A Bound for the Derivative of Positive Real Functions

Reza, F.M.

doi:10.1137/1004005

Cited by 22 publications

(14 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…A DPIF,

Z ((), s)

, depends on the complex frequency parameter s , and it satisfies the properties of PRFs. These properties can be listed as follows: Z ( s ) is analytic in ℜ s ≥ 0 except possibly for poles on the axis of imaginaries,

Z false(\overset{s}{true} false) = \overset{Z false(s false)}{true}

ℜ Z ( s ) ≥ 0, in ℜ s ≥ 0 …”

Section: Introductionmentioning

confidence: 99%

Schwarz lemma for driving point impedance functions and its circuit applications

Örnek

Düzenli̇

2019

Circuit Theory & Apps

View full text Add to dashboard Cite

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 + cp(s − 1)p + cp + 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.

show abstract

“…A DPIF,

Z ((), s)

Z false(\overset{s}{true} false) = \overset{Z false(s false)}{true}

ℜ Z ( s ) ≥ 0, in ℜ s ≥ 0 …”

Section: Introductionmentioning

confidence: 99%

Schwarz lemma for driving point impedance functions and its circuit applications

Örnek

Düzenli̇

2019

Circuit Theory & Apps

View full text Add to dashboard Cite

show abstract

“…Empedans fonksiyonları, ( ) Z s , kompleks frekans parametresi s 'ye bağlı pozitif reel fonksiyonlardır. Bir empedans fonksiyonu aşağıda verilen pozitif reel fonksiyonlara ait özellikleri taşıdığı takdirde fiziksel olarak gerçeklenebilmektedir (Reza, 1962)…”

Section: Introductionunclassified

Pozitif Reel Fonksiyonlar için Devre Uygulamaları

Örnek¹,

Düzenli̇²

2019

DÜMF Mühendislik Dergisi

View full text Add to dashboard Cite

“…Driving point impedance (DPI) functions are given as positive real functions (PRF) and they depend on the complex frequency parameter, s. A driving point impedance function is physically realizable if it satisfies the properties of positive real functions which are given below [21]:…”

Section: Introductionmentioning

confidence: 99%

Bound estimates for the derivative of driving point impedance functions

Nafi¹,

Düzenli̇²

2018

Filomat

View full text Add to dashboard Cite

In this paper, a boundary analysis is carried out for the derivative of driving point impedance functions, which is mainly used for synthesis of networks containing RL, RC and RLC circuits. It is known that driving point impedance function, Z(s), is an analytic function defined on the right half of the s-plane. In this study, we derive inequalities for the modulus of 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 and the sharpness of these inequalities is proved. Furthermore, an equation for the driving point impedance function, Z(s), is obtained as a natural result of the proved theorem in this study.

show abstract

A Bound for the Derivative of Positive Real Functions

Cited by 22 publications

References 1 publication

Schwarz lemma for driving point impedance functions and its circuit applications

Schwarz lemma for driving point impedance functions and its circuit applications

Pozitif Reel Fonksiyonlar için Devre Uygulamaları

Bound estimates for the derivative of driving point impedance functions

Contact Info

Product

Resources

About