Fields and Waves
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Fields and Waves. Lesson 1.2. SINE WAVES ON TRANSMISSION LINES. Standing Wave Patterns. Today’s Class:. look at effects of Sine Waves on Transmission Lines. generate Standing Wave Patterns - predict these. when load is mismatched waves sent down the line are reflected

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Fields and Waves

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Fields and Waves

Lesson 1.2

SINE WAVES ON TRANSMISSION LINES

Darryl Michael/GE CRD


Standing Wave Patterns

Today’s Class:

  • look at effects of Sine Waves on Transmission Lines

  • generate Standing Wave Patterns - predict these

  • when load is mismatched

    • waves sent down the line are reflected

    • incident and reflected waves interfere constructively and destructively

    • standing wave occurs


Transmission Lines

Incident Wave

Mismatched load

Reflected Wave

Standing wave due to interference

Do Experiment 1a, b and c


Transmission Lines - Standing Wave Derivation

Phasor Form of the Wave Equation:

where:

General Solution:


Transmission Lines - Standing Wave Derivation

Backward Wave

Forward Wave

TIME DOMAIN

Vmax occurs when Forward and Backward Waves are in Phase

CONSTRUCTIVE INTERFERENCE

Vmin occurs when Forward and Backward Waves are out of Phase

DESTRUCTIVE INTERFERENCE

Do Problem 1a


, are real for the moment (will be complex if load is complex

Assume

Forward Phase is =

Backward Phase is =

Difference in Phase is =

Transmission Lines - Standing Wave Derivation

Distance between Max and Min is l/2

Show this

Varies by 2p (distance between maxima)


Reflection Coefficient Derivation

Define the Reflection Coefficient:

Maximum Amplitude when in Phase:

Similarly:

Standing Wave Ratio (SWR) =


Reflection Coefficient Derivation

Let z=0 at the LOAD

Need a relationship between current and voltage:


Reflection Coefficient Derivation


Reflection Coefficient Derivation

At LOAD:

Use derived terms of V and I at z=0 (position of the LOAD)

Note that

OR


Max at LOAD

Min at LOAD

Standing Wave Pattern

Do Problem 1a - 1c

From experiment 1b,

Maximum occurs at LOAD for

Minimum occurs at LOAD for

In general,

IF ZL is REAL


What does

, look like?

Standing Wave Pattern

Do Experiment 2

When ZL is complex, so is GL

Define:

if z =0 at LOAD


Standing Wave Pattern

If z=L at LOAD and z=0 at SOURCE,

When Phase = p, FIRST MINIMUM occurs

Other MINs are displaced by l/2


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