NONIDEAL CONDUCTOR MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 219

Since the tangential component of the electric field must remain continuous, as
shown in equation (3-8), the electric field just outside the conductor surface can
be calculated with (5-40) evaluated at z =

0:

j) ωµ
2 σ

H ||

E || =

( 1 + n × (5-41)

Section 3.2.1 says the electric field must terminate normal to a perfectly con-
ducting surface, however, equation (5-41) shows that for a good conductor, a
tangential component of E must exist just outside the conductor . Since (5-40)
describes the electric field decaying with increasing depth z into the surface, there
must be power flow into the conductor. The time-averaged value of the Poynting
vector described in Section 2.6.1 is used to calculate the power absorbed per unit
area:

= a z (E + ) 2
2 η

S ave

(2-121)

The intrinsic impedance (2-53) at the surface of the conductor, η s , is calculated
with (5-37) and (5-41):

+ j) ωµ
2 σ

E c
H c = ( 1

η s (z = 0 ) = (5-42)

It is interesting to note that since √ µω/ 2 σ 1 /σ δ , (5-42) reduces to equation

(5-28), which is the series impedance of a transmission line:

=

+ j) ωµ + j) 1

σδ

( 1

2 σ = ( 1

Finally, the power flow per unit area into the conductor is calculated using
equation (2-121):

E c

2 2 σ 2
ωµσ
From (5-10), δ = √ 2 /ωµσ , yielding (5-43), which is the time-averaged power
absorbed by a flat conducting plane per unit area:

2 2 σ
ωµ =

2

4 σ H || 4 σ H ||

ωµ ωµ

S ave

= =

2 η

ωµδ H ||

2

S ave

W / m 2

= P plane = (5-43)

4

Equation (5-43) will allow for the solution of the resistive power losses of a good
conducting plane provided that the applied magnetic field

H || has been solved

for the idealized case of a perfect conducting plane.