Pozitif Reel Fonksiyonlar ve Devre Uygulamaları Üzerine Bazı Sonuçlar

Bu çalışmada, Schwarz lemmasının bir sınır versiyonu, süren nokta empedans fonksiyonları için sanal eksen üzerindeki s = 0 noktasında değerlendirilmiştir. Buna göre, Z(0) 0 = koşulu altında, Z s( ) fonksiyonunun türevinin modülü aşağıdan değerlendirilmiştir. Burada, elde edilen eşitsizliklerde, ( ) ... 1 ( ) p Z s c s = + - + b a fonksiyonunun Taylor açılımındaki Z( ) a , 1 c ve 2 c katsayıları kullanılmıştır. Aynı zamanda, bu eşitsizliklerin keskinliği ispatlanmıştır. Önerilen teoremlerde elde edilen empedans fonksiyonları kullanılarak bunlara karşılık gelen LC devreleri sentezlenmiş ve bu devrelerle ilgili figürler sunulmuştur.

Some Remarks on Positive Real Functions and Their Circuit Applications

In this paper, a boundary version of the Schwarz lemma has been considered for driving point impedance functionsats = 0point of the imaginary axis. Accordingly, underZ(0) 0 =condition, the modulus of the derivative oftheZ s( )function has been considered from below. Here,Z( ) a ,1cand2ccoefficients of the Taylor expansionof the( ) ... 1( )pZ s c s = + - + b afunction have been used in the obtained inequalities. The sharpness of theseinequalities has also been proved. Using the obtained driving point impedance functions in the proposed theorems,corresponding LC circuits have been synthesized and related figures have been presented.

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