Transmission Line Theory

# Transmission Line Theory - Transmission Line Theory...

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Unformatted text preview: Transmission Line Theory Transmission Line Theory ● Bridges gap between field analysis and basic circuit theory ● Analysis of transmission lines – Circuit theory based – Special case of maxwell's equations (EM based) ● Propagation of waves in transmission lines are similar to plane wave propagation Transmission Line Theory vs. Circuit Theory ● Fundamental difference is the electrical size ● Circuit Theory – Electrical length >> physical length ● Transmission Line Theory – Physical dimensions are a fraction of a wavelength or several wavelengths – Distributed parameter network – Voltages and currents vary in magnitude and phase over its length Transmission Lines ● Guiding structure for electromagnetic energy ● Usually represented as a 2 wire line – For TEM propagation, tx lines always have at least 2 conductors – Composed of conductors and dielectric Lumped-Elemenet Circuit Model ● Infinitesimal short length of transmission line with length Δz ● Lumped element Model is shown below Lumped-Element Circuit Model ● Circuit parameters are called distributed parameters – R is the series resistance per unit length (ohms/m) – L is series inductance per unit length (Henrys/m) – G is shunt conductance per unit length (Siemens/m) – C is shunt capacitance per unit length (Farads/m) ● Finite length of transmission line can be modeled as cascade of lumped element model ● What do these distributed parameters represent in the transmission line? Lumped-Element Circuit Model ● From the circuit model, performing KVL gives: ● Letting Δz approach zero, we have: V − R  z I − L  z ∂ I ∂ t − V  V = ٠  V =−{ L ∂ I ∂ t  I R } z  V  z =−{ L ∂ I ∂ t  I R } ∂ V ∂ z =−{ L ∂ I ∂ t  I R } Lumped-Element Circuit Model ● Performing KCL on the circuit ● Letting Δz approach zero and neglecting the ΔV terms, we have: I − G  z  V  V − C  z ∂ V  V  ∂ t − I  I = ٠ −[ GV  z  G  v...
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Transmission Line Theory - Transmission Line Theory...

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