copper roughness and si9000e - altium 1...• based on scratches on conductor surfaces • first...

Copper Roughness and Si9000e

1 Copyright © Polar Instruments 2017 polarinstruments.com

Copper Roughness and how to account for itMartyn Gaudion– October 2017 (Rev 1)

Copyright © Polar Instruments 2017 polarinstruments.com

Presented for Altium PCB2020



Acknowledgments

Alan Staniforth

Bert Simonovich



"All models are wrong

but some are useful"



George E. P. Box



Introducing Polar Instruments

Welcome to a presentation that will cover the following topics:

1. Overview and significance of copper roughness

2. Methods for calculating insertion loss with roughness



Overview of Copper Roughness

Current Distribution Through a Conductor

DC current is uniform through cross-sectional area of

conductor

AC current above ~10MHz flows mainly along “skin” of the

conductor

[1] Simonovich 2015, pg 5




Skin Depth Vs Frequency

μ0 = Permeability of free space in H/m

σ = Conductivity in S/m.

AC current above ~10MHz flows mainly along “skin” of the

conductor [2] Simonovich 2015, Slide 9




Copper is Roughened for Various Reasons

Roughness is always applied to promote adhesion to the dielectric

material

No such thing as a perfectly smooth PCB conductor surface

[2] Simonovich 2015, Slide 17




Profilometers Used to Measure Surface Roughness

[2] Simonovich 2015, Slide 23-24



Methods for Calculating Insertion Loss with Roughness

• Smooth Conductor

• Morgan-Hammerstad

• Groisse Method

• Huray “Snowball” Method




Garbage In = Garbage Out



Which is correct?



Measured or

modelled?




Loss Calculations

Total Loss = Insertion Loss of Dielectric +

Surface Roughness Coefficient X Insertion Loss of Conductor


21 Copyright © Polar Instruments 2017 polarinstruments.com[3] Bogatin et al., Pg. 5

Based on scratches on conductor surfaces


Morgan-Hammerstad




Morgan-Hammerstad

• Based on scratches on conductor surfaces

• First developed in 1949. Republished in 1975 by Hammerstad

• Saturates for rough conductor at low frequencies to a value of 2221 arc tan 1.4rough

smooth

αα π δ

∆ = +




Groisse

Also Saturates as the Ksr approaches 2.

Depending on Conductor roughness, predictions can go to higher frequencies than Hammerstad

Groisse Equation:1.6

1 exp2

rough

smooth

PP

δ = + − ∆




Huray

• The surface can be modelled using a pyramid of metal spheres called “snowballs”

[4] Huray, Paul G




Huray• The theory starts with a single snowball between conductors with

an electromagnetic wave incident on it.• The wave is both reflected (scattered) and absorbed

Cross Section Longitudinal View

[4] Huray, Paul G




Huray

• In the pyramid of snowballs, multiple scattering and absorption occurs. However, It is found that absorption dominates over scattering at the frequencies of interest

[5] Griesi G. et al.




Huray

• Equation12 2

216 1

2

is thepower lostis theareais thenumber of snowballsin area

is thedistribution of snowballsis theskin depth

jrough smooth i ii

smooth rough smooth i i

P A N aP A A a a

PAN Aj

π δ δ

δ

−

=

= + + +

∑

[4] Huray, Paul G




Huray

• In order to simplify the formula for practical use simulations, using different ball radii have been conducted.

[4] Huray, Paul G




Huray

• Simplification of the formula for a single effective ball radius

( ) 2

2

3 12 11

2

4is the Hall-Huray Surface Ratio

is the radius of all snowballsN is the number of snowballs in area

rough rough

smooth smooth

smooth

P ASR

P Aa a

NaSRA

aA

δ δ

π

= + + +

=

effective

[4] Huray, Paul G




Comparisons with Si9000e

-4,0E+02

-3,5E+02

-3,0E+02

-2,5E+02

-2,0E+02

-1,5E+02

-1,0E+02

-5,0E+01

0,0E+000,0E+00 2,0E+10 4,0E+10 6,0E+10 8,0E+10 1,0E+11

Att

enua

tion

(dB

/m)

Frequency (Hz)

Smooth

Hamm

Goisse

Huray




Practically How Do I do this?

?

?



References[1] Lambert (Bert) Simonovich, Practical Method for Modeling Conductor Surface Roughness Using Close Packing of Equal Spheres, DesignCon 2015[2] Lambert (Bert) Simonovich, Practical Method for Modeling Conductor Surface Roughness Using Close Packing of Equal Spheres Presentation, DesignCon 2015[3] Bogatin et al. Which one is better? Comparing Options to Describe Frequency Dependent Losses, DesignCon 2013[4] Huray, Paul G. The Foundations of Signal Integrity, pub. Wiley, 2010[5] Griesi G. et al. Electrodeposited Copper Foil Surface Characterisation for Accurate Conductor Loss Modelling DesignCon 2015.



“Si9000e insertion loss solver"




Images courtesy of Circuit foil Luxembourg

Thank you

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copper roughness and si9000e - altium 1...• based on scratches on conductor surfaces • first...

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