Bài giảng Electromagnetic Fields – Prob - Chapter 6 - Trần Quang Việt
Electromagnetic Fields – Prob – ch_6
P6.5. In the system shown in Fig.6.64, assume that Vg is a constant
voltage source of 100V and the switch S is closed at t=0. Find and
sketch: (a) the line voltage versus z for t=0.2s; (b) the line current
versus z for t=0.4s; (c) the line voltage versus t for z=30m; and (d)
the line current versus t for z=-40m.
t=0
S
Vg
vp=2x108m/s
vp=3x108m/s
z=0-
z=300m
z=0+
z
z
z=-300m
Fig.6.64
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Electromagnetic Fields – Prob – ch_6
P6.6. In the system shown in Fig.6.65(a), the switch S is closed at
t=0. The line voltage variations with time at z=0 and z=l for the first
5s are observed to be as shown in Fig.6.65(b) and (c). Find the
values of V0, Rg, RL, and T.
[V]z=0, V
100
90
t=0
ts
ts
S
0
6
2
4
(b)
RL
Rg
T=1/vp
[V]z=l, V
V0
100
75
6
z=l
(a)
z=0
0
2
4
(c)
Fig.6.65
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Electromagnetic Fields – Prob – ch_6
P6.7. The system shown in Fig.6.66 is in steady state. Find (a) the
line voltage and current, (b) the (+) wave voltage and current, and (c)
the (-) wave voltage and current.
Ts
100V
z=l
z=0
Fig.6.66
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Electromagnetic Fields – Prob – ch_6
P6.8. The system shown in Fig.6.67 the switch S is closed at t=0.
Assumse Vg(t) to be a direct voltage of 90V and draw the voltage and
current bounce diagrams. From these bounce diagrams, sketch: (a)
the line voltage and the line current versus t (up to t=7.25s) at z=0,
z=l, and z=l/2; and (b) the line voltage and line current versus z for
t=1.2s and t=3.5s.
t=0
S
T=1s
Vg(t)
z=l
z=0
Fig.6.67
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Electromagnetic Fields – Prob – ch_6
D7.4. A line of characterictis impedance 60 is terminated by a load
consisting of the series combination of R=30, L=1H, and
C=100pF. Find the values of SWR and dmin for each of the following
radian frequencies of the source: (a) =108; (b) =2x108; and (c)
=0.8x108.
Ans: (a) 2,0; (b) 14.94, 0.309; (c) 3.324, 0.115
D7.5. Standing-wave measurements are performed on a line of
characteristic impedance 60 terminated by a load ZR. For each of
the following sets of the standing-wave data, find ZR: (a) SWR=1.5, a
voltage minimum right at the load; (b) SWR=3.0, two successive
voltage minima at 3cm and 9cm from the load; and (c) SWR=2.0,
two successive voltage minima at 3cm and 7cm from the load
Ans: (a) (40+j0); (b) (180+j0); (c) (48+j36)
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Electromagnetic Fields – Prob – ch_6
D7.6. An air-dielectric line of characteristic impedance Z0=75 is
terminated by a load impedance (45+j60). Find the input
impedance of the line for each of the following pairs of values of the
frequency f and the length l of the line: (a) f=15MHz, l=5m; (b)
f=50MHz, l=3m; and (c) f=37.5MHz, l=5m
Ans : (a) (45-j60); (b) (45+j60); (c) (225+j0)
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Electromagnetic Fields – Prob – ch_6
P7.2. In the system shown in the Fig.7.42. the line is open-circuited
at the far end, the source voltage is: Vg(t) = V0cos(f0t)cos(3f0t)
and l=/4 at f=f0. Find the root-mean-square (rms) values of the line
voltage and line current at values of d/l equal to 0, 1/3, ½ and 1.
(Note: The rms value of the sum of the voltages of two harmonically
ralated frequencies is equal to the square root of the sum of the
square of the rms value of the individual voltages)
Open
Circuit
Fig.7.42
Vg(t)
d=0
d
d=l
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Electromagnetic Fields – Prob – ch_6
P7.3. In the system shown in the Fig.7.43(a). The source voltage is
periodic, as shown in Fig.7.43(b). Find the reading of the ammeter A
if it reads root-mean-square values.
Vg, V
V0
vp=108m/s
A
ts
Vg
2
-1/2 0 1/2 1 3/2
(b)
150m
(a)
Fig.7.43
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Electromagnetic Fields – Prob – ch_6
P7.12. A slotted coaxial line of characteristic impendance 75 was
use to measure an unknown load impendance. First, the receiving end
of the line was short-circuited. The voltage minima were found to be
20cm apart. One of the minima was marked as the reference point.
Next, the unknown impedance was connected to the receiving end of
the line. The SWR was found to be 3.0 and a voltage minimum was
found to be 6cm from the reference point toward the load. Find the
unknown load impedance.
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Electromagnetic Fields – Prob – ch_6
P7.17. For the system shown in Fig.7.51, find the input impedance of
the line and the time-average power delivered to the load.
Zg=(30+j40)
V
d=l
d=0
Fig.7.51
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Electromagnetic Fields – Prob – ch_6
P7.18. In the system in Fig.7.52, find : (a) the value of the load
impedance Zg that enables maximum power transfer from the
generator to the load; and (b) the power transferred to the load for the
value found in (a). (Hint: apply maximum power transfer theorem at
d=l)
(25+j50)
Zg
V
d=l
d=0
Fig.7.52
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Electromagnetic Fields – Prob – ch_6
P7.20. In the system shown in Fig.7.53, find the values of the
reactance X and the characteristic impedance Z02 of line 2 for which
the power delivered to the load ZR is a maximum.
Line 1
Zg=(40+j50)
Line 2
jX
ZR=(90+j75)
Vg
Fig.7.53
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