LIGHT BRUSH. Joseph Xiong. Willie Zeng. Final Report for ECE 445, Senior Design, Fall TA: Henry Duwe. Project No. 34

Transcription

1 LIGHT BRUSH By Joseph Xiong Willie Zeng Final Report for ECE 445, Senior Design, Fall 2016 TA: Henry Duwe 07 December 2016 Project No. 34

2 Abstract The Light Brush is designed to be a simple tool for anyone to use to draw to a monitor. The user would move a controller in the air and a camera would see the movements and output the corresponding movement to a monitor. The resulting project functions as intended but the detection process behaves a bit finicky as the user s surroundings could affect the performance. This report contains the design, testing, results, and conclusions of the design process. 1

3 Contents 1. Introduction 1.1 Statement of Purpose 1.2 Objectives Goals & Benefits Functions & Features 1.3 Block Diagram 2 Design 2.1 User Interface Output Input Power Supply Circuit Schematic 2.2 Data Analysis Initialization Filtering Functionality Output 3. Design Verification 3.1 User Interface PWM Circuit Power Supply 3.2 Data Analysis 4. Costs 2

4 4.1 Parts 4.2 Labor 5. Conclusion 5.1 Accomplishments 5.2 Uncertainties 5.3 Ethical considerations 5.4 Future work References Appendix A Appendix B Appendix C Appendix D Requirement and Verification Table Calculating Duty Cycles PWM Duty Cycle Results PWM Frequency Results 3

5 1. Introduction 1.1 Statement of Purpose Current digital drawing platforms are quite expensive like digital drawing pads and tablets, a Nintendo Wii system, and the Xbox Kinect. The Light Brush offers artists or aspiring artists the ability to draw digitally with a much cheaper design than the other alternatives. The Light Brush is designed to be a simple tool for the user to draw in the air using a box-shaped controller where the motion of the box would be translated through a camera and microcontroller and outputted to a monitor. The controller will allow the user to control a few features: choosing the color to draw with, changing the brush size, and being able to erase. 1.2 Objectives Goals & Benefits To be as accurate and as configurable as it s expensive counterparts [1][2], while remaining inexpensive Drawing without using paper and a pencil/pen/marker Accurately and quickly updates the color, location, and the brush size of the controller Functions & Features To create an accurate and configurable drawing onto a monitor based on the user s settings on the controller To display and constantly update/obtain the movement of the controller To provide a range of colors for the user to select To display and constantly update the color To provide a range of brush sizes for the user to select To display and update the brush size as needed 4

6 1.3 Block Diagram Figure 1. Block Diagram with the User Interface module on the left and Data Analysis module on the right 5

7 2 Design 2.1 User Interface This first section of design is the User Interface module which contains all components of the controller. The controller is a box-shaped device used by the user which signals to the Data Analysis module information about the movement of the controller, color the user wants to draw with, and if the user wants to change brush sizes Output There are three RGB LEDs used as the output of the controller. The configuration of which LEDs are on will show the Data Analysis module what the user is intending to do. Each LED represents the different information needed to shown to the Data Analysis module: the location of the controller, color to draw with, and if the brush size needs to be changed. The tracking RGB LED shows the location of the controller and is set to emit a white light. When this LED is on, the program should draw. The color of the color RGB LED shows which color the user wants to draw with and can be varied by the user. The brush size LED is set to red and when toggled, indicates a change in brush size is needed. To help the Data Analysis module differentiate which LED shining is which, the tracking LED is set to shine the brightest, the color LED next brightest, and the brush size LED the dimmest. Originally, infrared (IR) LEDs were considered for the tracking LED and brush size LED because the longer wavelength was thought to be interpreted differently by the camera than any color that could be emitted by the RGB LED. But the IR LEDs were not able to emit a consistent light at all angles so tilting this LED would change how bright the LED is seen by the camera. In addition, the IR LED was not seen as different by the camera but appeared as purple. This is most likely because at the wavelength of the IR signal, the red and blue sensors of the camera pick up the signal the most so it is seen as purple [3]. Since the IR LEDs are not seen differently from the camera than an RGB LED and does not emit a constant light, the RGB LED was decided as the better option to be used as the tracking LED and the brush size LED Input There are six input components to control the three RGB LEDs. Two push buttons and one switch control when the LEDs turn on and three variable resistance potentiometers are used to control the color of the color LED. The first button is used to control when the user wants to draw indicated by powering the tracking LED and color LED. The second button controls the brush size LED and this light turning on signals that the brush size needs to be changed. To limit further confusion on the Data Analysis module, the brush size LED will only turn on if both the buttons are pressed. Then two LEDs shining indicates that drawing should occur so the location of the tracking LED and the color from the color LED should be used to draw. But, if both buttons are pressed, three LEDs will be shining and this indicates the brush size should change and no drawing will occur. With only these two features, the 6

