Is the impedance of a transmission line related to its length or not ?

Discussion in 'General Electronics Chat' started by shengwuei, Aug 22, 2008.

  1. shengwuei

    Thread Starter Member

    Aug 22, 2008
    The general formula of transmission line impedance is as the following :
    ( refer to )

    where “l” is the length of the transmission line, indicating that the impedance of a transmission line changes along the line, which is straght forward to me to imagine the behavior of a transmission line

    On the other hand, if we consider the impedance of a microstrip, the formula becomes to :
    (refer to


    I assume there is a complex way to transform these two formulas from one another, but it is too complicated for me to go through the textbook.
    However, I still try to find any length related term in this formula but there seems none.
    Does it mean that the impedance of a microstrip is not related to its length ? But why ?

    Appreciate for your response.
  2. studiot

    AAC Fanatic!

    Nov 9, 2007
    A transmission line has constant impedance, independent of its length.

    Typical examples are the 75 ohm cable used for television signals, the 300 ohm cable used for radio signals.

    Of course the equations you quote assume an infinite line. That is the signal travels for ever away from the source.

    In practice we approximate this by terminating the line with its characteristic impedance which absorbs the signal completely, so none is reflected back.
  3. shengwuei

    Thread Starter Member

    Aug 22, 2008
    Hi Studiot,

    Thanks for the explanation.

    I just found if we set ZL=Z0 in the first formulat, Zin becomes ZL, meaning that Zin is indepentant of the transmission line length no matter how long or how short the line is. (And as you said, no reflection from the load)
    However, except the about case, Zin changes with the length of the transmission line.

    But the characteristic impedance of the transmission line(Z0) is indeed independant of the length, it's a constant for a given transmission line.