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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 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 Two-Port Network
To find the propagation constant of a symmetrical two-port network given the impedance measurements Z10c and Z15c, we start with the provided values:
- Z10c = 40∠0° (Impedance at port 1)
- Z15c = 20.3∠29.8° (Impedance at port 2)
Symmetrical Network Properties
In a symmetrical network, the parameters exhibit certain relationships, particularly:
- Z11 = Z22 (input and output impedances are equal)
- Z12 = Z21 (forward and reverse transfer impedances are equal)
Given that the network is symmetrical, we can use the average of the two impedances to determine the propagation constant.
Calculating the Average Impedance
- The average impedance can be calculated as:
Average Z = (Z10c + Z15c) / 2
Given the magnitudes and angles, convert the impedances to rectangular form:
- Z10c = 40 + j0
- Z15c = 20.3(cos(29.8°) + j sin(29.8°))
Calculating Z15c:
- Z15c ≈ 20.3(0.874 + j0.5)
- Z15c ≈ 17.7 + j10.15
Now, calculate the average impedance:
- Average Z = (40 + j0 + 17.7 + j10.15) / 2
- Average Z = (28.85 + j5.075)
Finding the Propagation Constant (γ)
The propagation constant can be expressed as:
- γ = α + jβ
Where α represents the attenuation constant and β represents the phase constant.
Using the average impedance, we can derive the values for α and β based on the characteristics of the transmission line and the network's operational frequency.
Conclusion
For a symmetrical two-port network, the propagation constant can be deduced from the average impedance, ensuring accurate analysis for signal transmission within the network.
To find the propagation constant of a symmetrical two-port network given the impedance measurements Z10c and Z15c, we start with the provided values:
- Z10c = 40∠0° (Impedance at port 1)
- Z15c = 20.3∠29.8° (Impedance at port 2)
Symmetrical Network Properties
In a symmetrical network, the parameters exhibit certain relationships, particularly:
- Z11 = Z22 (input and output impedances are equal)
- Z12 = Z21 (forward and reverse transfer impedances are equal)
Given that the network is symmetrical, we can use the average of the two impedances to determine the propagation constant.
Calculating the Average Impedance
- The average impedance can be calculated as:
Average Z = (Z10c + Z15c) / 2
Given the magnitudes and angles, convert the impedances to rectangular form:
- Z10c = 40 + j0
- Z15c = 20.3(cos(29.8°) + j sin(29.8°))
Calculating Z15c:
- Z15c ≈ 20.3(0.874 + j0.5)
- Z15c ≈ 17.7 + j10.15
Now, calculate the average impedance:
- Average Z = (40 + j0 + 17.7 + j10.15) / 2
- Average Z = (28.85 + j5.075)
Finding the Propagation Constant (γ)
The propagation constant can be expressed as:
- γ = α + jβ
Where α represents the attenuation constant and β represents the phase constant.
Using the average impedance, we can derive the values for α and β based on the characteristics of the transmission line and the network's operational frequency.
Conclusion
For a symmetrical two-port network, the propagation constant can be deduced from the average impedance, ensuring accurate analysis for signal transmission within the 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 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 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 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 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 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 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 if the network is symmetrical.?.
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