8 user can only change the color of the color LED while pressing the draw button, so to allow the user to change colors without drawing, the switch was implemented. When the switch is turned on, the color LED will shine and the user can see the color they are changing. Since only one LED is shining, the Data Analysis module will know that the color needs to be updated and will not draw. The three potentiometers are used to control the color RGB LED. Each potentiometer corresponds to one color of the RGB LED (red, green, and blue). The potentiometers control the color LED through a pulse width modulation (PWM) circuit. Instead of varying the current through the LED, the PWM circuit varies how often current is flowing through the LED essentially controlling how often the LED is powered. The more time that power is flowing through the LED, the brighter the LED shines. For example, if power is flowing through the LED about 70% of the time, the LED should shine at 70% of its maximum brightness. The circuit is shown in Figure 2. Figure 2. PWM Circuit Table1. 74AC14 Schmitt Inverter [5] Pin Name Description VDD GND (X)A Power Supply Ground Input to inverter 7

9 (X)Y Output to inverter The PWM circuit has four different components: a 74AC14 Schmitt Inverter Chip, a variable resistance potentiometer, two diodes, and a capacitor. The circuit uses the VDD and ground signals from the power supply and outputs the signal sent to the RGB LED. The PWM circuit varies the time the output outputs power versus not outputting power through the time it takes to charge and discharge the capacitor. The capacitor is charged and discharged through the potentiometer and changing the resistance of the potentiometer changes the charging and discharging time of the capacitor. More specifically, the capacitor starts discharged so the voltage at pin 1A is low (below the inverter threshold voltage). The inverter will invert this low signal resulting in the voltage at pin 1Y to be high (above the threshold voltage). This high voltage would then charge the capacitor through the potentiometer and diode until the capacitor is charged high enough that the voltage at pin 1A is now high and the chip inverts the signal to a low voltage at pin 1Y. Then the capacitor will discharge through the upward facing diode and the potentiometer. The capacitor charging indicates a low output signal and the capacitor discharging indicates a high output signal. This cycle of charging and discharging will keep continuing and the time it takes for the capacitor to charge and discharge is how the output signal is controlled. And the time it takes for the capacitor to charge and discharge is controlled by the potentiometer because of the varying resistance so this potentiometer controls the output of the PWM circuit. The time it takes for the capacitor to charge in the PWM circuit is shown in Equation 2.1. V V c RC s = 1 e t (2.1) The time it takes for the capacitor to discharge in the PWM circuit is shown in Equation 2.2. V V c RC s = e t (2.2) In both equations, V c refers to the voltage across the capacitor, V s refers to the supply voltage, t is the time it takes to charge/discharge, R is the resistance that the capacitor is charging/discharging through, and C is the capacitance of the capacitor. With these equations, the time it takes to charge and discharge a capacitor can be calculated and the duty cycle can be calculated as shown in Equation 2.3. D uty Cycle = t high t high + t low (2.3) 8

