Accuracy of the popular Wheeler inductance equation - etc.
Red Hot
Winfield Hill wrote:
> famous Wheeler eqn 596 uH
> Grover and NBS crowd 584
> Hazeltine's old eqn 544
>
The mean of the measurements is 567 uH. The accuracy of the equations is
then:
Wheeler 5%
Grover 3%
Hazeltine -4%
Each is thus a very useful equation for design approximation. This type
of 'error' can be attributed to the sum of the variations in things
like: dielectric constant of the insulation, humidity, measurement
error, etc.
Very interesting work. Thank you for the report.
----------
Winfield Hill
Last month we discussed various inductance formulas in a thread,
"Accuracy of the popular Wheeler inductance equation."
In a current thread, "20kV p-p, 300kHz / 600kHz coil design," in
this newsgroup, we've been discussing a special inductor designed
to provide the resonant energy storage for generating a continuous
20 to 30kV p-p signal for a molecular trap. The design goals for
my 30kV-coil project have motivated the development of some low-
loss coils along with measurements to explore various candidate
coil technologies and the theoretical literature.
One solenoid coil now under discussion has an interesting and
unusual construction, shown in cross-section below:
|<---- 1.0" ---->| bundle view
.-. .-. .-. .-.
| | | | | | | |
'-' '-' '-' '-'
The coil has 20 mini-bundles of 5 wires, 0.2" wide and stacked in
3 layers for easy winding, spaced 0.1" apart to reduce proximity-
effect losses and winding capacitance.
bundle wire order
_
top \ o o o o o o o o 4 5 4 5
mid \ o \ o \ o \ o \ 3 3
bottom o o o o o o o o \_ 1 2 1 2
How should the capacitance be calculated for this coil? Twenty
sets of three-layer current-sheets with a full set of mutual
inductances seems like painful overkill. But how well do the
traditional formulas do for this coil? What other formulas might
be applied to provide reasonable answers? This thread will try to
shed a little light on the issue by comparing the calculations by
various methods with (also uncertain) measurements.
[Specs: The coil has 100 turns of 756-strand #42 litz wire, with
a 0.100-inch diameter (i.e. the same as #10 wire). The overall
length of the coil is 20 * 0.3 - 0.1 = 5.90 inches. It's inside
diameter is 4.05 inches, while the mean and O.D. dimensions are
4.327 and 4.60 inches.]
Here are some candidate equations: First we have Harold Wheeler's
equation, first derived in 1925 to simplify complicated formulas
from NBS circular 74, and presented in his 1928 IRE paper:
(1) L = a^2 N^2 / (9a + 10b) uH/inch,
where a = mean radius, b = length and N = turns. This formula is
credited with an accuracy of better than 1% when used for coils
wih b / 2a > 0.4, i.e. length > 40% of the diameter. This formula
is very close to the respected Nagaoka formula and tables, and we
get
L = 4.327^2 * 100^2 / (77.9 + 236) = 596 uH.
Then, to deal with the fact of a non-zero thickness for the coil,
we have NBS formulas presented by Grover and others, and later
simplified by Snelling:
(2) L = Do N^2 k uH/mm,
with the value k plotted for various Di/Do inner-to-outer-diameter
ratios, vs the length/Do ratio. For our coil, length/Do = 1.28,
and Di/Do = 0.88 so the graph tells us k = 0.0005, and
L = 584 uH.
We also have a venerable equation, also related by Wheeler in his
1928 paper and credited to Prof L.A. Hazeltine (note: Wheeler
worked for Hazeltine Corporation in Hoboken, N.J.):
(3) L = 0.8 a^2 N^2 / (6a + 9b + 10c) uH/inch,
where a, b and N are as above and c = winding thickness. Wheeler
claims this equation is good to 1% when "the three terms in the
denominator are about equal." As the numbers below show, that
condition doesn't apply here:
L = 0.8 * 4.68 * 10^4 / (13.0 + 53.1 + 2.75) = 544 uH.
Without further ado, here's a summary of the results - ahem, can
you tell me the correct inductance of my coil?
equation (or method) calculation (or measurement)
famous Wheeler eqn 596 uH
Grover and NBS crowd 584
Hazeltine's old eqn 544
General Radio bridge 568
LC meter II digital 577 (corrected)
100 nF mica cap bank 560
20.0 nF mica cap 569
Jennings vacuum cap 562 to 564
GR 0.05% standard cap 563
misc others 570
Clearly, none of the three popular equations are very accurate
for my new 5-turn bank coil. Comments?
