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Transmision Line Question

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data
    A 3kW radio signal generator is connected via a transmission line having an attenuation of 0.4 dB/m.
    Generator and load impedance are matched to the line.
    i) How long may the line be, if the load must receive at least 1kW of power?
    ii) How much power is dissipated by the 7th metre of line?

    2. Relevant equations
    GAIN=10log(Pout/Pin)

    P=vi=v[tex]\hat{}[/tex]2 / Z = i[tex]\hat{}[/tex]2 * Z

    A = 32.5[tex]/[/tex]20log10F [tex]/[/tex] 20log10 D

    3. The attempt at a solution
    i)I used the GAIN formula to determine the power out and then i used the P=v^2/Z to find the impedance.
    Line is 2.7x10^-6 long.

    And i don't think this is correct, because i don't have any voltage value to input in the P=v^2/Z forumla.

    ii)I used the P=v^2/Z to find the power dissipated by the 7th meter of line.

    the answer is 38.5x10^-9

    Could someone tell me if this is correct.
     
  2. jcsd
  3. Sep 24, 2009 #2

    Redbelly98

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    Welcome to Physics Forums :smile:

    The 2.7x10^-6 m figure is wrong. But, maybe thinking about the following question can help get you started in the right direction:


    For 1 meter of line, and the given attenuation of 0.4 dB/m, how much power would there be (Pout=___?) for 1 m of line?​
     
  4. Sep 25, 2009 #3
    Thanks i'm glad to be here.

    Well this is what the result will be if the Pin=3kw & GAIN=0.4dB/m
    So by using the GAIN formula i get the result:

    Pout=3289.43W.
     
  5. Sep 25, 2009 #4

    Born2bwire

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    How can the power increase over a line of attenuation?
     
  6. Sep 25, 2009 #5

    Redbelly98

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    Good point. The transmission line causes attenuation, not gain.
     
  7. Sep 26, 2009 #6
    ok, well this is how i worked it out.

    GAIN=10log(Pout/Pin

    0.4=10log((Pout/3*10^3)

    0.04=log(Pout/3*10^3)

    10^0.04=(Pout/3*10^3)

    Pout=(10^0.04)*(3*10^3)

    Pout=3289.43W

    Have i done something wrong, coz i cant see anything wrong.
     
  8. Sep 26, 2009 #7

    Redbelly98

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    Something is wrong, since the power out should be less than the 3 kW input. That is the meaning of the word attenuation.

    Since the transmission line causes loss of power, -0.4 dB should be used for the gain.
     
  9. Sep 26, 2009 #8
    oh, now i know where it was wrong silly me -_-.
     
  10. Sep 26, 2009 #9
    Well after doing it again i got Pout=2736.03W.
     
  11. Sep 26, 2009 #10

    Redbelly98

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    Okay, that's right.

    Next, how many dB would give Pout = 1000W?
     
  12. Sep 26, 2009 #11
    ok, by using the GAIN formula:

    GAIN=10log(1000W/3000W)
    GAIN=-4.77dB/m
     
  13. Sep 26, 2009 #12

    Redbelly98

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    Okay, though the units are actually -4.77 dB (no "/m") in this calculation.

    Now to answer the question. How many meters of cable would give that -4.77 dB?
     
  14. Sep 26, 2009 #13
    could you tell me what formula to use?
     
  15. Sep 26, 2009 #14

    Redbelly98

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    At this point you don't need a formula to plug the numbers into. You'll need to think about what the numbers actually mean.

    Use the information in the problem statement, and the fact that you have 4.77 dB of attenuation.

    Good luck!
     
  16. Sep 26, 2009 #15
    thanks for the help, i think i get what you mean after thinking about it. If i came across anymore problems i will post them.

    so just to clarify, 4.77db would give you appox 11.9m. In ii) the power dissipated would be the amount of power dissipated from 1m times 7m which would give you the power dissipated for the 7th meter of line.
     
    Last edited: Sep 26, 2009
  17. Sep 26, 2009 #16

    Redbelly98

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    Yes, I agree. :smile:

    Your description doesn't make sense to me. The way I interpret the question is as follows:

    How much power is dissipated in the 7th meter, i.e. between x=6m and x=7m?
    To answer that, you'll need to calculate the power (think of it as Pout) at x=6m and at x=7m, given the 3000W Pin and the -0.4 dB/m power loss.
    From that you can figure out how much of the power was lost in that 7th meter.
     
  18. Sep 26, 2009 #17
    so, basically the value i found out from before of 2736.03W would then be multiplied by 7 to get the power lost in the 7 meters.
     
  19. Sep 26, 2009 #18

    Redbelly98

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    ...giving you 19kW lost. Which is quite impossible, given that there were only 3kW to begin with.
     
  20. Sep 26, 2009 #19
    ok, i made Pin=3000W & GAIN=-2.8dB
    From that i calculated the Pout as 1574.42W. So therefore the power loss from 7 meters of line is 1574.42W.
     
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