10 A few calculations of charging and discharging times have been done and are shown in Table 5 in Appendix B. Besides calculating duty cycles, frequency is another important variable to be calculated. f = 1 T (2.4) Where f is frequency and T is the period of the signal Power Supply The power supply to the controller is a 9V battery along with a 5V voltage regulator (LM7805). The voltage regulator uses a couple capacitors and with an input voltage of 5V to 18V [4] and will output a steady 5V signal which will be used for the rest of the circuit Circuit Schematic Figure 3. Circuit Schematic This circuit shows the power supply towards the left, push buttons that control the tracking LED and brush size LED in the center, and the PWM circuits and color LED on the right. 9

11 2.2 Data Analysis Figure 4. Software Logic Flowchart The flowchart (in Figure 4) shows the logic implemented in the Raspberry Pi, which utilized Python as its language. Note that the large FOR loop is necessary so that each frame can be analyzed within the video input. The logic can be split into 4 sections. The Initialization phase primarily sets up variables, that will be used later in the code, as well as setting up the frame/image for filtering. Next is the Filtering phase, which filters out the brighter objects, such as our LED s on our controller. The filtering process outputs these bright objects as contours (Figure 5). Once the area of the contours are obtained, we proceed to the Functionality process. This process contains all of our functions such as, 10

12 obtaining the location of the tracking LED, obtaining the color from the color LED, obtaining the brush size LED (if it is on), and drawing on an array. Finally, we output this array onto a monitor Initialization While the frames are being rapidly analyzed and processed, certain variables must be declared outside the large FOR loop, so that they may remain constant. One example is the color, if a color from the LED is detected, the color cannot change until further updated and therefore it must be saved outside the FOR loop. Furthermore, we must create an array for the input as well as an equivalent array for the output. We chose our input and output to have an array size of 640 x 480 pixels (X,Y). A larger array size will negatively affect the fluidity of drawing because the frames per second (FPS) will decrease Filtering This is the most important part of our project as well as the most problematic. We filter the inputted frame using the YUV color space. The definition of YUV is a color space in terms of one luma (Y ) and two chrominance (UV) components [6]. Simply put, the Y measures the brightness in the frame, while the UV measures the color. In comparison, all three components in the RGB (Red, Green, Blue) color space measures the color. Therefore, the importance of utilizing YUV is quite clear; the LEDs must be filtered out from the input by brightness. In addition, this allows us to differentiate the three LEDs by brightness. The tracking LED is the brightest, while the other two are dimmer. The tracking LED must be the brightest of the three LEDs so that there would be no confusion in which x,y coordinate to obtain from the three LEDs. Because the LEDs are assumed to be considerably brighter than anything else in the input frame, we set a high-end brightness filter. The output of which is shown in Figure 5. Figure 5. The Top image shows the frame before it is filtered. The bottom image is the output of the YUV filtering process. The white objects resemble the LEDs. From the outputted black and white image, the code is able to deduce which objects are LEDs. To recognize that the largest white object is the tracking LED, the code must first find the area of all three 11

13 white objects. The code obtains the area by recognizing each white pixel as a one and each black pixel as a zero. The white pixels (represented by one) are considered as contours. By adding all the ones that are connected (without any zeroes in between neighboring ones), we are left with the area of each white object. The function, cv2.findcontours outputs the (X,Y) coordinate location of the contours while cv2.contourarea outputs the area of all the contours. Fortunately, findcontours groups contours that are neighboring each other. For example, in Figure 5. it would group all the white pixels in the middle circle as one contour. Therefore as a result, the code finds the contourarea for three contours Functionality Each area is sorted. The largest area is the tracking LED, because it is the brightest. The X,Y coordinates are obtained so that the user can draw at the corresponding location. The second largest area is obtained so that we can find the RGB values from the second LED. The X,Y coordinates of the second largest area is taken from the second largest contour area, so the RGB values can be retrieved at the corresponding array point. For brush size to increase, all the user needs to do is press a button to turn on the third LED. Therefore, it is not necessary to calculate the area of the third white object. Instead, the code just needs to recognize a third white object. If the third white object is recognized (shown in Figure 5), the brush size can be incremented. Finally, the code can draw with the user specified brush size and color at the X,Y coordinate that has been obtained. It draws by editing the color values of the 640x480 output array Output This 640x480 output array is then ready to be displayed through a monitor. Of course, this is the process of analyzing, processing, and outputting only one frame that has been captured within milliseconds. Alas, the large FOR loop is necessary to display the next frame, and the next; this compilation of frames gives the viewers a steady stream of video output. Therefore, once it outputs the array, it goes back to the beginning of the loop to obtain the next frame. However, if the save button is pressed, the program saves the image and closes the program. 12

