# High-Speed Digital System Design ~ A Handbook of Intercon..

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An approximation of the effective resistance of the ground plane can be derived using a
technique similar to that used to find the ac resistance of the signal conductor. First, since
63% of the current will be confined to one skin depth (), then for the resistance calculation,
the approximation may be made that the ground current flows entirely in one skin depth, as
was approximated for the signal conductor ac resistance. Second, the equation
(4.5)
shows that 79.5% of the current is contained within a distance of ±3H (6H total width) away
from the center of the conductor. Thus, the ground return path resistance can be
approximated by a conductor of cross section A
ground
= × 6H. Substituting this result into
equation (4.1)
yields
(4.6)
The total ac resistance is the sum of the conductor and ground plane resistance:
(4.7)
(4.8)
Equation (4.8)
should be considered a first-order approximation. However, since surface
roughness can increase resistance by 10 to 50% (see "
Effect of Conductor Surface
Roughness
" below),
equation (4.8)
will probably provide an adequate level of accuracy for
most situations.
A more exact formula for the ac resistance of a microstrip can be derived through conformal
mapping techniques.
(4.9)
Equation set (4.9)
was derived using conformal mapping techniques and appears to have
excellent agreement with experimental results [
Collins, 1992
]. These formulas are
significantly more cumbersome than
(4.8)
but should yield the most accurate results.
Equation (4.8)
will tend to yield resistance values that are larger then those in
(4.9)
. Often,
the slightly larger values given by
(4.8)
are used to roughly approximate the additional
resistance gained from surface roughness.
Frequency-Dependent Conductor Losses in a Stripline.

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Summary :

## An approximation of the effective resistance of the ground plane can be derived using a technique similar to that used to find the ac resistance of the signal conductor. Substituting this result into equation (4.1) yields (4.6) The total ac resistance is the sum of the conductor and ground plane resistance: (4.7) (4.8) Equation (4.8) should be considered a first-order approximation.

Tags : conductor,equation,ground,deried,current,roughness,approximation,surface,mapping,skin,signal,approximated,quot
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