02-03 Transmissionline - Week 2 Topic: TRANSMISSION LINE...

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1 Transmission Line Fundamentals Circuit Elements Resonators TL 1.1 TL 1 TL 1.2 TL 1.3 Week 2 Topic: TRANSMISSION LINE ANALYSIS (Review) Concepts: Introduction; Transmission line equations; Reflection coefficient, standing waves and impedance (Pozar Sec. 2.1, 2.3); Transmission line open & short sections as circuit elements (Pozar Sec. 2.3); Transmission line resonators (Pozar Sec. 6.2); Reflection Coefficient Standing Wave Ratio Input Impedance Fundamentals Lumped Element Model Transmission Line Equation TL 1.1 TL 1.1.1 TL 1.1.2 TL 1.1.3 TL 1.1.4 TL 1.1.5 Wave Solutions TL 1.1.2(a) Propagation Constant and Characteristic Impedance TL 1.1.2(b) Special Cases: Lossless and Low loss TL 1.1.2(c)
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2 R=Series Resistance per unit length for both conductors, in /m L=Series Inductance per unit length, for both conductors, in H/m G=Shunt Conductance per unit length, in S/m C=shunt capacitance per unit length, in F/m Transmission Line Section Lumped-Element Model TL 1.1.1 Lumped-Element Model Why this Model? Capacitor Electric Field Inductor Magnetic Field Passive Circuit Elements stores energy Resistor ohmic Loss dissipates energy Dielectric Leakage Loss stores energy TL 1.1.1 Lumped-Element Model Basic circuit elements: functions and effects +Q -Q Dielectric Inductor Capacitor E-field H-field Lossy dielectric
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3 These effects are uniformly distributed along the line Distributed Parameters: R ( /m), L (H/m), G (S/m), and C(F/m) Lumped Parameters for a section of length z (m): R z( ), L z (H), G z (S), and C z (F) Two Conductor Transmission Line Current flow along the conductor Magnetic Field Electric Field Produces Inductive Potential difference between the conductors Capacitive Produces Conductor loss Resistive Dielectric loss Conductive Causes Lumped Element Model Series combination Parallel combination Lumped Inductor Lumped Capacitor Lumped Resistor Lumped Conductance consider a transmission line section of length ) 10 / (say λ << z Two conductor Transmission Line Lumped-Element Model Magnetic Field Electric Field TL 1.1.1 Lumped-Element Model Reflection Coefficient Standing Wave Ratio Input Impedance Fundamentals Lumped Element Model Transmission Line Equation TL 1.1 TL 1.1.1 TL 1.1.2 TL 1.1.3 TL 1.1.4 TL 1.1.5 Wave Solutions TL 1.1.2(a) Propagation Constant and Characteristic Impedance TL 1.1.2(b) Special Cases: Lossless and Low loss TL 1.1.2(c)
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4 + V 1 - + V 4 - + V 2 -+ V 3 - Loop A I 1 I 4 I 2 I 3 Node B Lumped Element Model (Node A in figure) = = N n n V 1 0 = = N n n I 1 0 () 0 , , , , = + t z z v t t z i z L t z zi R t z v ( ) ( ) 0 , , , , = + + + t z z i t t z z v z C t z z zv G t z i Applying Kirchoff's Voltage Law in Loop A Applying Kirchoff's Current Law at node B 0 1 4 3 2 1 = = = N n n I I I I I 0 4 3 2 1 1 = = = V V V V V N n n TL 1.1.2 Transmission Line Equation TL 1.1.2 Transmission Line Equation (continued) ( ) 0 , , , , = + t z z v t t z i z L t z zi R t z v ( ) ( ) 0 , , , , = + + + t z z i t t z z v z C t z z zv G t z i ( ) ( ) t t z i L t z Ri z t z v = , , , ( ) ( ) t t z v C t
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This note was uploaded on 12/19/2009 for the course ELECTRONIC elm 421 taught by Professor Arifergin during the Fall '09 term at Gebze Institute of Technology.

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02-03 Transmissionline - Week 2 Topic: TRANSMISSION LINE...

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