Question

6.6. A lossless 100-12 transmission line is to be matched with a 100 +j100- 12 load using a double-stub tuner (Figure P6.6). Separation between the two stubs is 1/8 and the characteristic impedance is 100S2. A load is connected right at the location of the first stub. Determine the shortest possible lengths of the two stubs to obtain the matched condition, and find the VSWR between the two stubs. 228 IMPEDANCE-MATCHING NETWORKS 100 +j1002 10022 W/8 Figure P6.6

Answer 1

(2 Mark YL on smith chaw as point A. Move on constant a Godle to meet rohaled (1+jb) Step 3 Grele. marked by green bi -> Now move from pont A (42) on constant a Grele cas arrow ) to meet rolaled (12jb ) arele at Point B and C. Step 4 Calculate susceptance of first steb. Two Possible susceptance value of frost stub Sucep lance of Pomi B- Duscep lonce of Point A 0.14 - (-0.5) = 0.14 +0.5 = 0.54 Similarly and value by = Susceptance of Point C- susceptance of Point A by 1.9-(-0.5) Step 5 Pick the shortest Shub. -Now we move from short (Point) as shown on smith Chaut in clockwise ( tow ards gencraker), 61 comes first than bé. - We are moving from short because sheb shown is shoot Creuiled stub only. So Distance from I to point (j0.54) is length u dost stub so de = 0.25 +0.078 7 - 1.9+0.5 = 2.4 Scanned with CamScanner

3 So ly = 0.32 8 7 And given as o is Step 6 Tramform Point B do Point B do 7/8 peehon to reach on (+jb) Circle . Take radius as OB and o as centes extend B , such that el meel (3+j! Gode cet point D Steb? Find suseep tance required for 2nd Stub. If we note down the admiltence a point D, el is Yo = (1 +2 0.72) So suceptance required for comkeele matching b2 -0.72 such thal Overcell admilance becomes 1. Su, Required Duceplance is b2 = -0.72. Step 8 find Find Length of As b2 = -2 0.72 marked on the smith ehou. So Dishonce from the short point is given they 0.2 a de = (0.45 2- 0.257) 0.22 Length of 2nd Stub. 2 Distance Length of the 2nd Stub 12 = 0.22 An. Scanned with CamScanner

-0.22 0.3282 ds. K da 100-12 100+j100 or OD 218 Stepe Calculate VSWR blw two stub. Take are OB and o as a center draw a corde which cut the real axis at point E. This circle is know as constant VSWR arele wane and VSWR (Voltage standing the value of the kaho) value of Legislance al seal axi's is the of point E. 2.1 And So VSWR = CS Scanned with CamScanner