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Voltage Reflection Coefficient

Voltage Reflection Coefficient. At the load ( z = 0):. Reflection coefficient. Normalized load impedance. Voltage Reflection Coefficient. Standing Waves. voltage magnitude. current magnitude. Standing-Wave Pattern. Voltage magnitude is maximum.

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Voltage Reflection Coefficient

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  1. Voltage Reflection Coefficient At the load (z = 0): Reflection coefficient Normalized load impedance

  2. Voltage Reflection Coefficient

  3. Standing Waves voltage magnitude current magnitude

  4. Standing-Wave Pattern Voltage magnitude is maximum When voltage is a maximum, current is a minimum, and vice versa

  5. Standing Wave Patterns for 3 Types of Loads

  6. Maxima & Minima Standing-Wave Pattern

  7. Maxima & Minima (cont.) S = Voltage Standing Wave Ratio For a matched load: S = 1 For a short, open, or purely reactive load:

  8. Input Impedance At a distance d from the load:

  9. Input Impedance At input, d = l:

  10. Cont.

  11. (cont.) Cont.

  12. (cont.)

  13. Short-Circuited Line For the short-circuited line: At its input, the line appears like an inductor or a capacitor depending on the sign of

  14. Open-Circuited Line

  15. Short-Circuit/Open-Circuit Method • For a line of known length l, measurements of its input impedance, one when terminated in a short and another when terminated in an open, can be used to find its characteristic impedance Z0andelectrical length

  16. Instantaneous Power Flow

  17. Average Power

  18. The Smith Chart • Developed in 1939 by P. W. Smith as a graphical tool to analyze and design transmission-line circuits • Today, it is used to characterize the performance of microwave circuits

  19. Complex Plane

  20. Smith Chart Parametric Equations Equation for a circle

  21. Smith Chart Parametric Equations rL circles rL circles are contained inside the unit circle xL circles Only parts of the xL circles are contained within the unit circle

  22. Complete Smith Chart Positive xLCircles rL Circles Negative xLCircles

  23. Reflection coefficient at the load

  24. Input Impedance

  25. Impedance to Admittance Transformation

  26. (c) (d) (a) (b)

  27. Given: S = 3 Z0 = 50 Ω first voltage min @ 5 cm from load Distance between adjacent minima = 20 cm Determine: ZL

  28. Matching Networks

  29. Examples of Matching Networks

  30. Lumped-Element Matching Choose d and Ys to achieve a match at MM’

  31. Cont.

  32. Single-Stub Matching

  33. Transients Rectangular pulse is equivalent to the sum of two step functions

  34. Transient Response Initial current and voltage Reflection at the load Load reflection coefficient Second transient Generator reflection coefficient

  35. Voltage Wave T = l/upis the time it takes the wave to travel the full length of the line

  36. Current Wave Reflection coefficient for current is the negative of that for voltage

  37. Steady State Response

  38. Bounce Diagrams

  39. Summary

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