At 06:03 PM 2/25/99 -0800, Douglas McKean wrote:
>I'm not an experienced board designer but ...
>I've seen this discussed in _High Speed Digital Design_
>by Howard Johnson and Martin Graham. They use a thing
>called "Rent's Rule". It's an equation that gives you
>average trace spacing by putting in a few parameters
>and it goes like this ...
>
>#1) ave. trace pitch = (2.7*M*[X*Y]^0.5)/N
>
> M = number of routing layers
> N = number of connections
> X = board width in inches
> Y = board length in inches
Johnson and Graham discuss Rent's Rule, including the assumptions on which
it is based. It does not apply to all kinds of designs. I haven't used
Rent's Rule, relying more on density and intuition, but, on theory at
least, it would seem to be a useful tool which I plan to investigate
further by comparing its results with actual routed boards.
p. 216:
"Rent noticed that most large square boards, when divided into quadrants,
reveal half their wiring going between quadrants and half staying within
each quadrant. Further subdividing of each quadrant reveals the same
distribution. If, upon traveling between two quadrants, we assume (this is
very hypothetical) a wiring length on average equal to the spacing between
quadrants, we arrive at a total average wiring length equal to
three-eighths of a board side.
"Knowing the average wire length and the number of wires we can compute the
total board surface area occupied by those wires using any trace pitch.
This knowledge, in the form of Equation 5.27 [which is shown above as #1],
shows the [average] trace pitch [as a fraction of an inch] required to
route N connections on a fixed-size board [of dimensions X by Y in inches]
using M layers.
(The "number of connections" is the number of connection segments. If there
is a rat's nest display, it will be the number of rat's nest lines. Pins
assigned to power planes don't count (and neither do the power planes
count, as Mr. McKean noted). The number of connections will be the number
of signal pins minus the number of nets.
"Of course, if we have some other information about the routing
requirements, such as large buses or other structures, we should use it.
Given no other information, we can attempt to calculate the required trace
spacing using Rent's idea...."
Note that there is an assumption, in Rent's original conjecture, that the
board is square. The rule and conjecture may break down if the aspect ratio
differs greatly from 1. The standard "IBM PC" card, for example, can
present difficulties because of its great length compared to its height. My
intuition is that if the ratio of maximum component pin grid height to
minimum board dimension were low enough, Rent's Rule will be useful.
Further, the assumption may drastically overstate expected trace length for
a design which can be locally routed with high completion, as is common in
analog designs with many discrete components as well as in efficiently
bussed digital designs, or digital designs which can be efficiently placed.
To use Rent's Rule, one must understand that traces may be confined to
routing channels. If, for example, a board were packed with .100 pitch
DIPs, routing channels in one direction would be limited to the number of
traces which will fit between pins, per each tenth of an inch. While one
may well be able to route more traces per inch in the other axis, after
considering that vias will be required, it might be prudent to use the same
maximum number of traces per inch in both directions, which would in this
case yield a trace pitch of 0.1 inch for one-throughs (say 0.012 track and
space) or 0.05 inch for two-throughs (say 0.008 trace and space) or 0.033
for three-throughs (say 0.006 trace and space).
But Johnson and Graham say "Don't count on filling more than half the
spaces between pins." In the other direction they note that "Inner layers
of surface-mounted boardsmayhave more routing space available than DIP
boards. The number of vias is roughly the same, but the vias are smaller in
surface-mount designs since IC pins don't have to stick through them...."
And there are plenty of other considerations, some mentioned by Johnson and
Graham, and some not. To use Rent's Rule, I'd recommend taking the time to
understand it and its assumptions, rather than simply applying it as a
magic formula....
[log in to unmask]
Abdulrahman Lomax
P.O. Box 690
El Verano, CA 95433
################################################################
DesignerCouncil E-Mail Forum provided as a free service by IPC using LISTSERV 1.8c
################################################################
To subscribe/unsubscribe, send a message to [log in to unmask] with following text in the body:
To subscribe: SUBSCRIBE DesignerCouncil <your full name>
To unsubscribe: SIGNOFF DesignerCouncil
################################################################
Please visit IPC's web site (http://www.ipc.org) "On-Line Services" section for additional information.
For technical support contact Hugo Scaramuzza at [log in to unmask] or 847-509-9700 ext.312
################################################################
|
