**From:** Bill Owsley (*owsley@cisco.com*)

**Date:** Fri Sep 01 2000 - 14:26:30 PDT

**Next message:**George_Tang@Dell.com: "RE: [SI-LIST] : "skin effect/depth calculation results""**Previous message:**C Deibele: "[SI-LIST] : "skin effect/depth calculation results""**In reply to:**C Deibele: "[SI-LIST] : "skin effect/depth calculation results""**Next in thread:**George_Tang@Dell.com: "RE: [SI-LIST] : "skin effect/depth calculation results""

and then someone will bring up the surface finish of the copper - how

smooth is it ? has it been 'rolled' or plated ?

This surface finish has an effect on loss, so I've heard...

At 02:34 PM 09/01/2000 +0200, C Deibele wrote:

*>Hi Everyone,
*

*>
*

*>Yesterday we discussed so many different parts of skin effect and copper
*

*>
*

*>losses. After reading so many good points brought up by everyone,
*

*>namely the
*

*>effect of the perimeter of the trace, as well as the characteristic
*

*>impedance of
*

*>the trace, I had really wanted to study the effects of increasing the
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*>trace
*

*>width and the copper losses associated with increasing the trace width.
*

*>
*

*>As a background, remember that
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*>
*

*>I(z)=Const/Zo exp^{-i Beta z}
*

*>
*

*>where Beta is the wavenumber...
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*>Const is a constant
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*>z is a position on the z axis
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*>and Zo is the characteristic impedance.
*

*>
*

*>so dI/I = -dZo/Zo (for a given point in z)
*

*>
*

*>==>Increasing Zo decreases the current flowing on the conductor.
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*>==>decreasing the current on the conductor decreases the copper losses
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*>on the
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*>conductor.
*

*>==>Increasing Zo means the trace width gets *smaller*
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*>
*

*>So, the question I ask is: Which effect wins?
*

*>
*

*>There is no simple answer to this question because the characteristic
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*>impedance
*

*>is not a simple linear function of geometry. Take for instance coax,
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*>which is
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*>one of the easiest geometries/topologies to study:
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*>Zo=60 ln(b/a)
*

*>
*

*>If we restrict our attention to geometries where the frequency is high
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*>enough
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*>such that the skin depth, delta, is much greater than a
*

*>i.e. delta >>a, then quite simply,
*

*>
*

*>dZo/Zo=-da(r)/[a(r) ln (b/a(r))]
*

*>
*

*>so, inserting this relationship into the equation of I
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*>
*

*>dI/I=-dZo/Zo=da(r)/[a(r) ln (b/a(r))]
*

*>
*

*>the denominator clearly shows that there is not a nice linear
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*>relationship. Now stripline is also nonlinear....So, this says that
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*>there is probably NEVER a nice and easy rule to decide whether making a
*

*>trace wider, or thicker will reduce copper losses.
*

*>
*

*>so, the change in the characteristic impedance is not something simple
*

*>to
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*>describe -- namely there are regimes where a simple change in radius may
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*>be
*

*>easily described by the inverse nature, other regimes where the
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*>logarithmic
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*>properties are dominated...and a regime where the mix is the important
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*>property.
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*>
*

*>So, I attempted to study one simple property. I used Ensemble v. 7 and
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*>simulated a simple stripline geometry. copper upper conductor, copper
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*>lower
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*>conductor, copper trace, and perfect vacuum in the middle (We were
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*>restricting
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*>our discussions to copper loss...*NOT* dielectric loss)
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*>
*

*>So, the results were fairly convincing, for a stackup as follows
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*>
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*>copper ground
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*>50 mil vacuum
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*>copper trace
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*>50 mil vacuum
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*>copper ground
*

*>
*

*>All the traces were simulated were 1800 mils long
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*>The reflection data was nearly identical (on the order of 0.005%) ...so
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*>I won't
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*>post it....
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*>trace at 140 mils http://www.geocities.com/simulations00/140.jpg
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*>trace at 130 mils http://www.geocities.com/simulations00/130.jpg
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*>
*

*>and examine the following:
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*>
*

*>trace at 14 mils http://www.geocities.com/simulations00/14.jpg
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*>trace at 13 mils http://www.geocities.com/simulations00/13.jpg
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*>
*

*>These two sets of results clearly show that there is a discrepancy based
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*>on the distributed nature of the transmission line circuit.
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*>
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*>So, the first set shows that a wider trace has less loss.
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*>the second set shows that the skinnier trace has less loss.
*

*>
*

*>I do not want to get into any argument about semantics about the English
*

*>of the problem. This is to say, skin effect, or skin depth.
*

*>
*

*>Craig Deibele
*

*>
*

*>
*

*>
*

*>**** To unsubscribe from si-list or si-list-digest: send e-mail to
*

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*

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*

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*

*>****
*

----------------------------

Bill Owsley, owsley@cisco.com

919) 392-8341

TMBU Compliance

Cisco Systems

7025 Kit Creek Road

POB 14987

RTP. NC. 27709

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