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Math Help - 1. Give a detailed derivation telegraph equation. 2. derive expressions

  1. #1
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    Post 1. Give a detailed derivation telegraph equation. 2. derive expressions

    Please give me a helping hand on these two. thanks.
    ************************************************** ************************************************** **
    1. Give a detailed derivation telegraph equation (first principle). Say that the telegraph equation are a second order differential equation.

    You will show that the equation(s) to the telegraph equation will give you

    I_x= Ae^(-γ x) +Be^(γ x)
    V_x= (Ae^(-γx) +Be^γx)/Z_o
    Recall γ = a+ j b

    2. Derive expressions for; Z_o =f (primary constant)
    a =f (primary constant)
    b =f (primary constant)
    In terms of primary constants.


    Note that I is for current, V is for voltage and Z is for impedance.
    ************************************************** ********
    Last edited by mikal; January 2nd 2008 at 02:22 AM.
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  2. #2
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    Quote Originally Posted by mikal View Post
    Give a detailed derivation telegraph equation (first principle). Say that the telegraph equation are a second order differential equation.

    You will show that the equation(s) to the telegraph equation will give you

    I_x= Ae^(-γ x) +Be^(γ x)
    V_x= (Ae^(-γx) +Be^γx)/Z_o
    Recall γ =  + j 

    Derive expressions for; Z_o =f (primary constant)
     =f (primary constant)
     =f (primary constant)
    In terms of primary constants.


    Note that I is for current, V is for voltage and Z is for impedance.
    ************************************************** ********
    The only thing I know is that  \gamma^2 = (R+j\omega L)(G+j \omega C)
    And also that Z_0 = \sqrt{\frac{R+j \omega L}{G+j \omega C}}

    If R,L,C,G are your primary constants, then that is your formula
    >BUT<what is the following doing then?
    I_x= Ae^(-γ x) +Be^(γ x)
    V_x= (Ae^(-γx) +Be^γx)/Z_o

    Derive expressions for; Z_o =f (primary constant)
     =f (primary constant)
     =f (primary constant)
    In terms of primary constants.
    What is the function doing twice? I am lost about your interpretation!

    Explain what you want clearly!!
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  3. #3
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    Quote Originally Posted by mikal View Post
    Please give me a helping hand on these two. thanks.
    ************************************************** ************************************************** **
    1. Give a detailed derivation telegraph equation (first principle). Say that the telegraph equation are a second order differential equation.

    You will show that the equation(s) to the telegraph equation will give you

    I_x= Ae^(-γ x) +Be^(γ x)
    V_x= (Ae^(-γx) +Be^γx)/Z_o
    Recall γ = a+ j b

    2. Derive expressions for; Z_o =f (primary constant)
    a =f (primary constant)
    b =f (primary constant)
    In terms of primary constants.


    Note that I is for current, V is for voltage and Z is for impedance.
    ************************************************** ********
    If you type: "derivation telegraph equation" into Google what do you think
    you get?

    First hit is either this thread or your other one, and the second is this.

    RonL
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  4. #4
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    correcton

    Explain what you want clearly!![/QUOTE]

    The assignment was written exactly the same way I presented it. I corrected what you saw in another posting.
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  5. #5
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    Isomorp my answer... or kindly explain what you do not understand

    Isomorph, you asked>>>>>what is the following doing then?

    My answer>>>
    The lecturer wants us to derive the telegraph equation to get expressions for I_x (current) and V_x (voltage) in a transmission line.

    in this same thread you will find a correction to my first quote...

    or kindly explain what you do not understand


    What is the function doing twice? I am lost about your interpretation!

    Explain what you want clearly!![/QUOTE]
    Attached Files Attached Files
    • File Type: txt t.txt (1.1 KB, 30 views)
    Last edited by mikal; January 4th 2008 at 08:18 AM. Reason: addin attachement
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  6. #6
    Lord of certain Rings
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    Quote Originally Posted by mikal View Post
    Isomorph, you asked>>>>>what is the following doing then?

    My answer>>>
    The lecturer wants us to derive the telegraph equation to get expressions for I_x (current) and V_x (voltage) in a transmission line.
    in this same thread you will find a correction to my first quote...
    or kindly explain what you do not understand

    What is the function doing twice? I am lost about your interpretation!

    Explain what you want clearly!!
    Now it is a more clear, but not complete!
    What are primary constants? A and B ??
    Do you know the equations in terms of G,L,R,C? If you do, then you can compare terms and complete it.
    If you don't you have to read it up.
    Are you talking about these?:
    Z_0 = \sqrt{\frac{R+j \omega L}{G+j \omega C}}
    \gamma^2 = (R+j\omega L)(G+j \omega C)
    For me, G,L,R,C are primary constants
    Please describe the problem completely, I do not understand what Z_0, a, b in terms of primary constants mean
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  7. #7
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    re:Now it is a more clear, but not complete!

    Iso, your question>>>>>Now it is a more clear, but not complete!
    What are primary constants? A and B ??

    My answer>>>>>
    You know that a+jb is in complex number form right?
    so, on the day of the lecture, I was the only one that asked the lecturer what he means by γ (since he mentioned that it can either be positive or negative) and he said that it is either amplification or attenuation.

    Do you know the equations in terms of G,L,R,C?
    >>>> Nope
    If you do, then you can compare terms and complete it.
    If you don't you have to read it up.
    Are you talking about these?:
    Z_0 = \sqrt{\frac{R+j \omega L}{G+j \omega C}}
    >>> YES! For Zo, you've got the answer.

    \gamma^2 = (R+j\omega L)(G+j \omega C)
    >>>>I need to know what γ is in terms of a+jb (complex numbers), not what γ^2 means.
    For me, G,L,R,C are primary constants
    the primary constants are R,C,L and Z.

    Please describe the problem completely, I do not understand what Z_0, a, b in terms of primary constants mean

    >>>>>answer
    in any analysis you are given primary constants and told to find secondary constants. the primary constants are R,C,L and Z.



    just for more understanding, the Be^(γ x) part of the two equations only exisit when there is a mismatch condition, so you can simply work with:
    I_x = Ae^(-γ x) and V_x = Ae^(-γx)/Zo , having in mind that γ= attenuation or amplification and why it bears the minus sign in the assignment is cos most of the time he teached only with attenuation. so the γ = a + jb, i guess is to be used so incase it is either amplification or attenuation.
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  8. #8
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    w^2LC

    please explain what is in the attachement...
    I have gone very far in the assignment ...thanks.
    Attached Files Attached Files
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