Litz wire resistance

A

amdx

Guest
I'm looking for a formula that I can use to find the a.c. resistance of litz
wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz
and #22 solid.

If possible please give me an example of it in use.
I have a book (Terman) that has two different formulas and I get the wrong
answer with both. (Ignorance on my part not the formula)

Mike
 
amdx wrote...
I'm looking for a formula that I can use to find the a.c. resistance
of litz wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz and #22 solid.

If possible please give me an example of it in use. I have a book
(Terman) that has two different formulas and I get the wrong answer
with both. (Ignorance on my part not the formula)
Click to expand...
If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time. As for ac resistance
of ordinary (fat) wire, you have the skin-depth formulas. But in
real-world situations, with multiple-layer windings, the proximity
effect can increase the ac loss by up to 20x over simple skin-depth
calculations. See Snelling for a good discussion.


--
Thanks,
- Win
 
Winfield Hill wrote:
amdx wrote...

I'm looking for a formula that I can use to find the a.c. resistance
of litz wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz and #22 solid.

If possible please give me an example of it in use. I have a book
(Terman) that has two different formulas and I get the wrong answer
with both. (Ignorance on my part not the formula)


If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time. As for ac resistance
of ordinary (fat) wire, you have the skin-depth formulas. But in
real-world situations, with multiple-layer windings, the proximity
effect can increase the ac loss by up to 20x over simple skin-depth
calculations. See Snelling for a good discussion.
Click to expand...
Fr = 1 + ((5*p^2-1)/45)*DELTA^4

p = no of effective layers

DELTA = layer thickness/skin depth = d/delta

d = copper wire OD*sqrt(pi/4) ie thickness of equivalent rectangular
conductor

This is only true at one frequency (ie that at which delta is
calculated). For arbitrary waveforms, you can do a Fourier transform to
get the coefficients of all the harmonics, and do lots of calculations.

Hurley et al published a cute way to extend this to any arbitrary
periodic waveform without knowledge of the fourier coefficients of the
waveform - "optimising the AX resistance of multilayer transformer
windings" IEEE trans. Power Electronics vol. 15 no. 2 March 2000, pp369-376.

multiply Dowells Fr (above) by:

[I'rms/(2*pi*Fo*Irms)]^2

Fo = fundamental frequency

Irms = rms value of I(t)

I'rms = rms value of dI(t)/dt


its pretty clear that for I(t) = Ipk*sin(2*pi*Fo*t) this scalar = 1

Cheers
Terry
 
On Wed, 09 Mar 2005 01:39:38 GMT, "amdx" <amdx@worldnet.att.net>
wrote:

I'm looking for a formula that I can use to find the a.c. resistance of litz
wire at a frequency.
Click to expand...
Charles Sullivan at Dartmouth and his students have done quite a bit
of work on this topic. Go have a look at their publications at:
http://engineering.dartmouth.edu/other/inductor/papers.shtml

Also the a.c. resistance of a solid wire.
Click to expand...
The case of an isolated, solid, cylindrical wire is one of the few for
which an exact analytical solution exists. This result was known to
Maxwell.

Given: c, the conductivity of copper at room temp = 1/1724
f, the frequency in Hz
d, the diameter of the wire in inches
j, Sqrt(-1)
x, an auxiliary variable = 2.54 * Pi * Sqrt(2*j*f*c)

Then the ratio of the resistance of the wire at frequency f to the DC
resistance is given by:

Fr = Rac/Rdc = Re(x/2*(J0(x)/J1(x))

Re() means Real Part, and J0() is the Bessel function of the first
kind of order 0, J1() is the Bessel function of the first kind of
order 1.

