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Re: [TowerTalk] Ground wire impedance

To: K4SAV <>,
Subject: Re: [TowerTalk] Ground wire impedance
From: Jim Lux <>
Date: Wed, 12 Jul 2006 21:23:37 -0700
List-post: <>
At 08:14 PM 7/12/2006, K4SAV wrote:
>Jim Lux wrote:
>..."Hmm.. but, if I had four AWG 10 wires laying side by side, that's
>like a 0.4 inch wide by 0.1 inch high strap... i.e. the L should be 0.40
>uH (give or take) for the 10 foot run.  I suspect that 4 AWG16 (roughly
>0.05" diameter) wires spanning half an inch would have about the same
>inductance, and 4 AWG16s is a lot cheaper than a single AWG4, or,
>perhaps, an 0.05x0.5" strip.  As you show in your table, (and you
>mention above) you have to spread over a MUCH wider distance to
>materially reduce the L."...
>Without calculating anything, this sounds correct.
>..."Where I'm going with this is that there might be some very
>convenient, and inexpensive, ways to get a fairly low inductance
>connection comparable to AWG4, and potentially easier to handle.  For
>instance, there's AWG16 ribbon cable that shows up surplus every once in
>a while.  Or, perhaps, if there's a "deal" on cheap extension cords.  If
>DC resistance isn't the issue, you don't really need the copper mass of
>a big solid chunk.  Something with fairly small copper strands separated
>by plastic, paper, other fillers, can have an impedance for RF and/or
>lightning that's pretty acceptable.  Think of it as quasi Litz wire."...
>Maybe. If you are thinking of above ground point-to-point wiring this
>might work OK.

That was the idea.. above ground, cheap, etc.

>If you are thinking buried wires for lightning
>protection, you will lose the ground contact with insulated wire which
>will reduce its effectiveness.  And you can't use uninsulated buried
>stranded without loosing the strand-to-strand contact. Now the next
>interesting question. Will the impedance increase? From the calculations
>in my original table, the INDUCTANCE is the dominate parameter, but that
>was for solid wire.
>Unfortunately inductance and skin resistance of stranded-twisted, or
>stranded-braided, or Litz wire is very difficult to calculate when you
>don't have strand to strand contact.

No kidding.. Terman has some equations, but it turns out that they only 
work for some very specialized cases with a lot of symmetry.  Most folks 
faced with this problem either do it empirically (measure it) or use some 
sort of finite element analysis code.  Analytical solutions are very 
complex: There's some interesting papers I ran across when looking for 
multiport S parameter measurements that look at things like effective Z of 
ribbon cables with alternating ground and signal, etc.  Page after page of 
equations, conformal mappings to deal with insulation, etc., all winding up 
in a result  with a concluding statement like: "manufacturing and 
environmental variations restrict the practical utility of this 
analysis".  I read this as "you'd better measure it"

>There are a number of parameters to
>worry about with these configurations which make it difficult to
>calculate anything, and measurements aren't that easy either.  Most have
>uncontrolled physical configurations (except Litz wire) so you have to
>worry about currents in individual strands getting out of phase with
>other strands. And how is skin resistance effected by currents in
>another conductor immediately next to it? I could guess at the effects,
>but it would just be a guess. If you know of any data, either measured
>or calculated, for inductance or skin resistance of these wire
>configurations I would be interested.

If the strands are small compared to the spacing, you do the calculation by 
using the geometric mean distances (Nth root of the product of N 
terms).  If the strands are not small, then it gets more complex, and you 
either resort to approximations for things like "proximity effect" (Grover 
is the usual primary source on these sorts of things).

For FEM codes, the free demo versions of most of the electromagnetics codes 
will do a fine job on this sort of problem. Take a look at Sonnet Lite 
( or Ansoft Maxwell SV ( 
)  In general, take a look at:  One 
that looks interesting in their list is MMTL.

I haven't tried it, but a friend suggested FastHenry 
(   Hey, it's free, at least.

And, of course, you can use NEC4: One of the applications that NEC4 was 
developed for was determining feedpoint Z on big EMP simulators which use 
electrodes that look like a bunch of parallel wires tapering to a feed 
point. I don't know that NEC4 actually will model proximity effects though. 
It does do straight skin effect.

There's actually a fair amount of literature for Litz wire. It's used in 
making transformers for switching power supplies.  There's also analytical 
methods for wire that essentially looks like stranded wire with all the 
strands insulated, where the configuration of strands is very regular (e.g. 
7 strand standard lay).  google for "inductance" and "Litz wire" and 
somewhere in the  first 20 or 30 hits, there'll be a gold mine.. someone 
has a bibliography of basically every useful paper on calculating 
inductance in the last 100 years.

I just found it on my website (doh!)..

An enormous compendium of inductance references compiled by Dr. Marc Thompson.

Dr Thompson has a new paper out that covers approximation techniques:

Thompson, M. , "Inductance Calculation Techniques -- Part II: 
Approximations and Handbook Methods", Power Control and Intelligent Motion, 
December 1999 - 26 April 2001

The above paper doesn't cover the parasitic C or R, though.

>Jerry, K4SAV
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