14 3. Design Verification 3.1 User Interface PWM Circuit There are a few requirements that needed to be tested for the PWM circuit. The first is for the PWM circuit to output a signal with a duty cycle from 0% to 100%. This was tested by using an oscilloscope and measuring between the output of the PWM circuit and ground. Since the potentiometer has a range of motion of about 315, the circuit was tested at various degrees: 0, 90, 180, and 315. The results are shown in Table 6 of Appendix C but the circuit was able to provide a duty cycle from 0% to 100% Since the color LED will be cycling between on and off, the requirement is for the frequency being over 70 Hz [7]. This was calculated using the waveforms from the PWM duty cycle test and requirement. The Red, Blue, and Green LEDs of the RGB LED was tested. The results are shown in Table 7 of Appendix D. The Blue and Green LEDs were able to pass the requirement of 70 Hz but the Red LED had instances of being under 70 Hz Power Supply Since the circuit works best when a steady power source is supplying the components, we made requirements for the power supply namely the output of the LM7805 voltage regulator should stay at a voltage of 5 V ± 0.2 V. Figure 6 shows the waveform of this output from an oscilloscope. 13

15 Figure 6. Output of Voltage Regulator. Max Voltage = V, Min Voltage = V Although the minimum voltage was a bit lower than was required, the power supply was still able to power the rest of the circuit. The lower voltage was most likely the cause of the load of many components on the power supply. 3.2 Data Analysis For the software end, pre-processing the inputted frame array is crucial for accuracy at a longer distance of usage (beyond 5 feet). Image flipping and image dilation are two examples of frame processing. Although crucial, flipping and dilating drastically lowers the frames per second (FPS) [8]. The frames per second standard (35 FPS) that we have set is important for the fluidity of drawing the brush size. The purpose of dilation is so that the LEDs are more accurate at a distance greater than five feet. At a distance greater than five feet, the camera s input of the LED becomes unreliable with specks of light, which is caused by outside light factors and angle changes. If we have chose not to implement dilation, we would see the benefit of a ten FPS increase, but the controller would then have to be limited to less than five feet. Figure 7 shows the after effect of dilation at a distance of five feet. The image flipping technique is explained in the Conclusion. 14

16 Figure 7. The before and after effect of dilation Fortunately, even with dilation we achieved 35 Frames per second. Frames per second is inversely proportional to the time it takes to complete the entire code. Thus, to obtain the frames per second, the code takes each evaluated frame and divides it by the time it takes to perform all of the code s calculations and functionalities (this is done consistently for all frames obtained by the large FOR loop). 1 f rame per second = t (2.5) Another crucial software implementation is obtaining a pure red, green, blue (RGB) value from our second LED in our array. The RGB color scale ranges from bland, washed out colors with a small red value to dark, too-close-to-black colors with too large of a green and blue value. Therefore, if we were to display red, such as the example shown in Figure 8, we would check if the red value is larger than the green, blue values, and set a filter to only display the red if the red value is greater than a value of 120, and the green and blue values are less than 100, which eliminates a bland red, or a red that is too dark. 15

17 Figure 8. The blue box represents the type and values of pure color we want for each of the RGB values. In this example, we are viewing the acceptable colors for red. To further confirm that the displayed or drawn color is accurate and pure, we draw on an equivalent colored background. For example, we would test if it was able to draw a pure red by drawing on a red background and we would compare the differences between the background and our marks. 16

