Aerial Cable Impedance Problem: Calculating Signal Amplitude & Energy Transfer

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SUMMARY

The discussion focuses on calculating the signal amplitude and energy transfer in an aerial feeder cable system with characteristic impedances of 75Ω and 120Ω. A 100μV signal received at the aerial results in a transmitted signal amplitude of 61.03μV into the second cable, calculated using the voltage divider formula. Additionally, the energy fraction carried by the reflected wave can be determined using the equation (16Z(0)^2 * Z(1)^2) / ((Z(0) + Z(1))^4), which relates to the power conservation principle stating that incident power equals reflected power plus transmitted power.

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  • Understanding of characteristic impedance in transmission lines
  • Familiarity with voltage divider formulas
  • Knowledge of power conservation in electrical circuits
  • Basic concepts of wave reflection and transmission in cables
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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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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
 

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