Aerial Cable Impedance Problem: Calculating Signal Amplitude & Energy Transfer

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In summary, the amplitude of the signal transmitted into the second cable is 61.03μV. For the second part, the fraction of energy carried by the reflected wave is calculated using the formula (16Z(0)^2 * Z(1)^2) / ((Z(0) + Z(1))^4), where Z(0) is the characteristic impedance of the first cable (75Ω) and Z(1) is the characteristic impedance of the second cable (120Ω). This gives a fraction of energy of 0.2 or 20%. Finally, the incident power is equal to the reflected power plus the transmitted power, as shown by the equation P(inc) = P(ref) + P(trans
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p834
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Homework Statement


An aerial feeder cable (characteristic impedance 75Ω) is connected to a long cable of characteristic impedance 120Ω. If a 100μV signal is received at the aerial, calculate the amplitude of the signal transmitted into the second cable. What fraction of energy is carried by the reflected wave from the change in impedance boundary? Show that the incident power = reflected power + transmitted power

But I am struggling with the other 2 parts, any ideas?
Thanks!


Homework Equations


For the second part of the question, I believe that you have to use the equation:
(16Z(0)^2 * Z(1)^2) / ((Z(0) + Z(1))^4)


The Attempt at a Solution

 
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  • #2
For the first part, I used the voltage divider formula:V2 = V1 * (Z2 / (Z1 + Z2))V2 = 100μV * (120Ω / (75Ω + 120Ω))V2 = 100μV * (120Ω / 195Ω)V2 = 61.03μV
 

1. What is aerial cable impedance?

Aerial cable impedance refers to the resistance that a cable has to an alternating electrical current flowing through it. It is measured in ohms and is affected by factors such as the cable's thickness, length, and material.

2. Why is calculating signal amplitude important in aerial cable impedance?

Calculating signal amplitude allows us to determine the strength of the electrical signal traveling through the cable. This is important because a weaker signal can lead to performance issues and may not deliver the intended energy transfer.

3. How is energy transfer affected by aerial cable impedance?

Aerial cable impedance can affect energy transfer by causing reflections and losses in the electrical signal. This can result in a decrease in the amount of energy that reaches the intended destination, leading to performance issues or signal degradation.

4. What factors influence the impedance of an aerial cable?

The thickness, length, and material of the cable are the main factors that influence its impedance. Additionally, the frequency and type of signal being transmitted can also impact the cable's impedance.

5. How can aerial cable impedance problems be solved?

Aerial cable impedance problems can be solved by using appropriate cable types and lengths, minimizing cable bends and twists, and using impedance matching techniques. It is also important to regularly check and maintain the cables to prevent any issues from arising.

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