--
Winfield Hill hi...@rowland.org _/_/_/ _/_/_/_/
The Rowland Institute for Science _/ _/ _/_/ _/
Cambridge, MA USA 02142-1297 _/_/_/_/ _/ _/ _/_/_/
_/ _/ _/ _/ _/
http://www.artofelectronics.com/ _/ _/ _/_/ _/_/_/_/
Winfield Hill
Winfield Hill, <hi...@rowland.org> said...
>
> [ snip ]
> How should the capacitance be calculated for this coil?
inductance
This simple mistyping was probably obvious from the context, but
I'm sorry anyway!
[ snip ]
I suspect the true inductance of the coil is about 563uH, and have
annotated the calculations and measurements below with a % error.
> equation (or method) calculation (or measurement)
> uH %
> famous Wheeler eqn 596 +5.8
> Grover and NBS crowd 584 +3.7
> Hazeltine's old eqn 544 -3.4
>
> General Radio bridge 568 +0.9
> LC meter II digital 577 +2.5
> 100 nF mica cap bank 560 -0.5
> 20.0 nF mica cap 569 +1.1
> Jennings vacuum cap 562 to 564 +/-0.2
> GR 0.05% standard cap 563 0.0
> misc others 570 +1.2
It would appear the most popular equations are high by about 3 to 6%
for my weird coil, which makes sense considering the open spacing. This
encourages flux leakage and reduces the mutual coupling between turns...
[Apologies if this article appears twice - due to news-server trouble.]
James P. Meyer
On 1 Oct 1997, Winfield Hill wrote:
> > equation (or method) calculation (or measurement)
> > uH %
> > famous Wheeler eqn 596 +5.8
> > Grover and NBS crowd 584 +3.7
> > Hazeltine's old eqn 544 -3.4
>
> It would appear the most popular equations are high by about 3 to 6%
> for my weird coil, which makes sense considering the open spacing. This
> encourages flux leakage and reduces the mutual coupling between turns...
I haven't done the research needed to answer the following
question, but perhaps I can impose on someone here to save me the work.
Are all those famous old formulas derived from first principles,
or are they simply derived from "curve fitting" a series of measurements
made on coils of varying geometry?
Jim
Winfield Hill
James P. Meyer at jim...@acpub.duke.edu says...
The "Grover and NBS crowd" formulas were laboriously derived from
"first principles" but with certain simplifying assumptions such as
current sheets, etc. They may have inaccuracies relating to fringe
effects, etc, especially at high frequencies.
Wheeler's famous equation was published in his short paper in the
Proceedings of the I.R.E. "Simple Inductance Formulas for Radio
Coils" October, 1928, pages 1398-1400.
In this paper, he says
"The new formulas are patterned after an empirical formula
derived by Professor L.A. Hazeltine some years ago, for the
inductance of a multi-layer coil."
This refers to the "Hazeltine's old eqn" which he is apparently
publishing for the first time, and which we see ever now and then
in the literature. But he then says his own formula was derived
from the NBS Circular 74, which is not empirical:
"The new formulas were derived empirically from the inductance
formulas and curves in Circular 74 of the Bureau of Standards.
The corresponding coil formulas of this circular, however,
either rely on tables or include expressions which are
inconvenient to compute. For this reason there was a need for
more convenient formulas, even with the loss of some accuracy,
for use in the laboratory."
The NBS crowd was into the 0.01% accuracy scene, and Wheeler felt
compelled to apologize for his simple formula, even though it in
fact matches the complex NBS answers to better than 0.5 to 1% over
its entire wide useful range, namely single-layer solenoids with
length > 0.4 diameter.
If one finds coils which are not well predicted by the simple Wheeler
equation, then I think these will also be poorly predicted by the
thin-current-sheet single-layer theoretical NBS formulas. My own
measurements on a set of 20 coils of all types, which started this
thread, showed Wheeler's equation to be nicely accurate.
The reduced accuracy for various multilayer coil formulas is also
another matter. For example, how good is Hazeltine's old formula?
My coil of the Oct 1 post is unusual - it has a 2:1:2 layer with
a 1:3 winding gap, creating a fill efficiency of only 55%.
No wonder none of the simple formulas get closer than 3 to 5%.
