Prof. David R. Jackson Dept. of ECE Notes 3 ECE Microwave Engineering Fall 2011 Smith Chart Examples 1

Find Z(-d) Example 1 a 2 Impedance chart

b c Example 1 (cont.) 3

Find Y(-d) Example 2 a 4 Admittance chart

Example 2 (cont.) b c 5 Admittance chart

Simple answer: * When adding elements in series use Z -chart * When adding elements in parallel use Y -chart Which Chart to Use? 6

 Use reactively loaded section of transmission line. most common to use open or short load Non-absorbing load ( R L = 0 ) Using Reactive Loads 7 Impedance chart Reactance

Susceptance Using Reactive Loads (cont.) 8 Admittance chart

Use a short-circuited section of air-filled TEM, 50  transmission line (  = k 0, g = 0 ) to create an impedance of Z in = -j25  at f = 10 GHz. Example 3 L = 1.28 cm 9 Impedance chart

Use an open circuited section of 75  ( Y 0 = 1/75 S ) air-filled transmission line at f = 10 GHz to create an admittance of Example 4 10 Admittance chart

Note: At d we have Want to pick d and Y s such that Y in = Y 0. Matching Circuit 11 Admittance chart

We want Choose Matching Circuit (cont.) 12 Admittance chart

Example 5 ZLZL Z0Z0 lsls Z0sZ0s d 13 In this example we will use the “usual” Smith chart, but as an admittance calculator.

Example 5 (cont.) X X X wavelengths toward load wavelengths toward generator Smith chart scale: Admittance calculator 14  plane SC OC (We’ll use the first choice.)

Example 5 (cont.) X Admittance calculator From the Smith chart: Analytically: 15

Quarter-Wave Transformer At f 0 : For  in = 0 16

Match 100  load to 50  transmission Line at f 0. Example 6 17