For some reference points:
.1 inch dia wire @ 50 kHz, Rac/Rdc = 2.42058
.05 inch dia wire @ 50 kHz, Rac/Rdc = 1.33069
22 Ga wire @ 20 kHz, Rac/Rdc = 1.00467
22 Ga wire @ 50 kHz, Rac/Rdc = 1.02865
22 Ga wire @ 100 kHz, Rac/Rdc = 1.10733
22 Ga wire @ 300 kHz, Rac/Rdc = 1.59314

But, beware. As Win mentions, when you wind wire into a coil, the
proximity effect can make Rac/Rdc for the coil much larger than the
value for an isolated wire.

Specifically 12/36 litz
and #22 solid.

If possible please give me an example of it in use.
I have a book (Terman) that has two different formulas and I get the wrong
answer with both. (Ignorance on my part not the formula)

Mike
Click to expand...
 
"Winfield Hill" <hill_a@t_rowland-dotties-harvard-dot.s-edu> a écrit dans le
message de news:d0llnt0121h@drn.newsguy.com...
amdx wrote...

I'm looking for a formula that I can use to find the a.c. resistance
of litz wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz and #22 solid.

If possible please give me an example of it in use. I have a book
(Terman) that has two different formulas and I get the wrong answer
with both. (Ignorance on my part not the formula)

If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time.
Click to expand...
Hi Win,

Do you remember in which instances this have been false? (maybe not true
litz wire but rather simply bundled wires)

I have a low noise preamp (2R equiv noise resistance, and next 0.2R/0.3R)
that have 1MHz BW. I'm planing to do the interconnect to the DUT with
specially made cable based on litz wire, but your comment worries me a
little.

Any thought?

BTW, did you receive the file I sent you a week ago?


--
Thanks,
Fred.
 
Fred Bartoli wrote...
Winfield Hill wrote...

If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time.

Do you remember in which instances this have been false? (maybe not
true litz wire but rather simply bundled wires)
Click to expand...
No, I generally use many-stranded litz wire from one of my custom-
made rolls. The cases I have seen where Rac for litz exceeds Rdc
are generally situations where the magnetic flux becomes highly
concentrated in one portion of the windings. E.g., in a toroid,
or in a many-layered coil situation where there would be a high
Rac proximity effect increase for ordinary thick wire.

I have a low noise preamp (2R equiv noise resistance, and next
0.2R/0.3R) that have 1MHz BW. I'm planing to do the interconnect
to the DUT with specially made cable based on litz wire, but your
comment worries me a little.
Click to expand...
I think you'll be OK. But don't know if litz is necessary, because
in a bridge, etc., fixture and wiring Rac can be nulled out.

BTW, did you receive the file I sent you a week ago?
Click to expand...
Yes, now, where did I put that?


--
Thanks,
- Win
 
"Winfield Hill" <hill_a@t_rowland-dotties-harvard-dot.s-edu> a écrit dans le
message de news:d0mv0601kis@drn.newsguy.com...
Fred Bartoli wrote...

Winfield Hill wrote...

If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time.

Do you remember in which instances this have been false? (maybe not
true litz wire but rather simply bundled wires)

No, I generally use many-stranded litz wire from one of my custom-
made rolls. The cases I have seen where Rac for litz exceeds Rdc
are generally situations where the magnetic flux becomes highly
concentrated in one portion of the windings. E.g., in a toroid,
or in a many-layered coil situation where there would be a high
Rac proximity effect increase for ordinary thick wire.
Click to expand...
Oh, that makes sense now. I guess you probably were in a situation where the
length of the "high concentration zone" was lower than the litz
"interwowing" step length (sorry I miss the word for this). This would
prevent the litz wire to do its work on that portion. Now, it you had
several layers, or several passages in the same zone, I think that would
have mitigated the effects on the average, unless you had a cumulative
effect due to bad luck (litz interwowing length about the wire length
between 2 passages).


I have a low noise preamp (2R equiv noise resistance, and next
0.2R/0.3R) that have 1MHz BW. I'm planing to do the interconnect
to the DUT with specially made cable based on litz wire, but your
comment worries me a little.