Also, I note that Hazeltine's old formula seems the poorest.
--
Winfield Hill hi...@rowland.org
Rowland Institute for Science
Cambridge, MA 02142
ma...@global.california.com
Watch for three things when doing measurements on air core coils:
1 Make sure the coil is more than 3 diameters (5, if you have the space)
away from *any* conducting surfaces else the coil's fields will induce
reflective eddy currents in the metal and change your readings by more
than 1-2% This metal can often be the box of your instrument.
2 Know the resistance (at each frequency) and the parallel capacitance of
the coil (pretty closely tied to the self resonance frequency).
3 *ALL* of the parasitic components you model as lumped elements will
never be fixed at each frequency due to distributed effects and skin
effects of the conductors.
Be aware that Litz wire works great as long as *every* wire in the bundle
is in the exact same field over its length! If not, you then have shorted
turns of a transformer with their loops of currents flying around, all
clouding the issue for you, too.
- Robert -
PS Great piece of work! Just noticed that the two readings of inductance
done with 100nF and 20nF imply the self resonance of the coil somewhere
around 280KHz. Is that true? [The self resonance makes the inductance
look larger as you go up in frequency]
Also, does the GR bridge read the total impedance of the inductor? or only
the reactive part of the inductor? Most of these bridges operate around
1KHz which would make the impedance of the coil around 1.1 ohm and it
would only take .14 ohm to throw the impedance reading off by 1%
Winfield Hill
ma...@global.california.com, <ma...@global.california.com> said...
>
> Watch for three things when doing measurements on air core coils:
>
> 1 Make sure the coil is more than 3 diameters (5, if you have the space)
> away from *any* conducting surfaces else the coil's fields will induce
> reflective eddy currents in the metal and change your readings by more
> than 1-2% This metal can often be the box of your instrument.
CHECK.
> 2 Know the resistance (at each frequency) and the parallel capacitance of
> the coil (pretty closely tied to the self resonance frequency).
CHECK.
> 3 *ALL* of the parasitic components you model as lumped elements will
> never be fixed at each frequency due to distributed effects and skin
> effects of the conductors.
Ahem, check....
> Be aware that Litz wire works great as long as *every* wire in the bundle
> is in the exact same field over its length! If not, you then have shorted
> turns of a transformer with their loops of currents flying around, all
> clouding the issue for you, too.
CHECK.
> PS Great piece of work! Just noticed that the two readings of inductance
> done with 100nF and 20nF imply the self resonance of the coil somewhere
> around 280KHz. Is that true? [The self resonance makes the inductance
> look larger as you go up in frequency]
What! I assume you're referring to the data from the "Re: 20kV p-p,
300kHz / 600kHz coil design" thread, 29 Sept posting (for the
acrylic-form version of the 600kHz solenoid), shown below.
=> resonating corr. calc calc effective
=> capacitor kHz Q L (uH) X_L r_s
=>
=> 1 6.95uF 2.548 28 561.4 9.1 0.326
=> 2 0.20 14.995 150 563.2 53.7 0.365
=> 3 0.10 21.26 207 560.4 76.1 0.374
=> 4 0.02 47.15 398 569.4 168.9 0.441
=> 5 8809pF 71.01 496 569.3 254.3 0.527
Could you explain your calculations and conclusion?
Or was it some other data? I'm beginning to lose track here!
> Also, does the GR bridge read the total impedance of the inductor? or only
> the reactive part of the inductor? Most of these bridges operate around
> 1KHz which would make the impedance of the coil around 1.1 ohm and it
> would only take .14 ohm to throw the impedance reading off by 1%
I assume the venerable old GR OrthoNull bridge separates the reactive and
resistive parts. However, I don't have a manual. Maybe someone who knows
for sure can contribute.
JoseSainz
Big snip
> I assume the venerable old GR OrthoNull bridge separates the reactive and
> resistive parts. However, I don't have a manual. Maybe someone who knows
> for sure can contribute.
The GR bridge has both R and X wheels and can make meassurements at the
frequency of interest. Actually having meassured VLF sized objects, the
repeatability is <10% in 14-30 kHz, even using the beat oscillator (or scale).
Accuracy (repeatability) though improves nearer to 1 MHz as the impedances
get larger.
Jose
(PS getting used to Aussie time here in WA)
Winfield Hill
JoseSainz, <jose...@aol.com> said...
