DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

INDIAN INSTITUE OF TECHNOLOGY ROORKEE

EC-631 Prob. Sheet – 2

1. For a line of characteristic impedance 60 ohms, find the location nearest to the load

and the characteristic impedance of a quarter-wave transformer to achieve a match for

(a) R = 1/9, (b) R = - 0.5j, (c) R = j/3.

2. For each of the following values of ZR terminating a line of Z0 = 60 ohm, find the

smallest value of ds and corresponding smallest value of ls of a single shunt stub of

characteristic impedance 60 ohm required to achieve a match between the line and (a)

ZR = 30 ohms, (b) ZR = (12-24j) ohms. Repeat your computations for a series stub.

3. Repeat prob. 2 using Smith Chart.

4. Find the following using Smith Chart: (a) normalized i/p impedance of a line of

length 0.1 and terminated in a normalized load impedance (2 + j) ohms, (b) the

normalized i/p impedance of a short-circuited stub of length of length 0.17 , (c) the

normalized i/p admittance of an open-circuited shunt stub of length 0.06 .

5. For a transmission line of Z0 = 100 ohms, terminated in (80 + 200j) ohms, find the

following using the Smith Chart: (a) reflection coefficient of the load, (b) dmin, (c)

SWR, (d) Z(d=0.1 ) (e) Y(d=0.1 ), (f) location nearest to the load where Re[Y(d)] =

Y0.

6. Standing wave measurements on a line of Z0 = 50 ohms give a SWR of 5 and a

voltage minimum at a distance of 5/12 from the load. Using the Smith Chart, find

the load impedance.

7. A line of Z0 = 100 ohms is terminated in a load impedance (50+65j) ohms. Using the

Smith Chart, find (a) SWR on the line, (b) minimum SWR that can be achieved on the

line by connecting a stub in parallel with the load, (c) the minimum SWR that can be

achieved by connecting a stub in series with the load.

8. A transmission line of Z0 = 50 ohms is terminated in a certain load. The SWR is found

to be 5 and the first voltage minimum at 0.1 from the load. Using the Smith Chart,

find the location nearest to the load and the length of short-circuited shunt stub to

achieve a match.

9. Standing wave measurements on a line of Z0=50 ohms indicated a SWR of 3 and the

location of the first voltage minimum at 0.16 from the load. Assuming a stub

located at 0.1 from the load and a second stub located at 0.725 from the load, find

the lengths of the two short-circuited shunt stubs of 50 ohm characteristic impedance

to achieve a match.

10. A transmission line of characteristic impedance 50 ohm is terminated in a load

impedance of (30 – j40) ohms. Solve the single and double stub matching problems

with shunt stubs of characteristic impedance of 50 ohm. For the double-stub matching

problem, assume the distance between the stubs to be 0.375 λ.

11. An L-section matching network is to be used to match the load impedance of prob. 10

to a line of characteristic impedance 50 ohms at a frequency of 1 GHz. Determine all

possible solutions for the matching problem using Smith Chart.

12. Repeat problem 11 for a load impedance of (100 + j50) ohms.

13. Derive an expression for the input impedance for the problem11 with the designed L-

section networks. Write a MATLAB programme to plot the input VSWR for the two

matching solutions and determine the match bandwidth in each case if the maximum

tolerable VSWR is 2.