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The input impedance of short-circuited line of length l where λ/4 < l < λ/2, is
- a)resistive
- b)inductive
- c)capacitive
- d)none of the above
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The input impedance of short-circuited line of length l where λ/4 <...
l < λ/4, ZL = 0
, if Zd comes +j kZC then inductive, If Zd comes -j kZC then capacitive.
for 0 ≤ l ≤ 1/4, λ ≤ l ≤ 3λ/4 will be inductive.
Most Upvoted Answer
The input impedance of short-circuited line of length l where λ/4 <...
The input impedance of a short-circuited line of length l where λ/4 < l="" />< λ/2="" is="" purely="" imaginary="" and="" is="" given="" />
Zin = jZ0*tan(βl)
where Z0 is the characteristic impedance of the line, β is the propagation constant, and l is the length of the line.
Since the line is short-circuited, the voltage at the input end of the line is zero. Therefore, the input impedance is determined by the current flowing through the line.
If the line length is λ/4, then βl = π/2, and the input impedance becomes:
Zin = jZ0*tan(π/2) = infinity
This means that the line appears as an open circuit at the input end.
If the line length is between λ/4 and λ/2, then βl is between π/2 and π, and the input impedance is purely imaginary and varies with frequency.
For example, if l = λ/3, then βl = 2π/3, and the input impedance becomes:
Zin = jZ0*tan(2π/3) = j√3*Z0
This means that the line appears as a capacitive reactance at the input end.
Overall, the input impedance of a short-circuited line of length l where λ/4 < l="" />< λ/2="" is="" a="" function="" of="" the="" line="" length="" and="" the="" characteristic="" impedance="" of="" the="" line,="" and="" it="" varies="" with="" frequency.="" λ/2="" is="" a="" function="" of="" the="" line="" length="" and="" the="" characteristic="" impedance="" of="" the="" line,="" and="" it="" varies="" with="" />
Zin = jZ0*tan(βl)
where Z0 is the characteristic impedance of the line, β is the propagation constant, and l is the length of the line.
Since the line is short-circuited, the voltage at the input end of the line is zero. Therefore, the input impedance is determined by the current flowing through the line.
If the line length is λ/4, then βl = π/2, and the input impedance becomes:
Zin = jZ0*tan(π/2) = infinity
This means that the line appears as an open circuit at the input end.
If the line length is between λ/4 and λ/2, then βl is between π/2 and π, and the input impedance is purely imaginary and varies with frequency.
For example, if l = λ/3, then βl = 2π/3, and the input impedance becomes:
Zin = jZ0*tan(2π/3) = j√3*Z0
This means that the line appears as a capacitive reactance at the input end.
Overall, the input impedance of a short-circuited line of length l where λ/4 < l="" />< λ/2="" is="" a="" function="" of="" the="" line="" length="" and="" the="" characteristic="" impedance="" of="" the="" line,="" and="" it="" varies="" with="" frequency.="" λ/2="" is="" a="" function="" of="" the="" line="" length="" and="" the="" characteristic="" impedance="" of="" the="" line,="" and="" it="" varies="" with="" />
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