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Schwarz lemma for driving point impedance functions and its circuit applications
Author(s) -
Örnek Bülent Nafi,
Düzenli Timur
Publication year - 2019
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.2616
Subject(s) - mathematics , electrical impedance , mathematical analysis , function (biology) , lemma (botany) , point (geometry) , analytic function , topology (electrical circuits) , combinatorics , geometry , engineering , electrical engineering , ecology , poaceae , evolutionary biology , biology
Summary In this paper, a boundary version of the Schwarz lemma is investigated for driving point impedance functions and its circuit applications. It is known that driving point impedance function, Z ( s ) = 1 + c p ( s − 1) p + c p + 1 ( s − 1) p + 1 + ..., p > 1, is an analytic function defined on the right half of the s‐ plane. Two theorems are presented using the modulus of the derivative of driving point impedance function, | Z ′ (0)|, by assuming the Z ( s ) function is also analytic at the boundary point s = 0 on the imaginary axis with Z 0 = 0 . In the obtained inequalities, the value of the function at s = 1 and the derivatives with different orders have been used. Finally, the sharpness of the inequalities obtained in the presented theorems is proved. Simple LC circuits are obtained using the obtained driving point impedance functions.