本篇論文探討以直交表(Orthogonal Array,OA)進行迭代設計，目標在設計一符合FCC規格頻段要求(3.1GHz~10.6GHz)的超寬頻(UWB)單極小天線之設計，期待能在有限且少量的迭代次數內，使天線特性達到UWB頻段的要求。本研究採用平面式的結構，針對厚0.8mm的FR4基板（相對介電係數為4.4、Dielectric Loss Tangent為0.02）的環境來進行設計、模擬，並和實作結果相驗證，以快速研製一體積小、重量輕、低成本、容易製作的超寬頻帶(UWB)單極小天線。
首先依據UWB單極天線的結構，選定待設計/調控之結構參數以及每一參數之位準(level)個數，據此建立一適當的直交表。再以電磁模擬軟體進行直交表所列的部份因子實驗及少量而有限次數的迭代，針對模擬結果計算不同實驗之適應值，以進行天線參數最佳化，並規劃在少量而有限的迭代次數後，判斷是否已達到UWB頻段規格要求的目標。
與其它參數設計法則相較，直交表最大的特色在於每個參數因子的位準出現的次數均等，當以此特性來取代全因子實驗，此方法可達到降低搜尋次數、加快參數設計流程，又可維持對問題解空間的進行全域搜尋。為此，一般皆藉由直交表均勻搜尋的概念，再結合逐步縮減搜尋範圍(Range Reduction)的技巧，以落實最佳化搜尋。
本論文除了根據待定參數因子在某些選定頻率點的回應表進行最佳化的迭代搜尋，並引進隨機亂數（高斯分佈）以修正參數因子的位準(level)值，藉由此一在直交表結合引入亂數的作法，以及多段式的範圍縮減技巧等，目的在使其收斂過程更有效率及/或收斂結果更接近全域之最佳解。

This thesis investigates a new antenna design method by utilizing the orthogonal array (OA) for a small ultra-wideband (UWB) monopole antenna that meets the frequency band (3.1GHz~10.6GHz) of FCC requirements. By application of the OA in the design course of iterative procedure, it is found that the antenna characteristics can meet the requirements of UWB band within limited and relatively few iterations. In this study, a planar structure is tested under the enviroment of FR4 substrate with thickness of 0.8mm and relative dielectric coefficient 4.4, dielectric loss tangent 0.02. An UWB antenna is designed, simulated, and fabricated. The simulated results are verified by experimental ones. The goal is to examine a systematic approach to design an antenna structure by avoiding blind try-and -error. In this case, the objective is to quickly develop a small , light weight, low cost UWB monopole small antenna.
        At first, based on the structure of the UWB monopole antenna to be examined, we can select suitable design/control parameters, and reasonable number of level for each parameter, thus an appropriate orthogonal array is established. Then through electromagnetic simulation software we can conduct the fractional factorial “experiments“ listed in the orthogonal array such that the fore-mentioned limited and relatively few number of iterations can be performed. The simulation results can then be used to calculate the fitness value of each experiment for sucessive optimization of the antenna parameters. At the end of each iteration/generation, the best canditate is updated and checked to see whether it has reached the design goal – to meet the requirements of UWB frequency band.
        As compared to other methods of parameter design, the distinguished characteristic of utilizing orthogonal array for parameter design is that the number of occurrences of each parameter level is the same and/or equally-balanced for every parameter.  When this method is employed to replace the full factorial experiment, it can reduce search times very effectively. In addtion to the speed up for the parameter design process, the method employed also maintain the global search for the solution space. To this end, the characteristic of uniform/balanced searching through the utilization of orthogonal array is combined with the technique of range reduction (gradual reduction of the search range iteratively) to implement the optimal search. 
        This thesis not only carried out the iterative optimization search for the unknown design parameters according to the response table of the design parameters at several selected frequencies, but also proposed the introduction of the random numbers (Gaussian distribution) to modify the parameters levels. By the combination of random numbers with the orthogonal array, plus multi-stage technique of range reduction, the goal is aim to make the convergence process more efficient, within limited number of iterations, and/or the convergence result is closer to the optimal solution.

