1. 16.360 Lecture 12 Last lecture: impedance matching Vg(t) A’ A Tarnsmission line ZLZL Z0Z0 Z in Zg IiIi Matching network Z in = Z 0

2. 16.360 Lecture 12 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

3. 16.360 Lecture 12 Today 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).

4. 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)

5. 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 = + …

6. 16.360 Lecture 12 V1  L V1  gV1 - + + V1 - =  L V1 + V2 + - =  L V2 + =  gV1 -

7. 16.360 Lecture 12 Bounce Diagram  =  g  =  L T 2T 3T 4T 5T

8. 16.360 Lecture 12 An example Z 0 = 75 ,  r = 2.1, Vg = ?, Z lf = ?, L f = ? 12  s 6V 3V t V