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An overhead line with surge impedance 400 ╬й is terminated through a resistance R. A surge traveling over the line does not suffer any reflection at the junction if the value of R is
20┬а╬й
200┬а╬й
800┬а╬й
None of the above
None of the above
A surge traveling on an overhead line with surge impedance ZcтАЛ experiences no reflection at a junction terminated with a resistance R if and only if the resistance is matched to the surge impedance, i.e., R=ZcтАЛ. Given ZcтАЛ=400┬а╬й, reflection is eliminated only when R=400┬а╬й.
A surge traveling on an overhead line with surge impedance ZcтАЛ experiences no reflection at a junction terminated with a resistance R if and only if the resistance is matched to the surge impedance, i.e., R=ZcтАЛ. Given ZcтАЛ=400┬а╬й, reflection is eliminated only when R=400┬а╬й.
╧Б=R+ZcтАЛRтИТZcтАЛтАЛ тАФ formula for reflection coefficient
R=ZcтАЛ тАФ condition for matched impedance (no reflection)
When a surge wave travels along a transmission line and encounters a change in impedance, a portion of the wave is reflected to maintain the continuity of voltage and current. The reflection coefficient ╧Б is defined as ╧Б=R+ZcтАЛRтИТZcтАЛтАЛ. For no reflection to occur, ╧Б must be 0, which implies R=ZcтАЛ.
Surge impedance (characteristic impedance) of an overhead line is typically between 400-500 ╬й.
When R>ZcтАЛ, the reflection coefficient is positive (voltage reflection).
When R<ZcтАЛ, the reflection coefficient is negative (current reversal).
Matched termination is essential to avoid standing waves in high-frequency transmission.
Eliminates voltage stress due to wave reflection
Ensures maximum power transfer to the termination load
Requires precise impedance matching, which is difficult for variable frequency surges
Power loss in the terminating resistance
High-voltage transmission line termination
Telecommunication cable impedance matching
For R=400┬а╬й, reflection coefficient ╧Б=400+400400тИТ400тАЛ=0.
Options A, B, and C provide 20┬а╬й, 200┬а╬й, and 800┬а╬й respectively, none of which equal 400┬а╬й.
D is correct тАФ Since the reflection coefficient is ╧Б=R+ZcтАЛRтИТZcтАЛтАЛ, no reflection occurs only if R=ZcтАЛ=400┬а╬й, which is not listed in the options.
Remember that ZcтАЛ for an overhead line is much higher (~400 ╬й)than for underground cables (~40 ╬й),which is a common point of confusion in power system transient calculations.