Darryl Michael/GE CRD 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 incident and reflected waves interfere constructively and destructively standing wave occurs

Transmission Lines Incident Wave Reflected Wave Mismatched load 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 Forward Wave Backward Wave V max occurs when Forward and Backward Waves are in Phase V min occurs when Forward and Backward Waves are out of Phase CONSTRUCTIVE INTERFERENCE DESTRUCTIVE INTERFERENCE TIME DOMAIN Do Problem 1a

Transmission Lines - Standing Wave Derivation Distance between Max and Min is /2 Assume, are real for the moment (will be complex if load is complex Forward Phase is = Backward Phase is = Difference in Phase is = Varies by 2  (distance between maxima) Show this

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

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

Standing Wave Pattern Do Problem 1a - 1c From experiment 1b, Maximum occurs at LOAD for Minimum occurs at LOAD for In general, Max at LOAD Min at LOAD IF Z L is REAL

Standing Wave Pattern Do Experiment 2 What does, look like? When Z L is complex, so is  L Define: if z =0 at LOAD

Standing Wave Pattern If z=L at LOAD and z=0 at SOURCE, When Phase = , FIRST MINIMUM occurs Other MINs are displaced by /2