18 4. Costs 4.1 Parts Table 2. Parts Costs Part Manufacturer Retail Cost ($) Bulk Purchase Cost ($) Actual Cost ($) 9V Battery(4 pack) Duracell LM7805 Voltage Fairchild Regulator Semiconductor Push Button x2 Sparkfun SPDT Switch ECE Services Shop RGB LED x3 Lucky Light Potentiometer ECE Services Shop (100kΩ) x3 1N5818 Diodes x8 ECE Services Shop kΩ Resistor x4 ECE Services Shop kΩ Resistor 2 ECE Services Shop kΩ Resistor x4 ECE Services Shop nF Capacitor x8 ECE Services Shop AC14 Schmitt Texas Instruments Trigger Inverter x3 Raspberry Pi 3 Raspberry Pi Model B Raspberry Pi Raspberry Pi Camera Module 32GB microsd SanDisk Total Labor Table 3. Labor Costs Name Hourly Rate Total Hours Invested Total Cost (Rate*2.5*Hours) Willie Zeng $ $17,

19 Joseph Xiong $ $17, TOTAL $35,

20 5. Conclusion 5.1 Accomplishments Our final product was working as expected with a few minor bugs. These bugs will be introduced in Future Work as well as their possible solutions. As for achievements in functionality, the Light Brush was able to draw accurately up to six feet. However, the color accuracy was limited to five feet. We were able to display a rich color of red, green, blue at the optimum range from two to five feet. If the user decides to draw beyond five feet, the color would become more bland and dull. The drawings however, were very smooth. We had an average of forty-five frames per second (FPS), which is ten FPS more than our proposed thirty-five FPS and fifteen FPS more than the standard for a television or movie. At first we struggled to get above twenty FPS, but with the assistance of our TA, Henry Duwe, we realized we could implement our functionalities in a more efficient manner. For example, originally, the software outputted a video that was flipped across the Y-axis in the user s perspective. The reason for this is because the camera is capturing everything in the perspective of the camera, which is facing the viewer. Hence, if the user moves the remote left, in the camera s perspective, the remote is moved to the right. Therefore, flipping the input image or output image was necessary to display the drawing. Although fixing the initial problem, the FPS problem arose. Using the flip image function was too costly because all the data originally stored in the array needed to be moved to the other side of the Y-axis. Also, we only needed to flip a single x coordinate of the tracking LED across the Y axis, not the entire image. We solved this issue by subtracting the x coordinate of the tracking LED from the max X value (640). The distance between these two points is then added to the minimum x value (0). An example is shown in Figure 6. By using this algorithmic method, we did not need to flip the entire image, which boosted our program by ten FPS. 19

21 Figure 9. The method in flipping the tracking coordinates without flipping the entire Image. The physical LED controller was constructed with enough distance between the three LEDs so that each brightness would not affect one another. Furthermore, the electrical components of the LEDs and their corresponding control worked exactly as planned. All red, green, and blue colors could be configured and mixed when the user configured the potentiometers. The buttons and switches were fully functional. 5.2 Uncertainties As electrical engineers, this project allowed us to explore the software frontier. This was a field that we were limited in knowledge on and wanted to use this opportunity to learn more. The coding aspect in our project was difficult as none of us had experience in Python and OpenCV. Trial and error was done multiple times to filter the LEDs correctly. We had difficulties obtaining only the brightness of the LEDs. Because our filter accepted a range of brightnesses, we sometimes mistakenly obtained the coordinates of a bright metallic object rather than our tracking LED. Calibrating the colors from the remote control with the software on the Raspberry Pi also involved the process of trial and error. Although we were able to obtain the colors accurately, we were only able to do so at a certain distance. Beyond 5 feet, the colors would be inaccurate and bland. Furthermore, the colors would update rapidly when the user draws. This is because the program is constantly searching for a different color to update its previous color. Moreover, the software relies on a camera and light, even the slightest angle change from the controller can be enough to alter what color the camera initially perceived from the LED. 5.3 Ethical considerations Our main ethical statement is, We will communicate honestly and with interest to improve our project, while following and properly citing guidelines, standard operating procedures, and datasheets. This is because our project uses a large amount of outside sources such as guides in the OpenCV library as well as LED datasheets. It is our duty to produce a completely original code and credit references when used. This statements goes hand in hand with numbers three and seven in the IEEE Code of Ethics [9]. 3. To be honest and realistic in stating claims or estimates based on available data. 7. To seek, accept, and offer honest criticism of technical work, to acknowledge and correct errors, and to credit properly the contributions of others. We adhere to statements three and seven by updating our notebooks frequently to indicated design changes and show our process of thinking. Furthermore, when we do not understand components or functionalities, we ask our TA, Henry Duwe for his honest technical opinion. We have come a long way 20

