Lect20TLineBasics - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 20 2009/10/14 Transmission Lines: The Basics Structures Transmission Line Equations 1 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: Instructor: Dr. Wesley E. Swartz Power Flow on Transmission Lines Problem Assignments There was no Demo this week (Fall Break) . Workshop 7 Problems (Thursday, October 15) : Problem 12.9: Oblique incidence on a dielectric. Problem 13.3: Characteristics of twin-lead transmission line. Homework 7 Problems (due Tuesday, October 20) : Problem 10.12: Plasma density and propagation time. Problem 10 17: Wave attenuation in sea water 2 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: Problem 10.17: Wave attenuation in sea water. Problem 12.11: Oblique incidence on a medium with complex conductivity. Guided Waves So far we have dealt with waves propagating in media with infinite dimensions. For many applications we need to guide electromagnetic energy in much the same way as water is guided by pipes. Transmission lines are the simplest structures that guide electromagnetic waves. A transmission line can be any two arbitrarily shaped metal conductors 3 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: that are very long and uniform in at least one dimension. x y Example: Two oddly shaped metal conductors that are very long and uniform in the z -direction. Transmission Line Structures (1) Co-axial cable d W ε a b 2 π Parallel-plates 4 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: d W C = W d L o μ = = a b log C = a b log 2 L o o C L = o C L = Capacitances and Inductances per unit length. Universal relation Transmission Line Structures (2) d/2 radius a d o C o 2 C o radius a Parallel metal wires For d >> a : Metal wire over ground plane For d >> a : 5 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: = a d log = a d log L o = a d log = a d log 2 L o o o C L = o o C L = Capacitances and Inductances per unit length. Universal relation Transmission Line Voltages Let the potential difference between the two conductors of a transmission line at location z is V ( z ) . Then the E-field line-integral in a plane parallel to the x - y plane at the location z is independent of the contour taken , and is related to the potential difference V ( z ) as: x y C 1 C 2 ( ) = = s d E s d E z V 6 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 20: The charge per unit length Q ( z ) on the transmission line at location z is: 2 1 c c () z V C z Q = Capacitance per unit length
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2 Transmission Line Voltages Now consider two different locations along the transmission line: Z 1 and Z 2 .
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Lect20TLineBasics - ECE 3030 Electromagnetic Fields and...

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