本論文針對具有完美隔離度的功率分配器進行了研究並提出設計方法。我們發現這類電路可以被轉換成一個對稱電路，這電路的兩輸出埠之間會有兩條幾乎完全相同的訊號路徑，唯一差別是一個1:-1變壓器。以此對稱關係，我們可以更系統化地設計等功率與不等功率分配器。而後者我們可以進一步簡化，成為一個斜對稱電路，相較於其他設計，這電路裡的傳輸線阻抗值差異較小，將更適合於高功率比分配器的應用。此外由於上述的對稱性，我們可以對輸入以及隔離埠進行奇偶模態分析，結果顯示其中一輸出埠的響應只跟偶模態有關，而另一輸出埠響應只由奇模態決定，因此能設計出左右不等頻寬的功率分配器。最後本論文利用幾個設計實例當作示範，並以電磁模擬與電路實作量測，成功驗證了上述觀點與設計步驟。

In this thesis, the design procedures of power dividers with perfect isolation have been developed. It is found that these circuits could always be converted into an equivalent one with two identical signal paths between its two output ports, if the 1:-1 transformer on one of the paths is ignored. Based on this symmetry, we have developed the design procedures of equally- and unequally-split power dividers. It is found that the latter could be simplified into a skew symmetric one with lower transmission-line impedance variation than other designs. Thus, it is more suitable for high power-split ratio applications. Also, with the help of aforementioned symmetry, we may apply the even-odd mode analysis to its input and isolation (dummy load) ports. The result shows that the responses of one output port are only related to the even-mode half circuit, while those of the other are only determined by the odd-mode equivalent. Therefore, it is possible to design a power divider with different bandwidths at two output ports. To validate these concepts and procedures, several examples are designed and successfully verified by electromagnetic simulations and experiments.

[1.1] E. J. Wilkinson, "An N-way hybrid power divider," IEEE Trans. Microwave Theory and Tech. vol. MTT-8, pp. 116-118, Jan. 1960.
[1.2] U. H. Gysel, "A new N-way power divider/combiner suitable for high-power application," IEEE MTT-S Int. Microw. Symp. Dig., vol. 75, pp. 116-118, May 1975.
[1.3] B. Ooi , W. Palei, and M. S. Leong, "Broad-banding technique for in-phase hybrid ring equal power divider", IEEE Trans. Microwave Theory Tech., vol. 50, no. 7, pp. 1790-1794, July 2002.
[1.4] H. Oraizi and A. R. Sharifi, "Optimum design of asymmetrical multisection two-way power dividers with arbitrary power division and impedance matching," IEEE Trans. Microwave Theory and Techniques, vol. 59, no. 6, pp. 1478-1490, June 2011.
[1.5] S. -F. Chao and Y. -R. Li, "Miniature filtering power divider with increased isolation bandwidth," in Electronics Letters , vol.50, no.8, pp.608-610, April 10 2014.
[1.6] J. -C. Kao, Z. -M. Tsai, K. -Y. Lin, and H. Wang, "A Modified Wilkinson Power Divider With Isolation Bandwidth Improvement," in Microwave Theory and Techniques, IEEE Transactions on , vol.60, no.9, pp.2768-2780, Sept. 2012.
[1.7] C. J. Trantanella, "A novel power divider with enhanced physical and electrical port isolation," in Microwave Symposium Digest (MTT), 2010 IEEE MTT-S International , pp.129-132, 23-28 May 2010.
[1.8] C. -F. Chen and C. -Y. Lin, "Compact Microstrip Filtering Power Dividers With Good In-Band Isolation Performance," in Microwave and Wireless Components Letters, IEEE , vol.24, no.1, pp.17-19, Jan. 2014.
[1.9] B. -C. Yang, Synthesis and Analysis of Gysel Power Divider, National Cheng Kung University, Thesis for Master of Science, July 2013.
[2.1] E. J. Wilkinson, "An N-way hybrid power divider," IEEE Trans. Microwave Theory and Tech. vol. MTT-8, pp. 116-118, Jan. 1960.
[2.2] U. H. Gysel, "A new N-way power divider/combiner suitable for high-power application," IEEE MTT-S Int. Microw. Symp. Dig., vol. 75, pp. 116-118, May 1975.
[2.3] B. -C. Yang, Synthesis and Analysis of Gysel Power Divider, National Cheng Kung University, Thesis for Master of Science, July 2013.
[2.4] R. Levy and J. Helszajn, “Specific equations for one and two section quarter-wave matching networks for stub-resistor loads,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, no. 1, pp. 55-63, Jan. 1982.
[2.5] M. C. Horton and R. J. Wenzel, "General theory and design of optimum quarter-wave TEM filters," IEEE Trans. Microwave Theory and Techniques, vol. MTT-13, pp.316-327, May 1965.
[2.6] G. L. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance-Matching Network, and Coupling Structure. McGraw-Hill, New York, 1964, Chap. 5, pp. 220.
[3.1] B. -C. Yang, Synthesis and Analysis of Gysel Power Divider, National Cheng Kung University, Thesis for Master of Science, July 2013.
[3.2] U. H. Gysel, "A new N-way power divider/combiner suitable for high-power application," IEEE MTT-S Int. Microw. Symp. Dig., vol. 75, pp. 116-118, May 1975.
[3.3] E. J. Wilkinson, "An N-way hybrid power divider," IEEE Trans. Microwave Theory and Tech. vol. MTT-8, pp. 116-118, Jan. 1960.
[3.4] R. Levy and J. Helszajn, “Specific equations for one and two section quarter-wave matching networks for stub-resistor loads,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, no. 1, pp. 55-63, Jan. 1982.
[3.5] J. J. Taub and B. Fitzgerald, “A note on n-way hybrid power divider,” IEEE Trans. Microw. Theory Tech., vol. 12, no. 2, pp. 260-261, Jan. 1964.
[3.6] C. -F. Chen and C. -Y. Lin, "Compact Microstrip Filtering Power Dividers With Good In-Band Isolation Performance," in Microwave and Wireless Components Letters, IEEE , vol.24, no.1, pp.17-19, Jan. 2014.
[3.7] R. B. Ekinge, “A new method of synthesizing matched broad-band TEM-mode three-ports,” IEEE Trans. Microwave Theory Tech., vol. MTT-19, pp. 81-88, Jan. 1971.
[3.8] R. Sato and E. G. Cristal, “Simplified Analysis of Coupled Transmission-Line Networks,” IEEE Trans., Microwave Theory and Techniques, vol.18, no.3, pp. 122-131, March 1970.
[4.1] B. -C. Yang, Synthesis and Analysis of Gysel Power Divider, National Cheng Kung University, Thesis for Master of Science, July 2013.
[5.1] B. -C. Yang, Synthesis and Analysis of Gysel Power Divider, National Cheng Kung University, Thesis for Master of Science, July 2013.
[5.2] C. -F. Chen and C. -Y. Lin, "Compact Microstrip Filtering Power Dividers With Good In-Band Isolation Performance," in Microwave and Wireless Components Letters, IEEE , vol.24, no.1, pp.17-19, Jan. 2014.