## 3 Experimental Results and Discussion
In addition, the printing location can be shifted in the printing direction (\(\Delta\)s), as shown in Figure 12. Also, after termination of the pulse voltage, the effects of the equivalent DC voltage could last a while. So, a small amount of jetting can occur after printing, which is indicated as \(\Delta\)e. However, it should be noted that there could be additional reason to cause shift in the printing direction. The fast stage movement can result in additional position error in the moving direction, since the substrate can move a significant distance relative to the nozzle while the jet travels to the substrate. If it is desired to connect multiple lines, the position shift in the printed line could result in the disconnection of lines. In the case of conductive line printing, this could result in open circuit failure problems. Note that the printing position may be affected by other causes, such as jet frequency, pulse voltage shape, and ink properties. To ensure the connectivity of the patterns in the case of high-speed 2D patterning, the offset compensation method is considered in this study, as shown in Figure 14. Note that the shifted position is usually small and could be easily compensated by means of software. Figure 12: Line printing using the dummy distance (\(d_{1}\), \(d_{2}\) = 3 mm) function of the EPU with \(d_{s}\) = 20 \(\upmu\)m.  
Figure 13: Effect of transient equivalent DC voltage. To demonstrate our proposed method, we used 2D patterns with the pattern size of (0.5 mm \(\times\) 0.5 mm), as shown in Figure 15a. In the case of printing by using the conventional constant jetting frequency approach, the printing speed was set to be as low as 0.05 mm/s to minimize the end point effects, as shown in Figure 15b. Figure 15c shows the magnified image of the printed results, and no end point effects can be found. However, if the printing speed is too low, it is not efficient, because it will take considerable time to print the desired pattern. To increase the printing speed, the frequency also needs to be increased accordingly. Figure 15d shows the printed results using the conventional constant frequency jetting of 1750 Hz with target printing speed of 52.5 mm/s. Here, the acceleration and deceleration are set to 1 m/s\({}^{2}\). However, considering the acceleration and deceleration, when printing the lines with length less than 0.5 mm, the printing speed cannot reach the target speed, which means the printing speed varies throughout the printing process. Figure 15d shows that in the case of using conventional methods, a large amount of overlapping droplets are deposited at the end points of jetting. However, Figure 15e,f shows that in the case of printing using encoder sensors signals, there is no significant overlapping at the end points of the patterns, in spite of the high printing speed of 52.5 mm/s. In this experiment, a sufficient dummy length of 3 mm was used, so that printing speed would be constant at 52.5 mm/s throughout line printing. Note that 30 \(\upmu\)m offset of printing location is considered to compensate for the possible shift in the printing location. Note also that in Figure 15f, the start point and the end point show a slight difference in shape, due to the equivalent DC voltage behavior, as discussed in Figure 9:0 Nonetheless, when the printing speed is increased to more than 52.5 mm/s, the printed results in Figure 15e,f show reasonable uniformity of printed line. Here, trigger signals are generated at each distance of 30 \(\upmu\)m to print lines, and the corresponding jet frequency would be 1750 Hz. Note that in the case of higher frequency than 1.5 kHz, the equivalent DC voltage effects dominate the pulse voltage effects. As a result, the line can be connected by trigger signal based on a relatively large dot distance of 30 \(\upmu\)m. For better understanding, kindly refer to the video in Ref. [10]. Figure 9:1 Offset compensation. Figure 9:2 _Cont._