22 from the beginning of the project to our completed project. Ever since the first day we started on this project we have improved our project by abiding numbers five and six of the code of ethics. 5. To improve the understanding of technology; its appropriate application, and potential consequences. 6. To maintain and improve our technical competence and to undertake technological tasks for others only if qualified by training or experience, or after full disclosure of pertinent limitations. Originally, without any configuration in the resistor values, the LEDs shined too bright. Looking at the LED directly at a close range would damage the human eye. Fortunately, we changed the brightness of the LEDs so looking at the LEDs directly would not pose a health issue, which follows the ninth code in the IEEE code of ethics. 9. To avoid injuring others, their property, reputation, or employment by false or malicious action. 5.4 Future work On the LED controller end, the only improvement would be adding an ON/OFF button for the power supply, which would save battery power when the controller is not in use. Through our demonstrations, we have witnessed that the detection of color as well as the dependency on light buggy. For example, the color would become increasingly more bland as the distance increased between the camera and the remote. Also, because the filtering process on the software is so dependent on light, any object with a brightness high enough can be mistaken for an LED. This includes sunlight reflections off metallic or white objects creating glare as well as other LEDs or lights. Because the software relies so heavily on bright objects, it would often get confused between a shiny metallic object and the actual LED which it needs to detect. A better filter on the software end can be implemented to improve differentiating the two objects. An improved filter can be made for the color detection as well, especially for making the colors more pure. For example, when a color is detected at a distance of greater than five feet, and if the red values are greater than the blue and green, proportionally boost the red value. However, both these implementations will not completely remove the bugs. Therefore, to completely improve the accuracy of (wireless) signalling between the remote controller and the software on the Raspberry Pi, it would be best to use a gyroscope, accelerometer, and a bluetooth transmitter and avoid using any LEDs so the software would no longer be dependent on bright objects.. 21

23 22

24 References [1] Cintiq 27QHD Touch, Wacom. N.p., Available at: [2] Wii U Console, Nintendo. N.p., Available at: [3] CMOS Cameras, Thorlabs, Inc., Newton, NJ. Available at: [4] 3-Terminal 1A Positive Voltage Regulator, Fairchild Semiconductor Available at: [5] 74AC14 Hex Inverter with Schmitt Trigger Input, Fairchild Semiconductor Available at: [6] YUV, Wikipedia. Wikimedia Foundation. Available at: [7] Flicker Fusion Threshold, Wikipedia. Wikimedia Foundation. Available at: d [8] Frame Rate, Wikipedia. Wikimedia Foundation. Available at: [9] IEEE IEEE Code of Ethics, IEEE. N.p., Available at: [10] 7414 Data sheet, Texas Instruments Available at: 23

