An Easy Method to Discuss Properties of Simplified Solid-state Tesla Coil
Wireless transmission products are widely used in our daily life. In this research, we focus on knowing how solid-state tesla coil works in different conditions and finding the best parameters through an easy way. In our work, a commercial electroscope was used as detector for measuring the strength of radio wave created by our simplified tesla coils. In fact, many factors would lead to experimental erorrs such as detectors, selected types of NPN BJT components, applied voltage and measuring position of height. Therefore, all of the factors were under control to make sure of accuracy and precision for our designed measuring method. In our experiment, graphics of radio wave distribution around tesla coils were drew by mathemetic software of GeoGebra. It shows the BJT types of 2n2222 had good performance for wireless transmisstion efficiency. To our surprised, we found the extended wires (called antenna) from the top of tesla coil also had an ability to transfer electromagnetic energy, and had good retention if the extended wires were within the length of main coil’s height. Finally, the shape’s and size’s effect was determined by our testing work. The result shows that pipe’s length, pipe’s diameter and turns ratio of two coils had great influence on tesla coil’s transmission efficiency. It was found that the tesla’s performance would be more efficient if wire was used to make the length twice rather than make the diameter twice. However, the turns ratio of secondary coil to primary coil would change while making the length twice. To avoid that, we fixed the length and decrease the turns of primary coil. At last, we found tesla coil must work at the turns of primary coil higher than two. Furthermore, the frequency of radio wave not only had less relationship with their length or diameter but also had less relationship with types of BJT In our study, our handmade tesla coil was succesfully applied for wireless charging and we find that the induced voltage decrease in propotion to cube root of distance between tesla coil and induced coil.
以不定方程探討正三角形衍生圖形之無縫密鋪關係
本研究探討正三角形衍生圖形與拼板個數的關係。 一、以A和B拼板無縫密鋪由 塊邊長 正三角形組成水平衍生圖形,發現 (一) a是奇數 條件:至少需t個B拼板 最大拼板數:A拼板(at^2-3t)/2個和B拼板t個(2▲1▼) 範圍:A拼板(at^2-3t)/2-3k個和B拼板t+k個(2▲1▼)、k個(1▲2▼) (二) a是偶數 條件:需要偶數個B拼板且兩類型個數相等 最大拼板數:A拼板(at^2)/2個 範圍:A拼板a/2 t^2-3k個和B拼板兩類型各k個 (三) 解的存在性 除a=1_ ,t=1與a=1_ ,t=2外,其餘必有解存在。 二、增加拼板種類 無縫密鋪邊長 正三角形衍生圖形,需 拼板m,n,p,q個, 則2m+3n+4p=at^2或2m+3n+8q=at^2 解的判斷法則 步驟1:找最大拼板的個數範圍 步驟2:根據最大拼板個數切割圖形,將剩餘區域切成可無縫密鋪圖形,最後剩餘不為 或 ,則可無縫密鋪 步驟3:利用n的奇偶性,計算A、B拼板。