NONIDEAL CONDUCTOR MODELS - Advanced Signal Integrity for High-Speed Digital Design - page 240

0

Huray roughness model
Measurement

− 5

− 10

− 15

− 20

− 25

0 5 10 15 20 25 30

Frequency, GHz

Figure 5-25 Accuracy of the Huray surface roughness model (5-65) constructed with
N =

20 spheres with a radius of a = 0 . 8

µ

m, assuming a hemispheroid tooth shape;

7-in. microstrip; ε r / tan δ = 3 . 9 / 0 . 0073 at 1 GHz; RMS roughness of copper foil

h RMS = 5 . 8

µ

m ,d peaks , RMS = 9 . 4

µ

m.

2.8

Hemisphere model (5-58)

2.4

Huray model (5-65)

2

Hammerstad model (5-48)

1.6

1.2

0.8

0 10 20 30 40 50

Frequency, GHz

Figure 5-26 Surface roughness correction factors for rough copper; Huray model
(5-65), hemisphere model (5-58), and Hammerstad model (5-48); RMS roughness:
h RMS

= 5 . 8 m ,d peaks , RMS = 9 . 4 m.

µ µ

for rough copper. The hemisphere model overpredicts at middle frequencies and
slightly underpredicts at high frequencies. As demonstrated by Figure 5-25, a
properly constructed Huray model predicts a realistic correction curve.
The frequency dependence of the skin effect resistance and total inductance
using the Huray equation for surface roughness is implemented with (5-66a) and