1. Problem on stub design with different characteristic impedances. For line , R0= 50 ohms and for stub , R0= 100 ohms.

Parameters to be calculated are i) position of stub, ii) value and iii) length.

i) Mark Yl on smith chart.ii) Find Yd from the chart.

iii) Find position of stub ( distance from Yl to Yd )iv) Value of stub – j1.35 / j2.7 --- These values is incorrect. Solution can be found as shown

below.1/Z = 1/Z1 + 1/Z2 - GeneralY = Y1 +Y2 - GeneralY11 = Yd + Ys - Specific to our problemY 11Y 0

=Y dY 0

+Y sY 0 s - Normalized values

Y 11Y 0xY 0=

Y dY 0xY 0+

Y sY 0 s

xY os

- Actual Values

Substituting for normalized values in the above equation, we get:

1 xY 0=(1− j 2 .7 )xY 0+Y s (normalized ) xY os

Now

Y s(normalized )=unknown parameter.

Y s(normalized )xY os= (1 - 1 + j 2.7) Y 0

Therefore Y s(normalized )= j 2.7 x

Y 0Y os = j 2.7 x

10050 = j 5.4

Y s(normalized )= j 5.4

v) Mark this on the smith chart and extend the arc.vi) Find the Length of the stub [ Ysc point – (extreme right) to the Ys ( normalized) point ]

marked on the chart.…………………………..Repeat the same to find second set of value

vii) Find (Y d1 ). Mark it on the chart.viii) Find position of stub ( distance from Yl to Yd1 )

ix) Then Find Y s1 as per above stepsx) Mark this on the smith chart and extend the arc.xi) Find the Length of the stub [ Ysc point – (extreme right) to the Ys1 ( normalized) point ]

marked on the chart.

Please solve this at home and we will have the verification of answers in the next class.