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# Fields and Waves

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

## Fields and Waves

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1. Fields and Waves Lesson 1.2 SINE WAVES ON TRANSMISSION LINES Darryl Michael/GE CRD

2. 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

3. Transmission Lines Incident Wave Mismatched load Reflected Wave Standing wave due to interference Do Experiment 1a, b and c

4. Transmission Lines - Standing Wave Derivation Phasor Form of the Wave Equation: where: General Solution:

5. 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

6. , 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)

7. Reflection Coefficient Derivation Define the Reflection Coefficient: Maximum Amplitude when in Phase: Similarly: Standing Wave Ratio (SWR) =

8. Reflection Coefficient Derivation Let z=0 at the LOAD Need a relationship between current and voltage:

9. Reflection Coefficient Derivation

10. Reflection Coefficient Derivation At LOAD: Use derived terms of V and I at z=0 (position of the LOAD) Note that OR

11. 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

12. What does , look like? Standing Wave Pattern Do Experiment 2 When ZL is complex, so is GL Define: if z =0 at LOAD

13. 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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