Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Question

How do you derive the Telegrapher's Equations for a lossy transmission line? Why is it the bottom equation? 

 

2.5.3 Input Impedance of a Lossy Line The impedance looking into the line varies with position, as the forwardand backward-traveling waves combine to yield position-dependent total voltage and current. At a distance from the load (i.e., z = −l), the input impedance seen looking toward the load is & Zinz= Zin Zo = ·l = Another form comes from substituting Equation (2.3.6) in Equation (2.5.4): V (z = −l) I(z = −l) = Zo- = Zo (Z1 + Zo)ere + (Z₁ — Zo)e¯^ - This equation is also known as the lossy telegrapher's equation. 1+|T|e(³0−2yl) 1-re(-2yl) (ZL + Zo) ere — (ZL — Zo)e-re ZL+Zo tanh y Zo+Zr tanh y = Zo = Zo 1+[Le-2ye 1- Le-2yl Z₁ cosh(yl) + JZ₁ cosh(yl) Zo cosh (yl) + JZ₁ cosh(yl) (2.5.4) (2.5.5)
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Transcribed Image Text:2.5.3 Input Impedance of a Lossy Line The impedance looking into the line varies with position, as the forwardand backward-traveling waves combine to yield position-dependent total voltage and current. At a distance from the load (i.e., z = −l), the input impedance seen looking toward the load is & Zinz= Zin Zo = ·l = Another form comes from substituting Equation (2.3.6) in Equation (2.5.4): V (z = −l) I(z = −l) = Zo- = Zo (Z1 + Zo)ere + (Z₁ — Zo)e¯^ - This equation is also known as the lossy telegrapher's equation. 1+|T|e(³0−2yl) 1-re(-2yl) (ZL + Zo) ere — (ZL — Zo)e-re ZL+Zo tanh y Zo+Zr tanh y = Zo = Zo 1+[Le-2ye 1- Le-2yl Z₁ cosh(yl) + JZ₁ cosh(yl) Zo cosh (yl) + JZ₁ cosh(yl) (2.5.4) (2.5.5)
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