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March 1999

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Subject:
From:
"Alderete, Michael" <[log in to unmask]>
Reply To:
TechNet E-Mail Forum.
Date:
Fri, 12 Mar 1999 08:29:12 -0800
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In-myung-

This relation looks like Rent's Rule, named after an IBM engineer.

1) In "Microelectronics Packaging Handbook," Ed. by R. Tummala, E.
Rymaszewski, and A. Klopfenstein, Chapman & Hall ITP, 2nd Ed. (1997), Vol.
I, pg. I-144, [This chapter is repeated in Vols. II & III as well]

"N=K * M^p ...

N= number of used input-output pins
K= average number of terminals used for an individual logic circuit
M= the number of circuits
p= is an exponent, a constant, (0<=p<=1)..."

"Empirically, 0.5<p<0.7 for predominantly logic circuits..."



2) In "High-Speed Digital Design," H. Johnson & M. Graham, Prentice Hall PTR
(1993),
pg.216, [estimating the required trace spacing on a board]

"...using Rent's idea:

p_aver = (x*y)^0.5 (2.7M) (N)^(-1)

where

N = number of connections (assumed distributed according to Rent's rule)
p_aver = average trace pitch, in.
X = Board width, in.
Y = Board height, in.
M = number of routing layers


3) The original reference to Rent's rule, and the background behind it, is:

B. S. Landman and R. L. Russo, "On a Pin versus Block Relationship for
Partitions of Logic Graphs," IEEE Transactions on Computers, Vol. C-20, no.
12, pp. 1469-1479, December 1971.

-------

The Rent relationship is assumed to apply hierarchically, seeming to work at
IC and board assembly levels alike. These references cover the observed
values of the coefficient and exponent constants, for different types of
microcircuits, modules and larger circuit subsystems (boards).

-Michael Alderete
Aerojet



You wrote...
------------------------------

Date:    Thu, 11 Mar 1999 18:09:33 +0900
From:    In-myung Song <[log in to unmask]>
Subject: [PCB]Anyone know that?

Isn't there who knows that

P = alpha * G^(beta)

where P is the total numbers of pins and G is the numbers of integrated
gates.

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