Microwave Engineering ECE 5317-6351 Microwave Engineering Fall 2015 Prof. David R. Jackson Dept. of ECE Notes 3 Smith Chart Examples

Example 1 a I (-d) + V (-d) - z z = 0 z = -d Find Z(-d) ZL z = 0 I (-d) z = -d Find Z(-d) Impedance chart a  plane

Example 1 (cont.) b c I (-d) + V (-d) - z z = 0 z = -d Impedance chart ZL z = 0 I (-d) z = -d c Impedance chart  plane

Example 2 a I (-d) + V (-d) - z Find Y(-d) z = 0 z = -d ZL z = 0 I (-d) z = -d Find Y(-d) Admittance chart a  plane

Example 2 (cont.) b c I (-d) + V (-d) - z z = 0 z = -d ZL z = 0 I (-d) z = -d b c Admittance chart  plane

Þ Þ Which Chart to Use? Simple answer: * When adding elements in series use Z-chart Þ ZA ZB ZC * When adding elements in parallel use Y-chart YA YB YC Þ

Using Reactive Loads Non-absorbing load (RL = 0)  Use reactively loaded section of transmission line. most common to use open or short load: or Impedance chart Reactance V (-d) + - z ZL z = 0 I (-d) z = -d  plane

Using Reactive Loads (cont.) Susceptance Admittance chart V (-d) + - z ZL z = 0 I (-d) z = -d  plane

Example 3 Use a short-circuited section of air-filled TEM, 50  transmission line ( = k0, g =0) to create an impedance of Zin = -j25  at f = 10 GHz. Impedance chart L SC 50, k0 L = 1.28 cm  plane

Example 4 Use an open-circuited section of 75  (Y0 = 1/75 S) air-filled transmission line at f = 10 GHz to create an admittance of : Admittance chart L OC 75, k0  plane

Matching Circuit Want to pick d and Ys such that Yin = Y0. d Z0 YS ZL Zin, Yin d ZL YS YA Z0 Admittance chart Want to pick d and Ys such that Yin = Y0. Note: At d we have  plane

Matching Circuit (cont.) Zin, Yin d ZL YS YA Z0 We want Choose:  plane Admittance chart

Example 5 ZL Z0 ls Z0s d In this example we will use the “usual” Smith chart, but as an admittance calculator.

(We’ll use the first choice.) Example 5 (cont.) Admittance chart (We’ll use the first choice.) X OC SC X X  plane Smith chart scale: wavelengths toward load wavelengths toward generator

Example 5 (cont.) From the Smith chart: Analytically: Admittance chart  plane Analytically:

Quarter-Wave Transformer At f0 : For in = 0 Hence, we have

Match 100  load to 50  transmission Line at f0. Example 6 Match 100  load to 50  transmission Line at f0.