Engineering of Distributed Systems Introduction to Waves

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Engineering of Distributed SystemsIntroduction
to Waves

• April 4, 2005

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The mythical equipotential wire
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But every wire has parasitics
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Why do wires act like transmission lines?
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Signals take time to propagate Propagating
Signals must have energy All conductors have
inductance and capacitance Inductance and
Capacitance Stores Energy
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Discrete Approximation to a Lossless Transmission
Line

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Fundamental Equations of Continuous Transmission
Lines

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Transmission Line Math
Lets try a sinusoidal solution for V and I
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Transmission Line Algebra
Divide Equations, then simplify
Simplify by substitution method
Propagation Velocity
Characteristic Impedance
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Why do wires act like transmission lines?
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Signals take time to propagate Propagating
Signals must have energy Inductance and
Capacitance Stores Energy An Infinite
transmission line looks like a
Resistor
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Why do wires act like transmission lines?
Signals take time to propagate Propagating
Signals must have energy Inductance and
Capacitance Stores Energy Without termination,
energy reaching the end of a finite
transmission line has nowhere to go - so it
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Echoes
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Modeling Reflections as Reverse Propagation
Direction

• Right Hand Boundary Constraint
• Open I 0
• Reverse Waveform
• Positive Voltage
• Negative Current
• Short V 0
• Reverse Waveform
• Negative Voltage
• Positive Current
• Left Hand Boundary Constraint?