FreeLists / si-list / [SI-LIST] Re: FW: Inductance of wire section

[Geoff Stokes <gstokes@xxxxxxxxx>]

A good way to check this is to use the MECL System Design Handbook, which
you can find on the ON Semi web site, treating the wire as a waveguide
transmission line carrying a simple transverse (TEM) wave.  On page 44, it
gives formula for Zo of wire over ground as 60 * ln (4h/d) ohms in air,
where h is distance to ground and d is wire diameter.  You need to assume a
reasonable ground spacing.  It's not too sensitive because of the log
function.  You usually get Zo between 100 to 250 ohms.  I have also checked
that equation with Bleaney & Bleaney "Electricity and Magnetism"  2nd
Edition (OUP 1965) page 305.

To find inductance and capacitance per unit length, there are two more
fundamental equations:

Wave velocity v equals 1/[sqroot(LC)]
Zo equals sqroot(L/C)

Divide them to get:

L equals Zo/v  henry per metre
Where v in free space is 3 x 10^8 m/s, and Zo comes from the handbook
equation.  For example, if h/d =10, Zo is 221 ohms, L is 738 nH per metre or
about 19 nH/inch.

By the way, you can multiply those 2 fundamental equations together to get:

C equals 1/(Zo * v)  farad per metre, in the example that's 15 pF per metre
or 0.38 pF per inch.

The transmission line is only an approximation because the wire gives and
takes radiation like an antenna, but it's better than just lumped elements.
Also I think there must be a variety of high frequency back-plane problems
where the inductance is not really enough to model the system.

Cheers
Geoff

> -----Original Message-----
> From: Ken Cantrell [mailto:Ken.Cantrell@xxxxxxxxxxxxxxxx]
> Sent: 04 September 2003 23:04
> To: McCoy.Bart@xxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: FW: Inductance of wire section
> 
> 
> K should be = .002, shouldn't it?
> 
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of McCoy, Bart O.
> Sent: Thursday, September 04, 2003 3:11 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] FW: Inductance of wire section
> 
> 
> 
> Well, you'll probably get a million replies with the same
> equation in 50 different forms, but here's one that I use
> for a straight-wire of circular cross-section inductance 
> calculation that will give you first order effects:
> 
> 
> L  =  K * length * [ ln(4*length/Diam) - 0.75 ]
> 
> L      = Inductance in nanohenries
> D      = Diameter of wire in cm
> length = Length of wire in cm
> K      = 2
> 
> 
> 22 Gauge wire....   I'll let you do the calculation given:
> 
> 20 Gauge AWG  = 0.0813 cm diameter
> 26 Gauge AWG  = 0.0406 cm diameter
> 
> 
> Hope that helps.
> 
>    - Bart
> 
> 
> 
> 
> -----Original Message-----
> From: sdb@xxxxxxxxxx [mailto:sdb@xxxxxxxxxx] 
> Sent: Thursday, September 04, 2003 2:53 PM
> To: si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Inductance of wire section
> 
> 
> Hi gang --
> 
> Please pardon me if this is a FAQ, but does anybody have a quick
> rule-of-thumb for the inductance to expect from a 1 cm length of 22
> gauge wire-wrap wire in free space?   Yes, I've searched the web &
> looked at a few pages which are far too detailed to be really useful
> -- all I want is an order-of-magnitude number, and the websites are
> all about calculating the number by integrating Maxwell's equations.  
> 
> So far, I've been using a figure of around 360 nH/m, which is the
> inductance of a common 50ohm transmission line.  If the real number is
> larger or smaller by a factor of 2 to 5 I don't care a lot, 
> but I would
> like to make sure that the "rule-of-thumb" number is *not* orders of
> magnitude larger or smaller than this.
> 
> What rule-of-thumb do you use?
> 
> Stuart
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