Welcome back, Jose. My old GR bridge is the model 1650A. Pretty standard
I expect. This bridge does pretty well at 1kHz with its internal oscillator,
and I assume it does well with an external oscillator for frequencies below
that and maybe up to 5kHz or so. Are you saying this bridge is only
moderately accurate in the 14 to 30kHz range (not too surprising), but is
useful up to 1MHz!?! That's really surprising, given the construction of
it's main X-wheel bridge resistor, which looks both inductive and capacitive.
But I'm eager to give it as shot!
I've quite a collection now of "calibrated" inductors and capacitors. These
have been measured (and corrected) at 500 to 750kHz with my little LC meter
II, and by the old LC-resonance technique.
John Woodgate
In article <616qea$j...@fridge.shore.net>, Winfield Hill
<hi...@rowland.org> writes
>ma...@global.california.com, <ma...@global.california.com> said...
>>
>> Watch for three things when doing measurements on air core coils:
>
>> PS Great piece of work! Just noticed that the two readings of inductance
>> done with 100nF and 20nF imply the self resonance of the coil somewhere
>> around 280KHz. Is that true? [The self resonance makes the inductance
>> look larger as you go up in frequency]
>
> What! I assume you're referring to the data from the "Re: 20kV p-p,
> 300kHz / 600kHz coil design" thread, 29 Sept posting (for the
> acrylic-form version of the 600kHz solenoid), shown below.
>
>=> resonating corr. calc calc effective
>=> capacitor kHz Q L (uH) X_L r_s
>=>
>=> 1 6.95uF 2.548 28 561.4 9.1 0.326
>=> 2 0.20 14.995 150 563.2 53.7 0.365
>=> 3 0.10 21.26 207 560.4 76.1 0.374
>=> 4 0.02 47.15 398 569.4 168.9 0.441
>=> 5 8809pF 71.01 496 569.3 254.3 0.527
>
> Could you explain your calculations and conclusion?
> Or was it some other data? I'm beginning to lose track here!
>
>
from the above data one can calculate Cs for pairs of results, as I am
sure you are aware. However, the differences between the values of Cs
calcualted from different pairs seem, unless I have made an arithmetical
error (which is very probable) to indicate that some of the results are
not too reliable. That is, assuming that the quoted values for Ct are
accurate to a high degree. I don't want to bore you with my results but
to suggest that you might look at this aspect yourself.
The key equation is, of course f1^2(Cs + Ct1) = f2^2(Cs + Ct2). You need
to preserve lots of significant figures, because Cs is less than 1 nF.
--
Regards, John Woodgate, Elector of Rayleigh. Phone +44 (0)1268 747839
Fax +44 (0)1268 777124. OOO - Own Opinions Only. You can fool some of
the people all of the time, but you can't please some of the people
any of the time.
ma...@global.california.com
I went strictly from the "conclusion" msg. However, thanks for including
the original data - now I have a whole new set of questions! <g>
Exactly how did you determine the resonance frequency? I use the phase
shift near the maximum which is very accurate compared to just looking for
a max.
Anyway, I somehow don't even get the numbers you have up there ?? Using
the most accurate cap values:
=> 1 6.95uF 2.548 28 561.4 9.1 0.326
=> 5 8809pF 71.01 496 569.3 254.3 0.527
I get 561.4uH and 570.3uH [not 569.3 ??], again implying that coil's
capacitance is around 660pF and that self resonance is around 260KHz. Is
it?
What is the esr of the 6.95uF? They can be anywhere from .02 to .3,
depending. What is the Rdc of the coil?
- Robert -
Winfield Hill
ma...@global.california.com, <ma...@global.california.com> said...
>
> I went strictly from the "conclusion" msg. However, thanks for including
> the original data - now I have a whole new set of questions! <g>
>
> Exactly how did you determine the resonance frequency? I use the phase
> shift near the maximum which is very accurate compared to just looking for
> a max.
I also used the phase shift = 0 frequency (which I saw was consistant with
the peak amplitude, but more accurately determined as you said).
> Anyway, I somehow don't even get the numbers you have up there ?? Using
> the most accurate cap values:
>
>=> 1 6.95uF 2.548 28 561.4 9.1 0.326
>=> 5 8809pF 71.01 496 569.3 254.3 0.527
>
> I get 561.4uH and 570.3uH [not 569.3 ??], again implying that coil's
> capacitance is around 660pF and that self resonance is around 260KHz.
