Lect21TLineSinusoidal

# Lect21TLineSinusoidal - ECE 3030 Electromagnetic Fields and...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 21 2009/10/16 Sinusoidal Waves on Transmission Lines RF and Microwave Circuits Impedance Transformations 1 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: Instructor: Dr. Wesley E. Swartz Open and Shorted Lines o Z s Z s V L Z 0 = z () [] t j s s e V t V ω Re = = z Where are We? Where are We Going? Up to now: The course has been very theoretical. Basics of fields and waves have been established. Various tools have been demonstrated to solve E & M problems. For the remainder of the course: More practical applications. 3 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: Applications will use the basics and the tools. Transmission Lines: A Review Voltage at any point on the line can be written as: o Z + V V z k j z k j e V e V z V + + + = Some common examples of transmission lines: Twin lead 4 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: Current at any point on the line can be written as: The characteristic impedance of a transmission line is: The dispersion relation for a transmission line is: z k j o z k j o e Z V e Z V z I + + = C L Z o = C L k = Co-axial line Wire over a ground plane Radar RF Pulse: connected with RG-58 5 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: RG-17 Hookup COAX 6 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: 50-Ohm 6-Inch COAX 7 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21:

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2 Transmission Line Circuits Consider a transmission line connected as shown below: o Z s Z s V L Z 0 = z = z z = o Z Transmission line impedance () [] t j s s e V t V ω Re = 8 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: z k j z k j e V e V z V + + + = z k j o z k j o e Z V e Z V z I + + = = L Z Load impedance = s Z Source impedance In general, voltage on a transmission line is a superposition of forward and backward going waves: The corresponding current is also a superposition of forward and backward going waves: Load Boundary Condition Boundary condition: o Z s Z s V L Z 0 = z = z z t j s s e V t V Re = z k j z k j e V e V z V + + + = z k j o z k j o e Z V e Z V z I + + = + V V + - 9 Rana and Swartz 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 21: At z = 0, the ratio of the total voltage to the total current must equal the load impedance: L o o Z Z V Z V V V z I z V = + = = = + + 0 0 This gives us the backward going wave amplitude in terms of the forward going wave amplitude 1 1 + = = Γ + o L o L L Z Z Z Z V V 1 1 + = + o L o L Z Z Z Z V V Define a load reflection coefficient , Γ L , as: Load Reflections Suppose Z L = 0 (short): o Z s Z s V + V V + + = = + = = Γ V V Z Z Z Z V V o L o L L 1 1 1 ( ) 0 0 = + = = + V V z V ( ) V V V z I + + = = = 2 0 and 0 = z = z z
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Lect21TLineSinusoidal - ECE 3030 Electromagnetic Fields and...

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