lec4 - • Material nonlinearities, (hysteresis) and...

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EE 3113 INTRODUCTION TO RF CIRCUIT DESIGN Lecture Notes for A-term 2003 LECTURE 4 Prof. R. Ludwig Department of Electrical and Computer Engineering Worcester Polytechnic Institute Worcester, MA 01609 copyright © 2003, R. Ludwig Copyright, 1998 © R. Ludwig
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EE3113_L4 2 General Transmission Line Equations • Detailed analysis of a differential section Note: Analysis applies to all types of transmission lines such as coax cable, two-wire, microstrip, etc.
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EE3113_L4 3 Kirchhoff’s laws on a microscopic level • Over a differential section we can again use basic circuit theory • Model takes into account line losses and dielectric losses • Ideal line involves only L and C
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EE3113_L4 4 Advantages versus disadvantages of electric circuit representation • Clear intuitive physical picture • yields a standardized two-port network representation • serves as building bocks to go from microscopic to macroscopic forms • Basically a one-dimensional representation (cannot take into account interferences from neighboring elements)
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Unformatted text preview: • Material nonlinearities, (hysteresis) and temperature effects are not accounted for EE3113_L4 5 ) ( ) ( ) ( ) ) ( ) ( ( z I L j R dz z dV z z V z z V Lim ω + = − = ∆ − ∆ + − Derivation of differential transmission line form ) ( ) ( ) ( ) ( z z V z z I L j R z V ∆ + + ∆ + = KVL : KCL : ) ( ) ( ) ( ) ( z z I z z zV C j G z I ∆ + + ∆ + ∆ + = ) ( ) ( ) ( z V C j G dz z dI + = − Coupled DE EE3113_L4 6 Traveling Voltage and Current Waves ) ( ) ( 2 2 2 = − z V k dz z V d where ) )( ( C j G L j R jk k k i r ω + + = + = kz kz e V e V z V + − − + + = ) ( kz kz e I e I z I + − − + + = ) ( ) ( ) ( 2 2 2 = − z I k dz z I d Left traveling wave Right traveling wave Phasor expressions EE3113_L4 7 General line impedance definition ) ( ) ( ) ( kz kz e V e V L j R k z I + − − + − + = ω − − + + − = = + + = I V I V C j G L j R Z ) ( ) ( ? Characteristic line impedance...
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This note was uploaded on 01/31/2012 for the course EE 4002 taught by Professor Scalzo during the Fall '06 term at LSU.

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lec4 - • Material nonlinearities, (hysteresis) and...

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