Signal Delay in RC Network

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