16 360 Lecture 9 Normalized admittance z and

16. 360 Lecture 9 Normalized admittance z and y are directly opposite each other on Smith Chart

16. 360 Lecture 9 Parameter equations Unit circuit Short Circuit load . B Open Circuit load

16. 360 Lecture 9 Normalized impedance Parameter equations

16. 360 Lecture 9 Parameter equations

16. 360 Lecture 9 An example Smith Chart Input impedance Wavelength toward generator (WTG) Smith Chart

16. 360 Lecture 9 An example find Zin (-0. 1 ) Smith Chart Constant | | circle, SWR Circle

16. 360 Lecture 10 SWR, voltage maximum and minimum If Smith Chart Recall: + |V(z)|max = |V 0| [1+ | |], when 2 z + r = 2 n. + |V(z)|min = |V 0| [1 - | |], when 2 z + r = (2 n+1).

16. 360 Lecture 10 An example A 50 - lossless line is terminated in a load ZL = (25+j 50). 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. Smith Chart

16. 360 Lecture 11 • impedance matching Zg Vg(t) A Ii Z 0 Zin Matching network ZL Tarnsmission line A’ Zin = Z 0

16. 360 Lecture 11 • single-stub impedance matching network Zg Vg(t) M Ii Y 0 Yin d A YL’ ZL Transmission line Yin = Yd’ + Ys’ 1 = Yin M’ Ys’ l A’ 1= Yd’ + Ys’ =1 Ys YL

16. 360 Lecture 11 Yin = Yd’ + Ys’ 1 = Yin Zg Vg(t) 1= Yd’ + Ys’ Y 0 + Ys’ A YL’ M’ Ys’ l =1 Re Yd’ = Yin d ZL Transmission line Yd’ + M Ii Ys’ Im A’ Ys YL

16. 360 Lecture 11 • single-stub impedance matching network Zg Vg(t) M Ii Y 0 d A Yin ZL Yd Transmission line An example A 50 - transmission line is connected to an antenna with in a load ZL = (25 -j 50). Find the position and the length of the short-circuited stub required to match the line. Smith Chart A’ M’ Ys l

16. 360 Lecture 12 • Transient on transmission line Zg Vg(t) Ii A ZL Z 0 Tarnsmission line A’ 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).

16. 360 Lecture 12 Step function and pulse function • step function U(t) = 1, if t>=0; U(t) = 0, if t<0 • single pulse function V(t) = U(t) – U(t-t 0),

16. 360 Lecture 12 • transient of a step function A Zg Vg(t) Ii ZL Z 0 Tarnsmission line A’ + - = LV 1 + - + V 2 = g. V 1 - + V 2 - = LV 2 + + g. V 1 + - V = V 1+ V 1 + V 2 + LV 1 …

16. 360 Lecture 12 + - = LV 1 - + + V 2 = g. V 1 + V 2 - = V 2 g. V 1 L - + LV 1

16. 360 Lecture 12 • Bounce Diagram = g = L T 2 T 3 T 4 T 5 T

16. 360 Lecture 12 • An example Z 0 = 75 , r = 2. 1, Vg = ? , Zlf = ? , Lf = ? V 6 V 3 V 12 s t