> Is it?
It's about 1.7MHz. See my answer for you re this question, buried within
the reply to John.
> What is the esr of the 6.95uF? They can be anywhere from .02 to .3,
> depending. What is the Rdc of the coil?
It's a low-esr mylar motor-starting capacitor, and I estimated this at
about 0.005 ohms to get a coil Q of 29 at 2.5kHz. Based on the data, it
can't possibly be much more than 0.01 or 0.02 ohms, which would make the
coil's Q higher at this frequency.
The Rdc of the coil is 0.260 ohms. This is the dominate loss at low
frequencies. I estimate that Rac/Rdc doesn't exceed the dc value by more
than 20% until 21kHz, and rises from there. According to the measurements
with my 100k resistor, at 150kHz the Q is about 740 and Rac/Rdc = 2.37.
Above that frequency, Rac/Rdc rises rapidly, lowering the Q.
For example, at 600kHz rac/rdc = 36 and the Q = 195. This is the value
that needs improvement. Now, shouldn't this discussion should be in the
"Re: 20kV p-p, 300kHz / 600kHz coil design" thread?
Bill Sloman
In article <19971005140...@ladder01.news.aol.com>, jose...@aol.com (JoseSainz) says:
>
<snip>
>Jose
>(PS getting used to Aussie time here in WA)
Western Australia runs on West Auatralian time, two hours later than the
eastern states where I grew up (Tasmania) and was educated (Tasmania,
Victoria). WA keeps on threatening to secede from the Commonwealth just
to stop the eastern states ringing them up early in the morning!
Bill Sloman, Nijmegen
Winfield Hill
John Woodgate, <j...@jmwa.demon.co.uk> said...
>
> Winfield Hill <hi...@rowland.org> writes
>> Robert Macy <ma...@global.california.com> said...
>>>
>>> Watch for three things when doing measurements on air core coils:
>>> [bigsnip]
>>> PS Great piece of work! Just noticed that the two readings of
>>> inductance done with 100nF and 20nF imply the self resonance of the
>>> coil somewhere around 280KHz. Is that true? [The self resonance
>>> makes the inductance look larger as you go up in frequency]
>>
>> What! I assume you're referring to the data from the "Re: 20kV p-p,
>> 300kHz / 600kHz coil design" thread, 29 Sept posting (for the
>> acrylic-form version of the 600kHz solenoid), shown below.
>>
>>=> resonating corr. calc calc effective
>>=> capacitor kHz Q L (uH) X_L r_s
>>=>
>>=> 3 0.10 21.26 207 560.4 76.1 0.374
>>=> 4 0.02 47.15 398 569.4 168.9 0.441
>>
>> Or was it some other data? I'm beginning to lose track here!
> Writing the total tuning cap. as Cs + Ct, where Ct is the added cap.,
> from the above data one can calculate Cs for pairs of results, as I am
> sure you are aware. However, the differences between the values of Cs
> calcualted from different pairs seem, unless I have made an arithmetical
> error (which is very probable) to indicate that some of the results are
> not too reliable. That is, assuming that the quoted values for Ct are
> accurate to a high degree. I don't want to bore you with my results but
> to suggest that you might look at this aspect yourself.
Thanks for your interest in my problem, and your careful exposition!
> The key equation is, of course f1^2(Cs + Ct1) = f2^2(Cs + Ct2). You need
> to preserve lots of significant figures, because Cs is less than 1 nF.
^^^^^^^^^^^^^^^^^^^^^^^^^^^
Exactly! Sheesh, fellas! Although I'm trying to be accurate, these
data points all have various errors! And yes, this is a good way to
calculate the Cs self and stray capacitance, but only if done with
small capacitor values! We can solve your equation for Cs getting,
Cs = C1 (g-m)/(1-g) where g = (f1/f2)^2 and m = C2/C1.
BTW, If f1 is the lower frequency (and C1 the higher-valued capacitor),
both g and m are less than 1. But it's the (g-m) term that raises our
eyebrows.
For the data values Robert picked, C1 = 100nF at 21.26kHz and C2 = 20nF
at 47.15kHz, we get g = (0.4509)^2 = 0.2033, and m = 0.20, so the g-m
term in the formula is 0.2033-0.2000. This is an error magnification of
2000/33 = 60, and a 1% error in capacitor measurement (or a 0.5% error
in resonant frequency measurement) becomes a 60% error in the Cs value!
