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dbr:PR
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dbr:Positive-real_function
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Positive-real function 正實函數
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Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis. They are complex functions, Z(s), of a complex variable, s. A rational function is defined to have the PR property if it has a positive real part and is analytic in the right half of the complex plane and takes on real values on the real axis. In symbols the definition is, In electrical network analysis, Z(s) represents an impedance expression and s is the complex frequency variable, often expressed as its real and imaginary parts; 正實函數（Positive-real functions）的縮寫是PR函數或是PRF，是在電路分析中會出現的一種數學函數。正實函數是複數函數Z(s)，其變數s也是複數。有理函數若在複平面的右半邊都有正的實部，且可解析，在實軸上都為實數，就是正實函數。 其定義可以表示為下式： 在電路分析中Z(s)表示阻抗，而s為S平面變數，也常用其實部及虛部表示： 則正實函數的定義會改為下式： 正實函數在電路分析的重要性在於正實函數的條件也就是電路可實現性的條件。Z(s)可實現為有理阻抗若且唯若其符合正實函數的條件。此情形下的可實現表示可以用有限個分立理想的被動線性元件（以電路來說就是電阻器、电感元件、电容器）來實現。
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正實函數（Positive-real functions）的縮寫是PR函數或是PRF，是在電路分析中會出現的一種數學函數。正實函數是複數函數Z(s)，其變數s也是複數。有理函數若在複平面的右半邊都有正的實部，且可解析，在實軸上都為實數，就是正實函數。 其定義可以表示為下式： 在電路分析中Z(s)表示阻抗，而s為S平面變數，也常用其實部及虛部表示： 則正實函數的定義會改為下式： 正實函數在電路分析的重要性在於正實函數的條件也就是電路可實現性的條件。Z(s)可實現為有理阻抗若且唯若其符合正實函數的條件。此情形下的可實現表示可以用有限個分立理想的被動線性元件（以電路來說就是電阻器、电感元件、电容器）來實現。 Positive-real functions, often abbreviated to PR function or PRF, are a kind of mathematical function that first arose in electrical network synthesis. They are complex functions, Z(s), of a complex variable, s. A rational function is defined to have the PR property if it has a positive real part and is analytic in the right half of the complex plane and takes on real values on the real axis. In symbols the definition is, In electrical network analysis, Z(s) represents an impedance expression and s is the complex frequency variable, often expressed as its real and imaginary parts; in which terms the PR condition can be stated; The importance to network analysis of the PR condition lies in the realisability condition. Z(s) is realisable as a one-port rational impedance if and only if it meets the PR condition. Realisable in this sense means that the impedance can be constructed from a finite (hence rational) number of discrete ideal passive linear elements (resistors, inductors and capacitors in electrical terminology).
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