices and the conventional \(B\)-\(H\) matrices [1; 10; 12; 13; 14]. \(|\Delta r_{ij}|\) for the touch event is equivalent to 20% of \(r_{ij}\). Received signals for \(r_{ij}\) and \(|\Delta r_{ij}|\) are the average values of a total of 256 samples where \(N_{chip}=15\). \(z_{x}\) calculated from the standard deviation of 256 received signals when a touch event exists. Specifically, a regular \(B\)-\(H\) matrix or a tuned \(H\) matrix was selected for the case in the case of \(n=4\) and \(m=2\). Errors between observed SNRs for \(r_{ij}\) and the one for the analytical model using (3), (12), and (15) and the fitting error are listed in the rightmost column. In practice, supply noises appearing at discrete ICs further degrade the SNR of the acquired signal [25]. We tried to fit the major components of (3) by the measurement. To characterize the noise variation dependent on the gain and the number of driving signals, \(z_{x}\) in (3) can be further simplified into the following relation:  
\[z_{x}^{2}\simeq n\alpha_{r}^{2}A+\alpha_{r}^{2}B+1/\alpha_{r}^{2}C \tag{17}\]  
where \(\alpha=\alpha_{r}\cdot\alpha_{1}\). \(\alpha_{r}\) and \(\alpha_{1}\) denote the relative gain and signal gain at \(n=1\), respectively. \(A\), \(B\), and \(C\) represent the scaled components from the driver noise, in-circuit noise including thermal noise, and the amplifier noise defined in (3), respectively. As we explained in Section 4.2, \(A\) and \(B\) are directly attenuated by the closed loop gain of the amplifier. In smaller \(\alpha\) (\(=\alpha_{r}\cdot\alpha_{1}\)), \(C\) can be inversely increased by (4). \(z_{x}\) extracted from the standard deviation of the received signals can be expressed by (17). By the result of fit errors, the model in (17) well agreed the measured \(z_{x}\) with less than 7%. Both the analytical model and the experimental result for \(z_{x}\) clearly show that \(z_{x}\) varies with respect to \(n\) and mostly proportional to \(\alpha_{r}\). As expected in (13) and (16), the SNRs of \(M\)-\(H\) sequences in \(r_{ij}\) and \(|\Delta r_{ij}|\) were determined by \(m\) and were better than those of \(B\)-\(H\) matrices.