I think you'll be OK. But don't know if litz is necessary, because
in a bridge, etc., fixture and wiring Rac can be nulled out.
Click to expand...
Now that I understand why, I think too it'll be OK.
And yes, I'll need this kind of link. The preamp is not for a bridge but for
qualifying very low noise levels out of a low noise supply and after an RC
LPF (200nVrms over 1MHz BW).


BTW, did you receive the file I sent you a week ago?

Yes, now, where did I put that?
Click to expand...
I can send it again along with a pretty girl pic to make sure you'll
remember this time :)


--
Thanks,
Fred.
 
I read in sci.electronics.design that Winfield Hill <hill_a@t_rowland-
dotties-harvard-dot.s-edu> wrote (in <d0mv0601kis@drn.newsguy.com>)
about 'Litz wire resistance', on Wed, 9 Mar 2005:

Yes, now, where did I put that?
Click to expand...
Is it still in the cake? (;-)
--
Regards, John Woodgate, OOO - Own Opinions Only.
The good news is that nothing is compulsory.
The bad news is that everything is prohibited.
http://www.jmwa.demon.co.uk Also see http://www.isce.org.uk
 
"amdx" <amdx@worldnet.att.net> wrote in message
news:utsXd.115925$Th1.7186@bgtnsc04-news.ops.worldnet.att.net...
I'm looking for a formula that I can use to find the a.c. resistance of
litz
wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz
and #22 solid.

If possible please give me an example of it in use.
I have a book (Terman) that has two different formulas and I get the wrong
answer with both. (Ignorance on my part not the formula)

Mike
Click to expand...
There is this nice librarian at the Central Application, Philips Product
Division Electronic Components and Materials. Eindhoven, The
Netherlands.....

Who, if you can find an appropriate e-mail and make the request will snail
mail you a copy of E.A.B No.3 parts 1 and 2.

That's Electronic Applications Bulletin. Vol 35, No.3 May 1978.

It's by J.Jongsma.

Bugger it..... I shall scan the bastard and post it in ABSE.... that'll be

news://alt.binaries.schematics.electronic

I'll leave you know when it's up.

If you don't have access to the above and want me to e-mail the thing then
my e-mail addy as shown is valid.

DNA
 
"Fred Bartoli"
<fred._canxxxel_this_bartoli@RemoveThatAlso_free.fr_AndThisToo> wrote in
message news:422f091f$0$16352$626a14ce@news.free.fr...
"Winfield Hill" <hill_a@t_rowland-dotties-harvard-dot.s-edu> a écrit dans
le
message de news:d0mv0601kis@drn.newsguy.com...
Fred Bartoli wrote...

Winfield Hill wrote...

If the skin depth is more than the litz-wire constituent diameter,
the argument is that Rac = Rdc. I have found this postulate true
much of the time, but not all of the time.

Do you remember in which instances this have been false? (maybe not
true litz wire but rather simply bundled wires)

No, I generally use many-stranded litz wire from one of my custom-
made rolls. The cases I have seen where Rac for litz exceeds Rdc
are generally situations where the magnetic flux becomes highly
concentrated in one portion of the windings. E.g., in a toroid,
or in a many-layered coil situation where there would be a high
Rac proximity effect increase for ordinary thick wire.


Oh, that makes sense now. I guess you probably were in a situation where
the
length of the "high concentration zone" was lower than the litz
"interwowing" step length (sorry I miss the word for this). This would
prevent the litz wire to do its work on that portion. Now, it you had
several layers, or several passages in the same zone, I think that would
have mitigated the effects on the average, unless you had a cumulative
effect due to bad luck (litz interwowing length about the wire length
between 2 passages).


I have a low noise preamp (2R equiv noise resistance, and next
0.2R/0.3R) that have 1MHz BW. I'm planing to do the interconnect
to the DUT with specially made cable based on litz wire, but your
comment worries me a little.

