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 r L circles x L circles r L circles are contained inside the unit circle Only parts of the x L circles are contained within the unit circle

5. Complete Smith Chart r L Circles Positive x L Circles Negative x L Circles

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

12. Given: S = 3 Z 0 = 50 Ω first voltage min @ 5 cm from load Distance between adjacent minima = 20 cm Determine: Z L 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’

17. Cont.

18. Single-Stub Matching

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

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

24. T = l/u p is the time it takes the wave to travel the full length of the line Voltage Wave

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

26. Steady State Response

27. Bounce Diagrams

30. Technology Brief 4: EM Cancer Zapper

31. Technology Brief 4: High Voltage Pulses

32. Summary