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If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.?
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If the measurement made on a box enclosing a two port network are Z10c...
Understanding the Problem
To find the propagation constant (γ) of a symmetrical two-port network, we start with the provided measurements:
- Z10c = 40 ∠ 0 degrees
- Z15c = 20.3 ∠ 29.8 degrees
Given that the network is symmetrical, we can use the characteristic impedance (Z0) and the measured impedances to derive the propagation constants.
Calculating the Characteristic Impedance
- The characteristic impedance (Z0) can be derived as follows:
Z0 = √(Z10c * Z15c)
- Substituting the values:
Z0 = √(40 * 20.3) = √812 = 28.5 ohms (approximately)
Finding the Propagation Constant (γ)
- The propagation constant (γ) is a complex quantity given by γ = α + jβ, where α is the attenuation constant and β is the phase constant.
- Since Z10c and Z15c are symmetrical, we can relate them to γ:
- Z10c = Z0 * (1 + e^(-γl)) / (1 - e^(-γl))
- Z15c = Z0 * (1 + e^(γl)) / (1 - e^(γl))
Calculating Attenuation (α) and Phase Constant (β)
- From the polar forms of the impedances, we can extract the real and imaginary parts to solve for α and β.
- Using the magnitude and phase:
- Magnitude: α can be estimated by the change in amplitude of Z.
- Phase: β can be inferred from the phase difference of the two measurements.
- After computation:
- α ≈ (1/l) * ln(Z15c/Z10c)
- β ≈ (1/l) * (∠Z15c - ∠Z10c)
Conclusion
By performing the above calculations, you can find specific numerical values for α and β, which represent the attenuation and phase constants respectively, critical for analyzing the performance of the two-port network.
To find the propagation constant (γ) of a symmetrical two-port network, we start with the provided measurements:
- Z10c = 40 ∠ 0 degrees
- Z15c = 20.3 ∠ 29.8 degrees
Given that the network is symmetrical, we can use the characteristic impedance (Z0) and the measured impedances to derive the propagation constants.
Calculating the Characteristic Impedance
- The characteristic impedance (Z0) can be derived as follows:
Z0 = √(Z10c * Z15c)
- Substituting the values:
Z0 = √(40 * 20.3) = √812 = 28.5 ohms (approximately)
Finding the Propagation Constant (γ)
- The propagation constant (γ) is a complex quantity given by γ = α + jβ, where α is the attenuation constant and β is the phase constant.
- Since Z10c and Z15c are symmetrical, we can relate them to γ:
- Z10c = Z0 * (1 + e^(-γl)) / (1 - e^(-γl))
- Z15c = Z0 * (1 + e^(γl)) / (1 - e^(γl))
Calculating Attenuation (α) and Phase Constant (β)
- From the polar forms of the impedances, we can extract the real and imaginary parts to solve for α and β.
- Using the magnitude and phase:
- Magnitude: α can be estimated by the change in amplitude of Z.
- Phase: β can be inferred from the phase difference of the two measurements.
- After computation:
- α ≈ (1/l) * ln(Z15c/Z10c)
- β ≈ (1/l) * (∠Z15c - ∠Z10c)
Conclusion
By performing the above calculations, you can find specific numerical values for α and β, which represent the attenuation and phase constants respectively, critical for analyzing the performance of the two-port network.
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If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.?
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If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.? 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 If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.?.
If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.? 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 If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the measurement made on a box enclosing a two port network are Z10c = 40angle 0 degree, Z15c = 20.3 angle 29.8 degree . Find the values of propagation constant along with attentuation constant and phase constant if the network is symmetrical.?.
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