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Lecture 4

# Lecture 4 - sense It is simply a ratio of magnitudes of the...

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EE 4002 RF Circuit Design Transmission Lines Part 2 General Impedance and Microstrip transmission lines

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General Impedance Defined: We can develop the impedance equation from what we have derived so far for traveling waves. 0 ( ) ( ) ( ) R j L R j L Z k G j C ϖ ϖ ϖ + + = = + ( ) ( ) ( ) dV z R j L I z dz ϖ - = + ( ) kz kz V z V e V e + - - + = + ( ) ( ) ( ) kz kz k I z V e V e R j L ϖ + - - + = - + Traveling voltage wave: KVL on an infinitesimal segment of a TL Writing equation in the form: yields an expression for impedance: V I Z = Execute derivative and solve for current:
Taking this further: Substitute the current wave equation in for I ( z ): ( ) ( ) ( ) kz kz kz kz k I z I e I e V e V e R j L ϖ + - - + + - - + = + = - + ( ) ( ) kz kz kz kz k I e V e R j L k I e V e R j L ϖ ϖ + - + - - + - + = + = - + 0 0 V I Z V I Z + + - - = = - 0 V V Z I I + - + - = = - 0 1 ( ) ( ) kz kz I z V e V e Z + - - + = - Finding like terms, and substituting the impedance equation yields: The characteristic line impedance is not an impedance in the conventional

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Unformatted text preview: sense. It is simply a ratio of magnitudes of the traveling waves. Lossless Transmission Line Model: We will now represent a TL Section with this model: Calculating Z o • Using table 2-1, (TL parameters R,L,G,C for various geometries) we can calculate Z for different TL geometries. • For simplicity, let’s assume the TL’s are lossless. Ex. Parallel Plate TL L C ( ) (0 ) ( ) (0 ) R j L j L L Z G j C j C C ϖ + + = = = + + L d Z C w μ ε = = Free Space Z o • The wave impedance is defined as: • For Free space and therefore for free space. Z μ ε = 377 Z = Ω = = Microstrip Transmission Line...
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