Re: [SI-LIST] : EFFECT OF LUMPED LOAD ON TRANSMISSION LINES

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From: ARiazi (ARIAZI@prodigy.net)
Date: Mon May 28 2001 - 18:11:35 PDT


Chandan Wrote:

> By the way, how does one decide the rise time length?
> Sometime in April, Abe Riazi (ServerWorks)
> provided us with the BELOW formula for critical
> length. (Refer to "Source termination of transmission
> line, April 23)
>
> Lc = k(Tr)/(Tpd)
> Where, Tr is rise time and Tpd is signal propagation
> delay.
> A good value for coefficient k is 1/6; and assuming
> FR-4 substrate
>
> Could someone derive this for me? or this this an
> empirical result?
>
The origin of Critical Length can be found in
High-Speed Digital Design-A Handbook of Black Magic
Page 7, Equation 1.3:

Length of rising edge = rise time/delay

The critical length then emerges via simple relation:

Lc = k * (length of rising edge)

The coefficient k can assume a range of values including
1/2, 2/5, 1/3, 1/4, 1/6, 1/8, 1/10. The selection
k=1/6 is an excellent choice for many (but not all) applications.

> I thought of using the following relationship:
> velocity = distance/time
> Therefore, Critical length = velocity of signals on
> the PCB * rise time
> Assuming a PCB propagation velocity that is half the
> speed of light,
> Critical length = 15cm/ns * rise time

Your assumption that PCB propagation velocity is half speed of
light ( or equivalently PCB signal propagation delay is twice propagation
delay of electromagnetic waves in free space) is correct.

Valuable insight can be gained by considering free space speed of light
( c ) and its reciprocal ( 1/c ) in several different units, i.e. :

c = 3E8 m/sec = 3E10 cm/sec = 30 cm/ns = 1.118E10 in/sec = 0.0118 in/ps
=11.8 in/ns

1/c = 84.67 ps/in = 0.08467 ns/in = 1.02 ns/ft

The equality 1/c = 1.02 ns/ft is approximately one half of a commonly used
value (e.g. 2 ns/ft ) for signal propagation delay on a PCB having FR-4
substrate.

The critical length expression you have given:

Critical length = 15cm/ns * rise time

appears based on k=1, which is regarded too large and rarely used.

My post dated March 27, 19999 contains additional information regarding
Critical Length .
Furthermore, comments by D.C. Sessions and Larry McMillan who detected
numerical errors in that post are quite instructive.

Best Regards,

Abe Riazi
ServerWorks

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