25 Appendix A Requirement and Verification Table Table 4. System Requirements and Verifications Requirement Verification Verificatio n status (Y or N) 1. The output of the PWM has a duty cycle ranging from 0% to 100% 1. Measure between the output of the PWM circuit and ground using an oscilloscope at varying potentiometer resistances. Calculate duty cycle using Equation 2.3 Y 2. At all levels of resistance for the potentiometer, the frequency of the PWM output is never lower than 70 Hz a. Valid for Red LED b. Valid for Green LED c. Valid for Blue LED 3. All seven mixtures of light (Red, Green, Blue, Yellow, Cyan, Magenta, White) are able to be outputted by the RGB LED 4. The power supply with voltage regulator stays at 5 V ± 0.2 V 2. Use the waveform from R&V test 1 and calculate the frequency using Equation For each color, a picture will be taken of the controller outputting that color then a filter will be placed on the image where the mask will have the corresponding color value greater than 150 (out of 255). For example, when testing Yellow, a filter of Red and Green greater than 150 and Blue at 0. If the color LED in the image passes through the filter, the color is verified. 4. Use an oscilloscope to measure the output of the voltage regulator and measure the maximum and minimum voltages. N Y Y Y N (but very close) 24

26 5. The code must run at an average of 35 Frames per second; Each function must be run through (pre-processing, filtering, displaying, etc.) at 35 Frames Per Second +/- 5 FPS 6. The Tracking of LED must be able to be detected at up to 6 feet and if the user can draw at a distance of 6 feet 7. The color LED must have an acceptable color ( acceptable color is defined and discussed in section 3.2 Data Analysis) 5. Set a timer ( time.time()) to time the entire code from start to finish, starting on when it obtains the frame and ending at when it displays the array. F rames per second = 1 must be equal to 35 time 6. Check to see if the (X,Y) coordinates are being constantly updated as the tracking LED is moved at a distance of 6 feet. If this distance does not work, start from 3 feet and work your way up to 6 feet by adding 1 foot at a time. 7. Test by drawing the color onto an equivalent colored background to see if the color drawn is +/- 10 values from the background color. I.e if the color is red, draw on a red background if the drawn red value is 110 and the background red value is 50, the implementation has failed Y Y Y 25

27 Appendix B Calculating Duty Cycles The duty cycle of the PWM circuit was calculated using Equations 2.1, 2.2, and 2.3. First the resistance of the potentiometer was taken at varying degrees (0, 90, 180, 315 ). Note that there are two resistances for the potentiometer at a certain position. Then using the datasheet of the 74AC14 Schmitt Trigger Inverter [10], the threshold voltage was found and is used in the equation as V c. Afterwards, the duty cycle was found. Table 5. Calculating Duty Cycles Degree R charge R discharge t charge (Vt+ = 1.7 V) t discharge (Vt- = 0.9 V) Duty Cycle Ω kω.19 μs 18.3 ms.001% kω kω μs ms 17.1% kω kω 3.67 ms 4.98 ms 42.43% kω 4.2 Ω 4.4 ms.72 μs 99.98% 26

28 Appendix C PWM Duty Cycle Results Note: the signal is inverted so all waveforms will be inverted. Figure 10. Red LED at 0 27

29 Figure 11. Red LED at 90 Figure 12. Red LED at 180 Figure 13. Red LED at

30 Figure 14. Green LED at 0 Figure 15. Green LED at 90 29

31 Figure 16. Green LED at 180 Figure 17. Green LED at

32 Figure 18. Blue LED at 0 Figure 19. Blue LED at 90 31

33 Figure 20. Blue LED at 180 Figure 21. Blue LED at 315 Table 6. PWM Duty Cycle Results Duty Cycle Red LED at 0 100% 32

34 Red LED at % Red LED at % Red LED at 315 0% Green LED at 0 100% Green LED at % Green LED at % Green LED at 315 0% Blue LED at 0 100% Blue LED at % Blue LED at % Blue LED at 315 0% 33

35 Appendix D PWM Frequency Results Using the waveforms taken from Appendix C, the period was found and frequency was calculated using Equation 2.4. Table 7. PWM Frequency Results Frequency Red LED at 0 Red LED at 90 Red LED at 180 Red LED at 315 Green LED at 0 Green LED at 90 Green LED at 180 Green LED at 315 Blue LED at 0 Blue LED at 90 Blue LED at 180 Blue LED at Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz Hz 34