Lecture 4

# Lecture 4 - EE 4002 RF Circuit Design Transmission Lines...

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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. () ( )() dV z RjL I z dz ω −= + kz kz Vz Ve + −− + =+ ( ) kz kz k Iz +− −+ =− + Traveling voltage wave: KVL on an infinitesimal segment of a TL Execute derivative and solve for current: Writing equation in the form: yields an expression for impedance: V I Z = 0 R jL R jL Z kG j C ωω ++ == +
Taking this further: Substitute the current wave equation in for I ( z ): () ( ) kz kz kz kz k Iz Ie Ve RjL ω +− −+ =+= + Finding like terms, and substituting the impedance equation yields: 0 0 V I Z V I Z + + = =− kz kz kz kz k k = + + 0 VV Z II == The characteristic line impedance is not an impedance in the conventional sense. It is simply a ratio of magnitudes of the traveling waves. 0 1

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Lecture 4 - EE 4002 RF Circuit Design Transmission Lines...

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