I think you'll be OK. But don't know if litz is necessary, because
in a bridge, etc., fixture and wiring Rac can be nulled out.


Now that I understand why, I think too it'll be OK.
And yes, I'll need this kind of link. The preamp is not for a bridge but
for
qualifying very low noise levels out of a low noise supply and after an RC
LPF (200nVrms over 1MHz BW).


BTW, did you receive the file I sent you a week ago?

Yes, now, where did I put that?


I can send it again along with a pretty girl pic to make sure you'll
remember this time :)
Fred.
Click to expand...
Sounds like I'd like that file also!
Mike
 
"Genome" <ilike_spam@yahoo.co.uk> wrote in message
news:iKEXd.2703$gM2.1646@newsfe3-gui.ntli.net...
"amdx" <amdx@worldnet.att.net> wrote in message
news:utsXd.115925$Th1.7186@bgtnsc04-news.ops.worldnet.att.net...
I'm looking for a formula that I can use to find the a.c. resistance of
litz
wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz
and #22 solid.

If possible please give me an example of it in use.
I have a book (Terman) that has two different formulas and I get the
wrong
answer with both. (Ignorance on my part not the formula)

Mike



There is this nice librarian at the Central Application, Philips Product
Division Electronic Components and Materials. Eindhoven, The
Netherlands.....

Who, if you can find an appropriate e-mail and make the request will snail
mail you a copy of E.A.B No.3 parts 1 and 2.

That's Electronic Applications Bulletin. Vol 35, No.3 May 1978.

It's by J.Jongsma.

Bugger it..... I shall scan the bastard and post it in ABSE.... that'll be

news://alt.binaries.schematics.electronic

I'll leave you know when it's up.

If you don't have access to the above and want me to e-mail the thing then
my e-mail addy as shown is valid.

DNA

I'll be looking for it.
Click to expand...
Thanks, Mike
 
"amdx" <amdx@worldnet.att.net> wrote in message
news:IFGXd.118501$Th1.6378@bgtnsc04-news.ops.worldnet.att.net...
"Genome" <ilike_spam@yahoo.co.uk> wrote in message
news:iKEXd.2703$gM2.1646@newsfe3-gui.ntli.net...

"amdx" <amdx@worldnet.att.net> wrote in message
news:utsXd.115925$Th1.7186@bgtnsc04-news.ops.worldnet.att.net...
I'm looking for a formula that I can use to find the a.c. resistance
of
litz
wire at a frequency.
Also the a.c. resistance of a solid wire.

Specifically 12/36 litz
and #22 solid.

If possible please give me an example of it in use.
I have a book (Terman) that has two different formulas and I get the
wrong
answer with both. (Ignorance on my part not the formula)

Mike



There is this nice librarian at the Central Application, Philips Product
Division Electronic Components and Materials. Eindhoven, The
Netherlands.....

Who, if you can find an appropriate e-mail and make the request will
snail
mail you a copy of E.A.B No.3 parts 1 and 2.

That's Electronic Applications Bulletin. Vol 35, No.3 May 1978.

It's by J.Jongsma.

Bugger it..... I shall scan the bastard and post it in ABSE.... that'll
be

news://alt.binaries.schematics.electronic

I'll leave you know when it's up.

If you don't have access to the above and want me to e-mail the thing
then
my e-mail addy as shown is valid.

DNA

I'll be looking for it.
Thanks, Mike
Click to expand...
Posted, you'll have to fiddle the page order. It's 18 jpgs.

DNA
 
"legg" <legg@nospam.magma.ca> wrote in message
news:iv8v215l28n0c66eqojfunlsa46ua9sp8a@4ax.com...
On Wed, 09 Mar 2005 15:36:46 GMT, "Genome" <ilike_spam@yahoo.co.uk
wrote:

It's by J.Jongsma.

I've been trying to get a look at this article by Jongsma, > since '82.

