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The Smith Chart

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. Complex Plane. Smith Chart Parametric Equations. Equation for a circle.

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The Smith Chart

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  1. 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

  2. Complex Plane

  3. Smith Chart Parametric Equations Equation for a circle

  4. 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

  5. Complete Smith Chart Positive xL Circles rL Circles Negative xLCircles

  6. Reflection coefficient at the load

  7. Input Impedance Constant SWR circle (standing-wave ratio)

  8. S: standing-wave ratio For

  9. Maxima and Minima

  10. Impedance to Admittance Transformation

  11. (c) (d) (a) (b)

  12. Given: S = 3 Z0 = 50 Ω first voltage min @ 5 cm from load Distance between adjacent minima = 20 cm Determine: ZL λ/2 = 20

  13. Matching Networks

  14. Examples of Matching Networks

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

  16. Cont.

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

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

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

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

  21. Steady State Response

  22. Bounce Diagrams

  23. Summary

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