Signals and Systems

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California State University, Bakersfield

Vida Vakilian

Department of Electrical and Computer Engineering, California State University, Bakersfield

Lecture 9(Wave Propagation in Transmission Lines)

Signals and Systems

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California State University, Bakersfield

Outline

Ø  Wave Propagation in transmission lines

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California State University, Bakersfield

Transmission-Line Equations

ac signals: use phasors

Telegrapher’s equations

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California State University, Bakersfield

Derivation of Wave Equations

Combining the two equations leads to:

Second-order differential equation

complex propagation constant

attenuation constant

Phase constant

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California State University, Bakersfield

Solution of Wave Equations

Proposed form of solution:

Using:

It follows that:

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California State University, Bakersfield

Solution of Wave Equations In general:

wave along +z because coefficients of t and z have opposite signs

wave along –z because coefficients of t and z have the same sign

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California State University, Bakersfield

Signals and Systems

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California State University, Bakersfield