DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

INDIAN INSTITUTE OF TECHNOLOGY ROORKEE

EC-631 Prob. Sheet 1

1. In the system shown in Fig.1, a wave carrying power P is incident on the junction aa from line 1. Find (a) the power reflected into line 1, (b) the power transmitted into lines 2 and 3.

2. In the system shown in Fig.2, an incident wave of voltage V+ strikes the discontinuity from left. Find the reflected wave voltage and current in line 1 and the transmitted wave voltage

and current into line 2.

3. For each of the following characteristics of standing wave on lossless short-circuited line, find the frequency of the wave exciting the line: (a) distance between successive current nodes is 1

m and dielectric is air, (b) the distance between successive current nodes is 1 m and the

dielectric is nonmagnetic with = 2.250, (c) the distance between successive nodes of instantaneous power flow is 1 m and the dielectric is air.

4. A lossless coaxial cable of characteristic impedance 50 ohms and having a nonmagnetic

dielectric of permittivity = 2.250 is short circuited at the far end. Find the minimum length for which the i/p impedance at 100 MHz is (a) a capacitor of value 10 pF, (b) a capacitor of

value 100 pF, (c) an inductor of value 0.25 H. 5. For a line open circuited at the far end, obtain the solution for the complex line voltage and

current and sketch the voltage and current standing wave patterns on the line.

6. A line of length l is short circuited at the far end. At the other end a voltage source of internal

impedance 100 ohm and voltage Vg(t) = 100 cos3 (0t) volts is connected. If l = /2 at f=f0,

find the r.m.s. values of the line voltage and current at l = 0, l/3, l/2, and l.

7. A transmission line of ch. imp. 50 ohms is terminated in la load (15-j20) ohms. Find the voltage reflection coefficient at the load, SWR on the line, and the location of first voltage

minima from the load.

8. Consider a transmission line of ch. imp. 50 ohms. When the line is terminated in a short circuit, successive voltage minima are found 20-cm apart. One of the minima is marked as a

reference point and the line is terminated in a load impedance. It is found that the SWR on the

line is 3 and a voltage minimum at a distance of 5.8 cm from the reference point on the side

toward the load. Find the load impedance.

9. Consider the transmission line shown in Fig. 3. Find at the input end, input impedance at the source end, current drawn from the source, and the power delivered to the load.

10. A line of ch. imp. 60 ohms is terminated in a load consisting of the series combination of

R=30 ohm, L=1 H, and C= 100 pF. Find the SWR and dmin for = 108 and = 0.8x108.

11. Consider a low-loss line system shown in Fig.4. Find the time-average power delivered to the input of the line, the time-average power delivered to the load, and the time-average power

dissipated in the line.

Ans. (2) 0.6 V+, -0.012 V

+, 0.4 V

+, 0.004 V

+, (4) 160, 75 m, 8/15, (3) 150 MHz, 100 MHz, 75MHz,

(4) 59.7 cm, 90.2 cm, 40.2 cm, (6) 0V, 0.559A; 22.96V, .319A; 27.95V, 0A; 0V,.559A, (9) .593-

133.16, 3.914, 0.065, (8) (37.45 + 48.365j), (9) 0.05-72, (39.86-50.54j), 48.26W, (10) 2, 0;

3.324, 0.115, (11) 20.32W, 14.91W, 5.41W.

Line-1(50-)lin

e-2(50

-)

line-3(50-)

a

a'Fig. 1

Line-1(50) 100- line-2(50-)

150-

Fig. 2

100

10+10j

30+40j

.725

50

Fig. 3

150

Fig. 4

100030 - j40

50

=0.01 Np/

10.2