[SI-LIST] Re: Inductance of Via
- From: "Issa, Elie" <Elie.Issa@xxxxxxxxxx>
- To: "'si-list@xxxxxxxxxxxxx'" <si-list@xxxxxxxxxxxxx>
- Date: Tue, 19 Jun 2001 11:18:08 -0500
Rich
"ur = Relative Permeability or Dielectric Constant"
Relative permeability is not equal Dielectric constant.
You probably meant that Dielectric constant = Relative permitivity
Regards
Elie
-----Original Message-----
From: Rich Peyton [mailto:p2rich@xxxxxxxxxxxxx]
Sent: Tuesday, June 19, 2001 10:55 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Inductance of Via
I'm not the original Rich -- But I have:
u0 = Permeability of free space = 1.2566*10-6 H/m
ur = Relative Permeability or Dielectric Constant
Rich
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Yibing Tang
Sent: Tuesday, June 19, 2001 11:38 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Inductance of Via
Thanks to Richard for detail illustration.
But I don't have the chance to read the original references. I still have
one question, what does the u0/ur mean?
Yibing
-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Richard Wheeler
Sent: Wednesday, June 13, 2001 10:12 AM
To: si-list@xxxxxxxxxxxxx
Cc: ytang@xxxxxxxxxxxxxxxxx
Subject: [SI-LIST] Re: Inductance of Via
Si Listers:
The generally published formula for partial inductance is a
simplification of the original formula, meant only for wires much longer
than their diameters (or spacing to the return path).
Original References:
Edward B. Rosa Published "The Self and Mutual Inductances of Linear
Conductors"
Bureau of Standards Bulletin 4, pp301 (1907);
B. of S. Sci Paper 169, p151 formula (98) (1912)
Frederick W. Grover republished The formulas in "Inductance
Calculations" (1945) (pp31 formulas 1, 3, 6, etc.)
Status of formulas in publications and on web:
Transcription errors have entered into the original formulas in many
publications and the errors have passed on to the next generation of
publications. Twelve months ago I collected eight formulas off the web
used for calculating via inductance . Each had slightly different
formulas and all were incorrect. Some of the published equations are
correct but missing the additional information regarding range of
applicability. I have determined by careful measurements that the
original formulas used by Rosa and Grover are indeed correct for pcb and
package vias if properly used.
The original partial inductance equations are:
Mutual inductance = uo/2/pi*len * [ ln{ len/sep + sqrt(1.0 +
len^2/sep^2) } - sqrt(1.0 + sep^2/len^2) + sep/len ]
(len is segment length, ln is natural logarithm, sep
is separation distance of current centroids.)
The partial self inductance of a wire segment is obtained by reducing
the separation in the mutual inductance formula to:
sep = dia/2 and adding internal inductance.
Lself = uo/2/pi*len * [ ln{ 2.0 * len/dia + sqrt(1.0 + 4.0*len^2/dia^2)
} - sqrt(1.0 + 0.25 * dia^2/len^2) + 0.5 * dia/len + ur/4) ]
(dia is diameter of wire segment and ur/4 is the internal
inductance of the wire)
Only when len >> dia or spa then the formula reduces to:
Lself ~ uo/2/pi*len* [ln (4*len/dia) -3/4 ] at low frequencies
including internal wire inductance
Lself ~ uo/2/pi*len* [ln (4*len/dia) -1] at high frequencies (ur/4
--> 0 at skin limited high frequencies)
uo/2/pi = 4*pi*1e-7( Henries/meter) /2/pi = 2.0e-7
henries/meter
= 200 nH/meter
= 2.0 nH/cm
= 200 pH/mm
= 0.2 pH/um
= 5.08 nH/inch
If the via len=dia/2
Using the simplified equation Lself = -1.56 nH/inch
Rosa's original equation gives Lself = +0.47 nH/inch (a plausible
value)
Remember: Four partial segment self inductances are always placed in
series with four mutual inductances between segments to obtain total
loop inductance, which is the only physical and therefore measurable
inductance.
I hope that this will help clarify the negative inductance confusion
when inductance formulas are applied to short length vias.
Richard
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Neeraj Pendse wrote:
>
> To Yibing:
>
> I checked up this formula from Dr. Johnson's book - and I feel that it
should
> be
>
> L = 5.08 * h * [ln(4h/d) - 1]
>
> Regards,
>
> Neeraj.
>
> "Tsuk, Michael" wrote:
>
> > Yibing Tang wrote:
> >
> > > I use a formula to calculate the inductance of through hole via,
> > > L=5.08h[ln(4h/d)+1]
> > > However, I find that it is not suitable for small ratio of h to d.
> > >From this
> > > formula,if decrease the ratio, I could get very lower inductance, even
> > > negative.
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