Did they, perhaps, also copy you Publication#207 from '86?

RL
Click to expand...
Unfortunately not, I didn't request it.

I've scanned the other one and posted it to the binaries newsgroup.

Like I said I e-mailed someone, it might have been the webmaster at Philips
website. He passed the request on and the librarian offered to snail mail me
photocopies.

You might try your luck.

DNA
 
Genome wrote...
I've scanned the other one and posted it to the binaries newsgroup.
Click to expand...
You put up pages 162 and 163, and page 211. What about the rest of it?


--
Thanks,
- Win
 
"Winfield Hill" <hill_a@t_rowland-dotties-harvard-dot.s-edu> wrote in
message news:d0pce90l96@drn.newsguy.com...
Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?


--
Thanks,
- Win
Click to expand...
Like it's my fucking problem that e-mail and newsgroup postings are shite.

You're the old bloke, why haven't you sorted it out?

http://genome.dna.tripod.com/jongsma/jongsma.html

DNA
 
Genome wrote...
Winfield Hill wrote ...
Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?

Like it's my fucking problem that e-mail and newsgroup postings are shite.
You're the old bloke, why haven't you sorted it out?
http://genome.dna.tripod.com/jongsma/jongsma.html
Click to expand...
Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
and placed them on s.e.d. for everyone's downloading convenience.


--
Thanks,
- Win
 
"Winfield Hill" <hill_a@t_rowland-dotties-harvard-dot.s-edu> wrote in
message news:d0r3jh0m3f@drn.newsguy.com...
Genome wrote...

Winfield Hill wrote ...
Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?

Like it's my fucking problem that e-mail and newsgroup postings are
shite.
You're the old bloke, why haven't you sorted it out?
http://genome.dna.tripod.com/jongsma/jongsma.html

Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
and placed them on s.e.d. for everyone's downloading convenience.


--
Thanks,
- Win
Click to expand...
Wonderful!

DNA
 
Winfield Hill wrote:
Genome wrote...

Winfield Hill wrote ...

Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?

Like it's my fucking problem that e-mail and newsgroup postings are shite.
You're the old bloke, why haven't you sorted it out?
http://genome.dna.tripod.com/jongsma/jongsma.html


Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
and placed them on s.e.d. for everyone's downloading convenience.


Hi Win,
Click to expand...

thanks for that. Just one question - what do I do with the pile of ASCII
stuff I see in SED?

Cheers
Terry
 
On Sat, 12 Mar 2005 09:35:13 +1300, Terry Given wrote:

Winfield Hill wrote:
Genome wrote...

Winfield Hill wrote ...

Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?

Like it's my fucking problem that e-mail and newsgroup postings are shite.
You're the old bloke, why haven't you sorted it out?
http://genome.dna.tripod.com/jongsma/jongsma.html


Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
and placed them on s.e.d. for everyone's downloading convenience.


Hi Win,

thanks for that. Just one question - what do I do with the pile of ASCII
stuff I see in SED?
Click to expand...
Set your font to courier.

Cheers!
Rich
 
Terry Given wrote:
Winfield Hill wrote:
Genome wrote...

Winfield Hill wrote ...

Genome wrote...

I've scanned the other one and posted it to the binaries newsgroup.

You put up pages 162 and 163, and page 211. What about the rest of it?

Like it's my fucking problem that e-mail and newsgroup postings are shite.
You're the old bloke, why haven't you sorted it out?
http://genome.dna.tripod.com/jongsma/jongsma.html


Hey, good job, DNA!!! I combined the .gifs into two .pdf files,
and placed them on s.e.d. for everyone's downloading convenience.


Hi Win,

thanks for that. Just one question - what do I do with the pile of ASCII
stuff I see in SED?

Cheers
Terry
Click to expand...
You have to combine and decode the files to restore the PDF file.
--
?

Michael A. Terrell
Central Florida
 
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