Re: [SI-LIST] : "skin effect/depth calculation results"

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From: Bill Owsley (owsley@cisco.com)
Date: Fri Sep 01 2000 - 14:26:30 PDT


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
>
>
>
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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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