# [SI-LIST] : Critical Length

Abe Riazi ([email protected])
Sat, 27 Mar 1999 09:13:41 -0800

Dear SI-List Members,

The critical length, which defines a boundary between the lumped and
distributed system elements, finds remarkable applications in the area
of signal integrity simulation. For instance, it can influence:
1. The need, or lack thereof, for simulation and its complexity.
2. The required level of model precision and hence extensiveness
of model verification and correction.
3. Interpretation of simulaion results.
Therefore, it is advantageous to determine the critical length at an
early stage of a SI simulation task.

This important transmission line parameter is calculated via:
Critical Length = k(Rise Time)/(Delay)
Where the ratio (Rise Time)/(Delay) is called the length of rising
edge, and the coefficient k can be defined only as an approximation.
Values given for K in literature include: 1/2, 2/5, 1/3 , 1/4, 1/6 and
1/8.

Presented below is a numerical example, which utilizes Rise Time and
Delay values within the PCI Bus specifications:
Delay = 2.0 ns/ft
Risetime = 1.5 ns
Let k = 1/6, then:
Critical Length = (1/6)(1.5 ns)/(2 ns/ft) = 1.5 Inches

Let us consider another example, selecting values applicable to the
Rambus Channel:
Delay = ( C )( Zo) = ( 2.9 pF/in)( 28 Ohms ) = 81.2 ps/in
Rise Time = 400 ps
Again letting k = 1/6, it follows:
Critical Length = 0.821 Inches
This result implies that trace segments and stubs smaller than 0.824
inches are lumped, whereas those larger than 0.824 inches are classified
as distributed. Such short critical lengths are often accompanied by
numerous design and simulation challenges.

A frequently asked question related to the critical length:
Why the rise time and not the signal frequency?
Of course, a high frequency signal, due to its narrow period,
imposes contrains on the rise and fall times and forces them to be
small. A low frequency digital signal may also exhibit sharp switching
transitions and it is still the edge rate, not the frequency nor the
period, which dictates the critical length.

As mentioned earlier, there is some uncertainty regarding the exact
value of its coefficient; nonetheless, the critical length provides a
powerful guideline for distinguishing the lumped and distributed circuit
constituents and offers a wide domain of applications.