目錄

中文摘要．．．．．．．．．．．．．．．．．．．．．．．．．．．I
英文摘要．．．．．．．．．．．．．．．．．．．．．．．．．．． III
第一章	序論．．．．．．．．．．．．．．．．．．．．．．．．． 1
1.1	簡介．．．．．．．．．．．．．．．．．．．．．．．．． 1
1.2	研究背景．．．．．．．．．．．．．．．．．．．．．．． 1
1.3	論文架構．．．．．．．．．．．．．．．．．．．．．．． 7

第二章	平面寬頻單極天線之設計原理．．．．．．．．．．．．．． 8
2.1	設計原理分析．．．．．．．．．．．．．．．．．．．．． 8
2.2	傳統寬頻天線的演化．．．．．．．．．．．．．．．．．． 13
2.3	全平面正方形單極天線初始結構的計算．．．．．．．．．．17
2.4	天線接地面和金屬貼片的結構參數原理分析．．．．．．．．19
2.5	連續直交表．．．．．．．．．．．．．．．．．．．．．．24

第三章	以連續直交表進行天線參數最佳化．．．．．．．．．．．．29
3.1	簡介．．．．．．．．．．．．．．．．．．．．．．．．29
3.2	設計天線參數及位準進行連續直交表的迭代．．．．．．．29
3.3	延伸連續直交表的迭代次數．．．．．．．．．．．．．．34
3.4	重新設計天線參數進行連續直交表的迭代．．．．．．．．42
3.5	將連續直交表位準引入亂數．．．．．．．．．．．．．．63
3.6	將連續直交表位準引入三次亂數．．．．．．．．．．．．79

