Signal Delay in RC Network

[Will]

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

 

[Joe McElvenney]

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.

 

[Joe McElvenney]

Will,

Sorry but managed to screw-up the URL. Try this -

http://www.ece.cmu.edu/~ee760/760docs/lec18.pdf


Cheers - Joe