使用單埠量測結果重建多埠電路之散射矩陣

Abstract

本論文提出以多個單埠之散射參數量測，據以重建多埠被動及主動電路之散射矩陣。降埠法係使用埠數少於n 埠之網路分析儀，以獲得一n 埠電路之散射矩陣，已知適用降埠法之網路分析儀埠數，最少為雙埠或三埠，本論文則將埠數進一步降至單埠，即最低埠數。 第二章闡述對一雙埠電路，如何使用輔助電路及單埠終端器，由多個單埠散射參數，重建該雙埠電路之散射矩陣。其重建結果進一步應用於降埠法，由多個單埠散射參數量測值，重建n 埠電路之散射矩陣。由於使用單埠終端器，對於主動電路可能造成振盪，因此本章亦敘述雙埠主動電路之散射矩陣重建方法。最後，對於多埠互易電路，則提出可不使用降埠法，重建其n 埠散射矩陣。 由於輔助電路在降低量測埠數至單埠極為重要，第三章則討論輔助電路之影響，藉由適當選擇輔助電路，可降低單埠量測實驗數目，減低重建時數值運算之困難，以及增加重建結果之準確性。 第四章則敘述四個實驗實例。包含三埠被動互易電路，三埠被動非互易電路以及雙埠主動電路。重建結果與直接散射矩陣量測結果比較，顯示其一致性，重建誤差亦予以討論。

In this dissertation, study results to reconstruct the scattering matrix (S-matrix) of a multiport network from a set of one-port scattering parameter (S-parameter) measurements are presented. Port reduction method (PRM) is a method to acquire the S-matrix of an n-port network by using a reduced port vector network analyzer (VNA). PRMs have shown that the minimum number of port of a VNA is two or three. This study attempts to go one step further to reduce the number of port to be one, which is the lowest number. In Chapter 2, reconstruction method using auxiliary circuits and one-port terminations to solve the S-matrix of a two-port network is described. The type-II PRM is then applied to the results for the reconstruction of the S-matrix of an n-port network. Since the terminations used in one-port measurement may cause an active network oscillation. Further development on reconstructing a two-port active network is given. Finally, the method in reconstructing the S-matrix of a multiport reciprocal network without using PRM is also presented. The use of auxiliary circuits plays an important role in reducing the number of measured port to be one. The effects of the auxiliary circuits are discussed in Chapter 3. By properly selecting the auxiliary circuit, one can reduce the number of one-port measurements, ease the problem encountered in the reconstruction, and increase the accuracy of the reconstructed results. Chapter 4 presents four experimental examples to verify the developed reconstruction methods. They include a three-port reciprocal network, a passive nonreciprocal network and a two-port active network. The reconstructed results are compared with the directly measured S-matrices. They are shown in good agreement. Errors of reconstructed results are also discussed.