TDR 可使用插入媒質的探測器，而用於同時測量電介質常數和導電率。   需要了解探測器的空氣間隔特性阻抗，才能夠自TDR波型最終值得到導電率，使用衍生自同軸纜線的不平衡探測器裝置就許多的應用裝置而言，最好使用一般均勻空隙間隔的纜線設計，來取代其外覆設計，因為這可排除不平衡轉換器的使用需求。到目前為止，即需要測量探測器的特性阻抗，或校準其已知導電率的精確度。本文說明如何藉由保形變換來降低探測器特性阻抗的情形。就細線路而言，可導出更簡單的公式，該公式則適用於手動計算。這些分析現象的精確度可藉由動量數值的精確度來評估，該數值在加入超基準函數，即可表現非常快速的收斂情形。保形變換所得到的特性阻其細線路的近似值，可發現其精確度可分別達到0.1%和1 %之間，作為所有研究報告指出的現場探測器作業而言，本結果即有助於使用不平衡探測器作為土壤鹽度的監控裝置。


Abstract—TDR is applicable for simultaneous measurements of both dielectric constant and conductivity with  a probe inserted into the medium. The air-spaced characteristic impedance of the probe is required to estimate the conductivity from the final value of the TDR waveform. Unbalanced probes derived from a coaxial line by replacing the outer shield with regularly spaced wires are favored for many applications due to saving the need for a balun.  Until now, it has been necessary either to measure probe characteristic impedance or to calibrate with already known conductivity for solution.  This paper shows how to deduce an expression for the probe characteristic impedance by using a conformal transformation.  For thin wires, a simpler formula suitable for manual calculation   has been derived.  The accuracy of these analytic expressions has been assessed by means of moments numerical solution which exhibits very rapid convergence as extra basis functions are added. The characteristic impedance formula obtained by conformal transformation and its thin wire approximation are found to be accurate to 0.1% and 1%, respectively, for all field probes reported. This will be helpful for the use of unbalanced probes in applications such as monitoring of soil salinity.

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