Open AccessOn boundary analysis for derivative of driving point impedance functions and its circuit applications
Author(s) -
Örnek Bülent Nafi,
Düzenli Timur
Publication year - 2019
Publication title -
iet circuits, devices and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 49
ISSN - 1751-8598
DOI - 10.1049/iet-cds.2018.5123
Subject(s) - resistor , inductor , capacitor , boundary (topology) , electrical impedance , mathematical analysis , function (biology) , topology (electrical circuits) , mathematics , electronic circuit , derivative (finance) , electrical engineering , engineering , combinatorics , voltage , evolutionary biology , biology , financial economics , economics
In this study, a boundary analysis is carried out for the derivative of driving point impedance (DPI) functions, which is mainly used for the synthesis of networks containing resistor‐inductor , resistor–capacitor and resistor–inductor–capacitor circuits. It is known that DPI function, Z ( s ) , is an analytic function defined on the right half of the s‐ plane. In this study, the authors present four theorems using the modulus of the derivative of DPI function, | Z ′ ( 0 ) | , by assuming the Z ( s ) function is also analytic at the boundary point s = 0 on the imaginary axis and finally, the sharpness of the inequalities obtained in the presented theorems are proved. It is also shown that simple inductor–capacitor tank circuits and higher‐order filters are synthesised using the unique DPI functions obtained in each theorem.