## 2 Vector Printing Method Using the Encoder Sensors of Two Axes
### Vector Printing without Using Encoder Signal  
Although the EHD jet can be produced by using DC voltage only, pulse voltage superposed with DC voltage has been commonly used, since the jetting can be controlled by an external trigger signal. Most previous EHD vector printing methods have been based on AC voltage, or pulse voltage with constant frequency from either external or internal trigger sources [4; 5; 6; 7; 8]. In this case, the drop placement spacing between 2 consecutive jettings, \(d_{s}\), can be determined by the motion (printing) speed, \(v\), and the jetting frequency, \(f\), as: \(d_{s}=\frac{v}{7}\). The droplet placement interval (or spacing) is an important parameter to form a connected line using a series of droplets. Note that the drop placement spacing should consider the droplet size deposited on a substrate to form a connected line by overlapping deposited dots. For example, if the deposited dot size on the substrate is \(d\), then the drop placement spacing, \(d_{s}\), should be around \(0.7\times d\) to make connected lines via a slight overlap of the droplets. If the spacing between droplets is too small, the pattern width becomes thick, due to heavy overlapping of droplets. However, if the spacing between droplets becomes more than the deposited droplet size, the deposited dots cannot make connected lines.  
To obtain uniform line width by achieving equally spaced deposited dots, the printing speed needs to be constant throughout the printing region (line) in the case of using constant jetting frequency. However, in order to print at target speed, \(v\), there should be an acceleration or deceleration region at the start point and end point of line, in which the printing speed changes from zero to the target speed, or vice versa. As a result, a significant amount of droplet can be deposited near the start and end points of the printed lines, compared to the rest of the regions. As the target printing speed or jetting frequency increases, the excessive overlapping of dots at the end points becomes more serious. Figure 2 illustrates non-uniformity in printed lines, which is caused by a large amount of droplet deposition at both end points of the line. Figure 3 shows the typical printed lines using the constant frequency method. Figure 3a shows that if the printing speed is low (less than 1 mm/s), the start and end points of the printed line are not significantly influenced by acceleration and deceleration. However, if the printing speed becomes more than 10 mm/s, the amount of droplets deposited at both ends increases significantly, according to the increase of printing speed. Figure 3b shows the printed results of patterns using a printing speed of 30 mm/s. The figure shows that it is difficult to increase the line density (the number of lines per unit distance), due to the large amount of droplets at the end points of the line. As a result, the target printing speed and jetting frequency have been limited to very low (less than 1 mm/s) in order to achieve reasonable printing quality.  
Figure 2: Non-uniform jetting due to printing speed variation.