Use Smith Chart for this question, A Z0 = 100 Ohm line is term with the load imp

Question

Use Smith Chart for this question, A Z0 = 100 Ohm line is term with the load impendance z1 = 25+25 Ohm We would like to use n series element b to match this load What is the length of the line where the normalized input impedance is : If the frequency is 1GHz find the value element (C or I.). Non we would like to use an open circuit stab to match this load. What it the length of the line where the normalized input admittance . II the characteristic impatience of the open circuit line is SO Ohm). find the length of the

Explanation / Answer

I dont have a smith chart so the correct procedure is explained so that u can directly put it on the smith chart .

1) Normalize the Load impedance with Zo i.e (25 + j25)/100 . plot this point on smith chart and name it as ZL.

2) draw a circle with the center as the 'center of the smith chart' and radius as the distance between the center and this point .

3) Draw another circle called matching circle . The matching circle intersects the earlier circle at 2 points. Name them as P1 and P2.

4) Now move on the 'Towards the generator circle' from the point ZL to the intersection point to the point P2. this distance between the ZL and the point P2 is the required distance which has impedance as 1-jb which can be read from the smith chart.

5) this b value is the reactance(XL or Xcdepending on the sign of it ... XL if it is positive, Xc if its negative) which can be found from Xc=1/jwc or XL=jwl as w=2*pi*f and f is given .

this completes the first question

for the second question we have to calculate the length of the line which would cancel this susceptance.

6) just calculate the distance between the open circuit point(OC) point and point P2 moving across 'circle towards the generator'..

7) this distance gives the length of the stub to balance the line ... this completes the impedance mathicng

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