Here's the data from "Re: 20kV p-p, 300kHz / 600kHz coil design" 29 Sept.
resonating corr. calc calc effective
capacitor kHz Q L (uH) X_L r_s
1 6.95uF 2.548 28 561.4 9.1 0.326
2 0.20 14.995 150 563.2 53.7 0.365
3 0.10 21.26 207 560.4 76.1 0.374
4 0.02 47.15 398 569.4 168.9 0.441
5 8809pF 71.01 496 569.3 254.3 0.527
6 2003 149.43 741 562.3 532.2 0.734
7 486 299.6 644 563.8 1073 1.694
8a 109 599.7 279 571.2 2148 7.82
8b 110 600.0 195 567.4 2148 11.22
9 43 876.0 104 570.2 3137 30.6
10 5 1509.3 82 570.2 5405 67.2
11 0 1765.6 calc
Clearly there's a problem reconciling the 3rd and 4th data lines, but
not from self capacitance! Note that the 10th line, with Cext = 5pF,
has a measured 1.5MHz resonance, and the 11th line showes a calculated
1.765MHz self-resonance frequency (based on a fitted 14.5pF self
capacitance and 560 uH inductance).
If we calculate Cs = C1 (g-m)/(1-g) for the 486 and 110pF data lines,
we get g = 0.24933 and m = 0.22634 and
Cs = 486pF (0.24933-0.22634)/(1-0.24933)
= 486pF 0.02299 / 0.751 = 14.88 pF
With Cs = 14.88 pF and L = 568 uH, we get fs = 1.73 MHz. Clearly
the self-resonant frequency is far above 280kHz!
ma...@global.california.com, <ma...@global.california.com> said...
> Anyway, I somehow don't even get the numbers you have up there ??
> Using the most accurate cap values:
>
>=> resonating corr. calc calc effective
>=> capacitor kHz Q L (uH) X_L r_s
>=>
>=> 1 6.95uF 2.548 28 561.4 9.1 0.326
>=> 5 8809pF 71.01 496 569.3 254.3 0.527
These values are excerpted from a spreadsheet, where the value for
L is calculated from the external resonating capacitance, plus the 5pF
(or 95pF) fixture capacitance and the (fitted) 14.5pF self capacitance.
Fred E. Davis
On 8 Oct 1997 22:14:38 GMT, hi...@rowland.org (Winfield Hill) wrote:
> Now about those syndication rights, I think first we have to come up
> with a decent plot!
I could've sworn you just posted a damn fine plot (temp.gif) in the
"Impressive litz-coil data" thread! (:D
ralph muha
In article <61h0ke$9...@fridge.shore.net>, hi...@rowland.org (Winfield Hill)
wrote:
: Hey, glad you're enjoying it! I think some of the other non-spectators
: may have burned out, wasting time typing the works of Shakespeare on
I'm enjoying it too! The whole thing deserved to be summarized on a
web page, in your design case-book...
: Now about those syndication rights, I think first we have to come up
: with a decent plot!
Just say that you're building the coil for a UFO propulsion system...
r
Winfield Hill
Kendall Castor-Perry at ken...@rather.not says...
>
>In article <61b565$3...@fridge.shore.net>, Winfield Hill
><hi...@rowland.org> writes
>
> [snip lots of stuff that thread-followers will have read]
>>
>>> What is the esr of the 6.95uF? They can be anywhere from .02 to .3,
>>> depending. What is the Rdc of the coil?
>>
>> It's a low-esr mylar motor-starting capacitor, and I estimated this at
>> about 0.005 ohms to get a coil Q of 29 at 2.5kHz. Based on the data, it
>> can't possibly be much more than 0.01 or 0.02 ohms, which would make the
>> coil's Q higher at this frequency.
> Can I ask a time-out sort of question here? I always get twitchy when I
> see 'mylar' and 'high Q' used together.
>
> A muscle-bound motor-start capacitor might have a low high frequency esr
> due to the thick foils it has, but in the region where its impedance is
> several orders of magnitude higher than that, the dielectric material is
> going to affect the Q of the capacitor, and mylar is not a star here.
> I find this to be true whatever the foil type is - tiny metallised
> polyester caps have just the same problem as great big film and foil
> ones - it's doen to the intrinsic nature of the material between the
> plates, which is scale-invariant (unless you're making molecule-sized
> caps!).