第四章	結論．．．．．．．．．．．．．．．．．．．．．．．．．84


圖目錄

圖 1.1無線通訊技術之(a)寬頻 (b)空間訊息量比較．．．．．．．．2
圖 2.1無窮長偶極圓錐形天線之立體結構．．．．．．．．．．．．． 11
圖 2.2有限長度h的偶極圓錐形天線．．．．．．．．．．．．．．． 12
圖 2.3（a）有限長度偶極天線（b）類比成有限長傳輸線．．．．．． 12
圖2.4 (a)λ/4單極天線(b)圓錐形天線(c)火山煙狀天線之二維結構圖．．．．．．．．．．．．．．．．．．．．．．．．．．．．14
圖 2.5 水滴狀天線之二維結構圖．．．．．．．．．．．．．．．．． 14
圖 2.6水滴狀天線的演化順序．．．．．．．．．．．．．．．．． 15
圖 2.7水滴狀天線的VSWR之頻率響應．．．．．．．．．．．．． 15
圖2.8水滴狀天線在（a）3GHz（b）6GHz（c）9GHz（d）12GHz 之輻射場型．．．．．．．．．．．．．．．．．．．．．．．．．．15
圖 2.9平面寬頻天線的演化圖．．．．．．．．．．．．．．．．． 16
圖 2.10圓柱體之立體結構，半徑為r、高度為L．．．．．．．．．． 17
圖 2.11矩形單極微帶天線的二維結構圖．．．．．．．．．．．．． 19
圖 2.12初始正方形單極天線的結構．．．．．．．．．．．．．．．21
圖 2.13接地面(ground)微小變動對S11參數之影響．．．．．．．．．22
圖2.14金屬貼片微小變動對S11參數之影響．．．．．．．．．．．．21
圖2.15初始正方形單極天線在間隙處由饋入線往金屬貼片端看入之阻抗圖．．．．．．．．．．．．．．．．．．．．．．．．．．．．23
圖2.16方形單極天線(g=0.7mm)由饋入線看入之Smith chart變化  圖．．．．．．．．．．．．．．．．．．．．．．．．．．．．23
圖2.17方形單極天線(g=0.7mm)之等效電路模型．．．．．．．．．24
圖2.18田口最佳化法流程圖．．．．．．．．．．．．．．．．．．28
圖3.1初始單極天線結構示意圖．．．．．．．．．．．．．．．．．30
圖3.2第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．31
圖3.3第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．31
圖3.4第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．32
圖3.5第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．32
圖3.6第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．33
圖3.7五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．．33
圖3.8修改天線參數後的天線結構示意圖．．．．．．．．．．．．．35
圖3.9第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．36
圖3.10第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．36
圖3.11第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．37
圖3.12第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．37
圖3.13第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．38
圖3.14五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．38
圖 3.15第六次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．39
圖3.16第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．39
圖3.17第六次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．40
圖3.18第七次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．40
圖3.19三次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．41
圖3.20重新設計參數後的天線結構示意圖．．．．．．．．．．．．46
圖3.21第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．46
圖3.22第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．47
圖3.23第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．47
圖3.24第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．48
圖3.25第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．48
圖3.26第六次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．49
圖3.27第七次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．49
圖3.28七次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．50
圖3.29第五次迭代(頻率點3.1GHz、6 GHz、7 GHz、8 GHz、9 GHz、10.6 GHz)做驗證實驗後的反射損耗圖．．．．．．．．．．．．．．．52
圖3.30第五次迭代(頻率點6GHz、7GHz、8GHz)做驗證實驗後的反射損耗圖．．．．．．．．．．．．．．．．．．．．．．．．．．．53
圖3.31針對頻率點6GHz、7GHz、8GHz再次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．．．．．．．．．．．．．．．．．53
圖3.32應用連續直交表最佳化後的天線結構示意圖．．．．．．．．54
圖3.33應用連續直交表最佳化後的天線結構實體圖．．．．．．．．54
圖3.34應用連續直交表最佳化後的天線反射損耗圖．．．．．．．．55
圖3.35應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@3.1GHz) ．．．．．．．．．．．．．．．．．．．55
圖3.36應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@4GHz) ．．．．．．．．．．．．．．．．．．．56
圖3.37應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@5GHz) ．．．．．．．．．．．．．．．．．．．56
圖3.38應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@6GHz) ．．．．．．．．．．．．．．．．．．．57
圖3.39應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@7GHz) ．．．．．．．．．．．．．．．．．．．57
圖3.40應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@8GHz) ．．．．．．．．．．．．．．．．．．．58
圖3.41應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@9GHz) ．．．．．．．．．．．．．．．．．．．58
圖3.42應用連續直交表最佳化於天線H-plane(X-Z平面)的輻射場型模擬與實測結果(@10.6GHz) ．．．．．．．．．．．．．．．．．．59
圖3.43應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@3.1GHz) ．．．．．．．．．．．．．．．．．．．59
圖3.44應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@4GHz) ．．．．．．．．．．．．．．．．．．．60
圖3.45應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@5GHz) ．．．．．．．．．．．．．．．．．．．60
圖3.46應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@6GHz) ．．．．．．．．．．．．．．．．．．．61
圖3.47應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@7GHz) ．．．．．．．．．．．．．．．．．．．61
圖3.48應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@8GHz) ．．．．．．．．．．．．．．．．．．．62
圖3.49應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@9GHz) ．．．．．．．．．．．．．．．．．．．62
圖3.50應用連續直交表最佳化於天線E-plane(Y-Z平面)的輻射場型模擬與實測結果(@10.6GHz) ．．．．．．．．．．．．．．．．．．63
圖3.51第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．66
圖3.52第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．67
圖3.53第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．67
圖3.54第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．68
圖3.55第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．68
圖3.56五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．69
圖3.57第四次迭代做驗證實驗後的天線結構示意圖．．．．．．．．69
圖3.58第四次迭代做驗證實驗後的天線結構實體圖．．．．．．．．70圖3.59第五次迭代做驗證實驗後的天線結構示意圖．．．．．．．．70
圖3.60第五次迭代做驗證實驗後的天線結構實體圖．．．．．．．．71
圖3.61第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．71
圖3.62第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．72
圖3.63第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．72
圖3.64第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．73
圖3.65第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．73
圖3.66五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．74
圖3.67第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．74
圖3.68第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．75
圖3.69第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．75
圖3.70第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．76
圖3.71第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．76
圖3.72五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．77
圖3.73第三次迭代做驗證實驗後的天線結構示意圖．．．．．．．．77
圖3.74第三次迭代做驗證實驗後的天線結構實體圖．．．．．．．．78
圖3.75第四次迭代做驗證實驗後的天線結構示意圖．．．．．．．．78
圖3.76第四次迭代做驗證實驗後的天線結構實體圖．．．．．．．．79
圖3.77第一次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．80
圖3.78第二次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．81
圖3.79第三次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．81
圖3.80第四次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．82
圖3.81第五次迭代做驗證實驗後的反射損耗圖．．．．．．．．．．82
圖3.82五次迭代實驗之反射損耗變化圖．．．．．．．．．．．．．83

表目錄

表 2.1　直交表OA(18,5,3,2) ．．．．．．．．．．．．．．．． 27
表 3.1  OA(18,5,3,2)在第一次迭代實驗之位準、適應值及訊號雜訊比．．．．．．．．．．．．．．．．．．．．．．．．．．．．51
表 3.2　第一次迭代實驗後經由計算所得之響應表．．．．．．．． 52
表 3.3　第一次迭實驗後代經由響應表所選取之最佳參數組合．．．． 52

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