## 2 Vector Printing Method Using the Encoder Sensors of Two Axes
### The Method of Using Two Encoder Signals for Vector Printing
#### 2.2.2 Two Functions of the EPU  
The Automatic Trigger Pulse Generation Function  
The basic function of the EPU is to generate trigger pulses in real-time at each pre-set drop spacing distance, \(d_{s}\), based on two encoder position signals. Note that for most EHD vector printing applications, simultaneous movement of 2 axes is required. Figure 5 shows the example of printing a line from point \(A(x_{1},y_{1})\) to point \(B(x_{2},y_{2})\). The number of generated encoder pulses of \(x\) and \(y\) axis movements during the printing process can be determined by \(x_{n}=\frac{|x_{2}-x_{1}|}{r}\), \(y_{n}=\frac{|y_{2}-y_{1}|}{r}\), respectively. Here, \(r\) is the resolution of the encoder signal. Note that we cannot use two encoder signals directly to generate a single channel jetting trigger. To generate single channel jetting trigger signals from two axes, the EPU counts the number of encoder pulses from the \(x\)-axis and \(y\)-axis in real-time. Figure 6 illustrates how the trigger signal for jetting with distance spacing of \(d_{s}\) is generated from two encoder signals. It should be noted that there can be round-off position errors of 0.5 \(\times\)\(d_{s}\) to generate jetting triggers with dot spacing of \(d_{s}\). In the case of connecting lines patterning such as repair applications, the round-off position errors could result in unconnected parts. So, in the case of practical application, additional trigger pulses can be added before starting and after printing the lines to ensure the connectivity of the pattern. Figure 5: Vector printing using equally spaced distance. (**a**) Vector movement of 2 axes, and (**b**) equally spaced distance for vector printing. Figure 6: Pulse voltage generation based on two encoder signals. If we use the jetting trigger based on droplet placement distance, \(d_{s}\), the total number of jetting trigger pulses should be \(\frac{\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}{d_{s}}+1\). Here, the addition of one extra trigger is added at the initial starting point. This also solves the non-printing problem of print on point A, since there is no encoder counting pulse at the first position of printing. When using the EPU, the jetting frequency, \(f\), is automatically varied according to printing speed, \(v\), as \(f=\frac{v}{d_{s}}\). As a result, the jetting frequency is likely to become very low during the acceleration and deceleration regions, compared to that of the target speed region, as shown in Figure 7.  
Printing Distance Counting Function  
To improve printing quality, we propose the printing method of using a constant jetting frequency region only by excluding the acceleration and deceleration regions. For the implementation, an additional length, the so-called dummy length, should be added to both ends of patterns to move stages for acceleration and deceleration purpose without printing. In the first dummy region, the EPU counts a pre-set number of non-jetting pulses to skip jetting in the acceleration region. Here, jetting triggering pulses are internally generated at each pre-determined spacing distance and are not connected to output for the EPU for jetting triggering. After finishing counting the dummy length, the jetting trigger will be connected to the output of the EPU, so that the jetting can be generated to print the pre-determined line length. After counting of the jetting trigger for printing, the jetting trigger pulse will no longer be generated, even when the stage is moving for the deceleration region (the latter dummy length). Figure 8 shows the proposed printing method using dummy length to exclude the acceleration and deceleration parts for printing. If we assume that the printing part is from \(A(x_{1},y_{1})\) to \(B(x_{2},y_{2})\), the movement should start from \(A^{\prime}_{1}(x^{\prime}_{1},y^{\prime}_{1})\) to \(B^{\prime}(x^{\prime}_{2},y^{\prime}_{2})\), as shown in Figure 8, so that the dummy distances, \(d_{1}\) and \(d_{2}\), can be added before A and after B, respectively.