The Gauss Hypergeometric Ratio As a Positive Real Function

1982 ◽  
Vol 13 (6) ◽  
pp. 1024-1040 ◽  
Author(s):  
Vitold Belevitch
Keyword(s):  
Real Function ◽  
Positive Real ◽  
Positive Real Function

Passive Synthesis of a Class of Fractional Immittance Function Based on Multivariable Theory

2018 ◽  
Vol 27 (05) ◽  
pp. 1850074 ◽  
Author(s):  
Guishu Liang ◽  
Yongming Jing ◽  
Chang Liu ◽  
Long Ma
Keyword(s):  
Real Function ◽  
Traditional Method ◽  
Synthesis Method ◽  
Important Research ◽  
Research Topics ◽  
Positive Real ◽  
Passive Synthesis ◽  
Positive Real Function ◽  
Variable Substitution ◽  
New Variables

Passive synthesis of fractional driving-point immittance function is one of the most important research topics in fractional circuits. The synthesis method for a class of fractional driving-point immittance function is proposed in this paper. Firstly, the immittance function of passive fractional circuit is transformed to multivariable positive-real function by proper variable substitution. Secondly, to synthesize the function, except one variable, other high-order variables are transformed to the combination of products of different one-order variables by introducing new variables. Thirdly, synthesize the new function by traditional method. At last, substitute elements inversely twice and the final circuit for fractional driving-point immittance function can be achieved. The method is verified by giving synthesis demonstration.

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