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A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ω at a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.
Q.
Find β
- a)0.2176 rad/m
- b)0.4352 rad/m
- c)0.6584 rad/m
- d)0.8712 rad/m
Correct answer is option 'A'. Can you explain this answer?
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A transmission line is lossless and is 25 m long. It is terminated wit...
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A transmission line is lossless and is 25 m long. It is terminated wit...
Lossless Transmission Line Characteristics
A lossless transmission line is characterized by its inductance (L) and capacitance (C) per unit length. These parameters determine the propagation velocity (v) and characteristic impedance (Z0) of the transmission line.
Given Parameters
Length of the transmission line (l) = 25 m
Load impedance (ZL) = 40 j30 Ω
Frequency (f) = 10 MHz
Inductance per unit length (L) = 300 nH/m
Capacitance per unit length (C) = 40 pF/m
Calculation
Step 1: Propagation Velocity (v)
The propagation velocity (v) can be calculated using the formula:
v = 1 / sqrt(L * C)
Substituting the given values:
v = 1 / sqrt(300 nH/m * 40 pF/m)
Converting the units:
v = 1 / sqrt(300 * 10^-9 H/m * 40 * 10^-12 F/m)
v = 1 / sqrt(12 * 10^-9)
v = 1 / (sqrt(12) * 10^-5)
v ≈ 8333.33 m/s
Step 2: Characteristic Impedance (Z0)
The characteristic impedance (Z0) can be calculated using the formula:
Z0 = sqrt(L / C)
Substituting the given values:
Z0 = sqrt(300 nH/m / 40 pF/m)
Converting the units:
Z0 = sqrt(300 * 10^-9 H/m / 40 * 10^-12 F/m)
Z0 = sqrt(7.5 * 10^-3)
Z0 ≈ 0.0866 Ω
Step 3: Wavelength (λ)
The wavelength (λ) can be calculated using the formula:
λ = v / f
Substituting the given values:
λ = 8333.33 m/s / 10^7 Hz
λ = 0.8333 m
Step 4: Phase Constant (β)
The phase constant (β) can be calculated using the formula:
β = 2π / λ
Substituting the calculated value of λ:
β = 2π / 0.8333
β ≈ 7.54 rad/m
Step 5: Lossless Transmission Line Phase Constant (α)
Since the transmission line is lossless, the phase constant (α) is zero.
Step 6: Total Phase Constant (γ)
The total phase constant (γ) can be calculated using the formula:
γ = α + jβ
Substituting the known values:
γ = 0 + j7.54
γ ≈ 7.54j rad/m
Step 7: Line Input Impedance (Zin)
The line input impedance (Zin) can be calculated using the formula:
Zin = Z0 * (ZL + jZ0 * tan(βl)) / (Z0 + jZL * tan(βl))
Substituting the known values:
Zin = 0.0866 Ω * (40
A lossless transmission line is characterized by its inductance (L) and capacitance (C) per unit length. These parameters determine the propagation velocity (v) and characteristic impedance (Z0) of the transmission line.
Given Parameters
Length of the transmission line (l) = 25 m
Load impedance (ZL) = 40 j30 Ω
Frequency (f) = 10 MHz
Inductance per unit length (L) = 300 nH/m
Capacitance per unit length (C) = 40 pF/m
Calculation
Step 1: Propagation Velocity (v)
The propagation velocity (v) can be calculated using the formula:
v = 1 / sqrt(L * C)
Substituting the given values:
v = 1 / sqrt(300 nH/m * 40 pF/m)
Converting the units:
v = 1 / sqrt(300 * 10^-9 H/m * 40 * 10^-12 F/m)
v = 1 / sqrt(12 * 10^-9)
v = 1 / (sqrt(12) * 10^-5)
v ≈ 8333.33 m/s
Step 2: Characteristic Impedance (Z0)
The characteristic impedance (Z0) can be calculated using the formula:
Z0 = sqrt(L / C)
Substituting the given values:
Z0 = sqrt(300 nH/m / 40 pF/m)
Converting the units:
Z0 = sqrt(300 * 10^-9 H/m / 40 * 10^-12 F/m)
Z0 = sqrt(7.5 * 10^-3)
Z0 ≈ 0.0866 Ω
Step 3: Wavelength (λ)
The wavelength (λ) can be calculated using the formula:
λ = v / f
Substituting the given values:
λ = 8333.33 m/s / 10^7 Hz
λ = 0.8333 m
Step 4: Phase Constant (β)
The phase constant (β) can be calculated using the formula:
β = 2π / λ
Substituting the calculated value of λ:
β = 2π / 0.8333
β ≈ 7.54 rad/m
Step 5: Lossless Transmission Line Phase Constant (α)
Since the transmission line is lossless, the phase constant (α) is zero.
Step 6: Total Phase Constant (γ)
The total phase constant (γ) can be calculated using the formula:
γ = α + jβ
Substituting the known values:
γ = 0 + j7.54
γ ≈ 7.54j rad/m
Step 7: Line Input Impedance (Zin)
The line input impedance (Zin) can be calculated using the formula:
Zin = Z0 * (ZL + jZ0 * tan(βl)) / (Z0 + jZL * tan(βl))
Substituting the known values:
Zin = 0.0866 Ω * (40
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A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer?
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A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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ample number of questions to practice A transmission line is lossless and is 25 m long. It is terminated with a load of zL =40+j30Ωat a frequency of 10 MHz. The inductance and capacitance of the line are L - 300nH/m, C = 40pF/m.Q.Findβa)0.2176 rad/mb)0.4352 rad/mc)0.6584 rad/md)0.8712 rad/mCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Electronics and Communication Engineering (ECE) tests.
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