## 4 Conclusions  
In conventional EHD vector printing based on constant frequency jetting, to print uniform line pattern, the printing speed should be no more than 1 mm/s.  
To increase the printing speed for EHD vector printing, we proposed a vector printing method using encoder sensor signals from two axes to generate trigger signals for jetting at each pre-set distance. To implement the method, we developed the so-called encoder processing unit (EPU) module, which is capable of changing various jetting parameters, such as dot spacing, the dummy distance, and the printing mode via printing software. By using the EPU, trigger pulses for jetting can be generated based on pre-set spacing distance, irrespective of the printing speed. By using the EPU, the printing speed can be increased by more than 10 mm/s without affecting the deposition amount in the end points.  
However, in the case of increasing the printing speed further, there are two uniformity issues at both ends: dot size (or deposition amount) variance and offset position in the printing direction. The main reason for slight dot size deviation of the first few droplets is that the jetting amount is related to the jet frequency. The jet frequency in the acceleration and deceleration regions is much lower than in the constant target speed region. As a result, the droplet amount is likely to be smaller than in the other region.  
To reduce the dot size variation, we implemented an additional counting function in the EPU, so that the acceleration and deceleration region can be excluded for printing. Nevertheless, in the case of using high jetting frequency, there were persistent printing uniformity problems at the end point, because the equivalent DC voltage due to pulse voltage dominated the pulse voltage. The equivalent DC voltage at the initial printing part is slightly lower than at the rest of the printing region. As a result, the equivalent DC voltage can shift the starting printing positon of lines in the printing direction. Another possible reason for the printed line offset is due to fast moving of the printing substrate relative to the nozzle, because the target positon can be moved to the moving direction, before the jet is deposited on the substrate. The shift in printing can result in disconnection in lines, if connected lines are needed. So, we proposed the use of a position offset compensation method in the case of high-speed application and showed successful implementation in the case of a printing speed of 50 mm/s.  
As a result of our proposed methods, uniform patterns could be printed in arbitrary printing direction for patterning with a printing speed of more than 50 mm/s, which is significantly higher than the conventional printing speed of less than 1 mm/s.  
Figure 15: 2D patterning with arbitrary printing directions (Supplementary Video, Ref. [10]). (**a**) Different printing directions for testing; (**b**) printing using the conventional constant jetting frequency method using jetting frequency of 10 Hz and low speed of 0.05 mm/s; (**c**) magnified printing result of (**b**); (**d**) printing at high frequency of 1750 Hz and target speed of 52.5 mm/s using the conventional constant frequency; (**e**) printing using the proposed equal spaced triggering of 30 μm and printing speed of 52.5 mm/s, with dummy lengths of 3 mm; and (**f**) magnified printing result of (**e**).  
**Acknowledgments:** This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2016R1D1A1B01006801), and partially supported by the Soonchunhyang University Research Fund.  
**Author Contributions:** [PERSON] created an initial idea of EPU to print uniform patterns near the end points of lines; and he guided [PERSON] and [PERSON] to carry out experiment and development. [PERSON] wrote the manuscript with help of [PERSON].  
**Conflicts of Interest:** The authors declare no conflict of interest.