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Signal Delay in RC Network

Discussion in 'Electronic Basics' started by Will, Aug 22, 2005.

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  1. Will

    Will Guest

    Hi all,

    (Just for interest) I'm now studying something related to RC network
    delay. One of the ways (Elmore's) to calculate the delay is:

    ---/\/\/---+---/\/\/---+---.....---+---/\/\/---+
    R1 | R2 | | Rn |
    --- --- --- ---
    C1 --- C2 --- --- --- Cn
    | | | |
    ___ ___ ___ ___
    = = = =

    time delay from left to right
    = (R1*C1) + (R1+R2)*C2 + ... (R1+R2+...+Rn)*Cn equ.(1)

    Now consider a 1-pi RC network below:
    ---/\/\/---+---/\/\/---+
    R1 | R |
    --- ---
    C/2 --- C/2 ---
    | |
    ___ ___
    = =

    Also consider a 2-pi RC network:
    ---/\/\/---+---/\/\/---+---/\/\/---+
    R1 | R/2 | R/2 |
    --- --- ---
    C/4 --- C/2 --- C/4 ---
    | | |
    ___ ___ ___
    = = =

    Interestingly, according to equ.(1), the time delay of both pi-model is
    the same!! (time delay = R1C + RC/2)

    However, some books say that the higher the order (higher pi) of the RC
    network, the more accurate and practical is the model.(Of course, it
    takes more time for simulation since there are more components in
    higher order RC network.) How come this is more accurate and practical
    provided that they have the same time delay using equ.(1)??? Is this
    because equ.(1) is just approximation and not accurate enough to
    describe the model??

    Any comment would be very appreciated :)

    Will
     
  2. Will,

    Don't know a thing about Elmore's Delay (remember "Elmer's
    Tune" though). However, I digress -

    Have a look at this tutorial where maybe there is an answer or
    two on the road to enlightenment, especially toward the end. It
    appears that it works but don't push the maths too far.

    http://www.ece.cmu.edu/~ee760/760docs/lec18.pdf#search='elmore delay'


    Cheers - Joe

    Who believes that the frequency domain is enough for one lifetime.
     
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