**From:** Bill Owsley (*[email protected]*)

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

**Next message:**[email protected]: "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:**[email protected]: "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
*

*>trace
*

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

*>
*

*>As a background, remember that
*

*>
*

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

*>
*

*>where Beta is the wavenumber...
*

*>Const is a constant
*

*>z is a position on the z axis
*

*>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.
*

*>==>decreasing the current on the conductor decreases the copper losses
*

*>on the
*

*>conductor.
*

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

*>
*

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

*>
*

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

*>impedance
*

*>is not a simple linear function of geometry. Take for instance coax,
*

*>which is
*

*>one of the easiest geometries/topologies to study:
*

*>Zo=60 ln(b/a)
*

*>
*

*>If we restrict our attention to geometries where the frequency is high
*

*>enough
*

*>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
*

*>
*

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

*>
*

*>the denominator clearly shows that there is not a nice linear
*

*>relationship. Now stripline is also nonlinear....So, this says that
*

*>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
*

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

*>be
*

*>easily described by the inverse nature, other regimes where the
*

*>logarithmic
*

*>properties are dominated...and a regime where the mix is the important
*

*>property.
*

*>
*

*>So, I attempted to study one simple property. I used Ensemble v. 7 and
*

*>simulated a simple stripline geometry. copper upper conductor, copper
*

*>lower
*

*>conductor, copper trace, and perfect vacuum in the middle (We were
*

*>restricting
*

*>our discussions to copper loss...*NOT* dielectric loss)
*

*>
*

*>So, the results were fairly convincing, for a stackup as follows
*

*>
*

*>copper ground
*

*>50 mil vacuum
*

*>copper trace
*

*>50 mil vacuum
*

*>copper ground
*

*>
*

*>All the traces were simulated were 1800 mils long
*

*>The reflection data was nearly identical (on the order of 0.005%) ...so
*

*>I won't
*

*>post it....
*

*>trace at 140 mils http://www.geocities.com/simulations00/140.jpg
*

*>trace at 130 mils http://www.geocities.com/simulations00/130.jpg
*

*>
*

*>and examine the following:
*

*>
*

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

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

*>
*

*>These two sets of results clearly show that there is a discrepancy based
*

*>on the distributed nature of the transmission line circuit.
*

*>
*

*>So, the first set shows that a wider trace has less loss.
*

*>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
*

*>[email protected] In the BODY of message put: UNSUBSCRIBE
*

*>si-list or UNSUBSCRIBE si-list-digest, for more help, put HELP.
*

*>si-list archives are accessible at http://www.qsl.net/wb6tpu
*

*>****
*

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

Bill Owsley, [email protected]

919) 392-8341

TMBU Compliance

Cisco Systems

7025 Kit Creek Road

POB 14987

RTP. NC. 27709

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

[email protected] In the BODY of message put: UNSUBSCRIBE

si-list or UNSUBSCRIBE si-list-digest, for more help, put HELP.

si-list archives are accessible at http://www.qsl.net/wb6tpu

****

**Next message:**[email protected]: "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:**[email protected]: "RE: [SI-LIST] : "skin effect/depth calculation results""

*
This archive was generated by hypermail 2b29
: Tue May 08 2001 - 14:29:25 PDT
*