1. 16.360 Lecture 9 Smith Chart Normalized admittance z and y are directly opposite each other on

2. 16.360 Lecture 9 Parameter equations. B Open Circuit load Short Circuit load Unit circuit

3. 16.360 Lecture 9 Normalized impedance Parameter equations

4. 16.360 Lecture 9 Parameter equations

5. 16.360 Lecture 9 An example Smith Chart Input impedance Smith Chart Wavelength toward generator (WTG)

6. 16.360 Lecture 9 An example Smith Chart find Zin (-0.1 ) Constant |  | circle, SWR Circle

7. 16.360 Lecture 10 Recall: Smith Chart If when 2  z +  r = 2n . | V 0 | [ 1 - |  |], + |V(z)| min = when 2  z +  r = (2n+1) . | V 0 | [ 1+ |  |], + |V(z)| max = SWR, voltage maximum and minimum

8. 16.360 Lecture 10 Smith Chart An example A 50-  lossless line is terminated in a load ZL = (25+j50) . Use the smith chart to find a) voltage reflection coefficient, b) the voltage standing-wave ratio, c) the distances of the first voltage maximum and first voltage minimum from the load, d) the input impedance of the line, given the line is 3.3, and e) the input admittance of the line.

9. 16.360 Lecture 11 impedance matching Vg(t) A’ A Tarnsmission line ZLZL Z0Z0 Z in Zg IiIi Matching network Z in = Z 0

10. 16.360 Lecture 11 single-stub impedance matching network Vg(t) A’ A Transmission line ZLZL Y0Y0 M Zg IiIi l d M’ Y in Y L’ Y s’ Y in = Yd’ + Ys’ YLYL YsYs 1 = Y in 1= Yd’ + Ys’ Yd’ Ys’ + = 1

11. 16.360 Lecture 11 Vg(t) A’ A Transmission line ZLZL Y0Y0 M Zg IiIi l d M’ Y in Y L’ Y s’ Y in = Yd’ + Ys’ YLYL YsYs 1 = Y in 1= Yd’ + Ys’ Yd’ Ys’ + = 1 Re Im Yd’ Ys’ = +

12. 16.360 Lecture 11 single-stub impedance matching network Vg(t) A’ A Transmission line ZLZL Y0Y0 M Zg IiIi l d M’ Y in YdYd YsYs An example A 50-  transmission line is connected to an antenna with in a load ZL = (25-j50) . Find the position and the length of the short-circuited stub required to match the line. Smith Chart

13. 16.360 Lecture 12 Transient on transmission line Vg(t) A Tarnsmission line A’ ZLZL Z0Z0 Zg IiIi If  1,  2,…,  n are transmitted on the transmission line at the same time, each frequency has its own location of voltage distribution. The total voltage V(z) is the sum of all these V  i (z).

14. 16.360 Lecture 12 Step function and pulse function step function U(t) U(t) = 1, if t>=0; U(t) = 0, if t<0 V(t) = U(t) – U(t-t0), single pulse function V(t)

15. 16.360 Lecture 12 transient of a step function A IiIi Vg(t) Tarnsmission line A’ ZLZL Z0Z0 Zg V1  L V1  gV1 - + + V1 - =  L V1 + V2 + - =  L V2 + =  gV1 - V2 + - V1 - + + + + V = + …

16. 16.360 Lecture 12 V1  L V1  gV1 - + + V1 - =  L V1 + V2 + - =  L V2 + =  gV1 -

17. 16.360 Lecture 12 Bounce Diagram  =  g  =  L T 2T 3T 4T 5T

18. 16.360 Lecture 12 An example Z 0 = 75 ,  r = 2.1, Vg = ?, Z lf = ?, L f = ? 12  s 6V 3V t V