Without addressing the properties of various dielectrics, I have taken
more specific measurements of the 7uF motor-run capacitor in question.
This data is from an H.P. 4263B LCR meter.
freq. C (uF) esr
ohms
100 Hz 6.911 xx
120 Hz 6.909 xx
1 kHz 6.900 0.031 Q = 745
10 kHz 6.943 0.026
100 kHz 7.806 0.034 oops!
I'm unsure how much of the Q = 745 measurement at 1kHz is due to the
inherent limitations of the H.P. LCR meter. Also, consider the 100kHz
data with skepticism. Note that at 100kHz a 6.9uF capacitor looks like
a -j0.23 ohm reactance, while an inductance of only 0.1uH looks like
+j0.06 ohms. As the subject capacitor had two 4" leads, this could
explain why the LCR meter had difficulty at 100kHz.
At any rate, the motor-start capacitor was very useful at 1.6kHz, where I
needed the Q measurements. Since its Q of 475 at this frequency is much
higher than the coil's LC resonance Q of less than 20, it serves very well
for the purpose. I guess the point is that with the nice low esr, while
not quite as good as I speculated, these motor-start jobs are still damn
fine power capacitors.
> As frequency rises, the problem gets even worse. I design a lot of
> active filters, and in my programs and spreadsheets I incorporate an
> empirical compensation for the dissipation shift of the various types of
> capacitor in use; for filters which need to be programmed over a range
> of frequencies, the change in parameters can spoil the response of even
> a moderate filter and I use these calculations to automatically force
> the move to a better dielectric. Qs of a few hundred at a few hundred
> kHz? Forget it! Polypropylene is much better.
>
> So is there a problem with this general type of experiment, involving a
> mylar cap but trying to evaluate a high Q inductor? Or am I just out of
> my (skin) depth?
Note that for all the 50kHz and up measurements, I have some very good
capacitors to use. The bank of 5 mica 0.02uF capacitors must have a Q
of well over 2000 to 5000, depending on the frequency. And my huge
Jennings 40 to 2300pF vacuum variable must surely be as near to perfect
as we can get here on the surface of the planet!
However, I am having considerable difficulty in obtaining believable
measurements in the L = 1000uH, f = 1MHz, Q=1000 or higher territory.
These are not easy measurements!
> Even if I am, these inductor threads are damn fine spectator sports
> - who has the syndication rights? (-8
Hey, glad you're enjoying it! I think some of the other non-spectators
may have burned out, wasting time typing the works of Shakespeare on
these LC-tank threads. As for me, it's getting more and more interesting
in the home stretch, as a high-performance coil comes within sight.
And meanwhile I have other projects to keep things interesting as well.
Now about those syndication rights, I think first we have to come up
with a decent plot!
--
Bill Sloman
<snipped content>
> Now about those syndication rights, I think first we have to come up
> with a decent plot!
What is wrong with the traditional - capacitor sees inductor, capacitor falls for inductor,
capacitor's family forces rejection of inductor due to inductor's low Q,
inductor is rewound with Litz wire, capacitor runs into rewound inductor at otherwise
boring symposium...
Kept Hollywood going for years.
Bill Sloman, Nijmegen
Kendall Castor-Perry
In article <61h0ke$9...@fridge.shore.net>, Winfield Hill
<hi...@rowland.org> writes
>
[snipped all of my previous and some of Win's]
> Without addressing the properties of various dielectrics, I have taken
> more specific measurements of the 7uF motor-run capacitor in question.
> This data is from an H.P. 4263B LCR meter.
>
> freq. C (uF) esr
> ohms
> 100 Hz 6.911 xx
> 120 Hz 6.909 xx
> 1 kHz 6.900 0.031 Q = 745
> 10 kHz 6.943 0.026
> 100 kHz 7.806 0.034 oops!
>
[snipped rest of Win's]
Hmmm, have I been beating up on polyester all these years unjustly? To
tell the truth I wasn't actually reading some of the thread properly and
had lost the plot on the use of the 7uF.
I guess my ideas on the scale invariance of arbitrarily connected arrays
of capacitor elements immersed in a medium with 'lossy' dielectric
constant can't be quite right. Trouble is I slung out all my
electromagnetic theory books shortly before I realised I'd be needing
them... point me in the right direction, guys!
Relevant to this thread is a short article (4 pages excl adverts) I just
read today (an abstract I'd ordered and forgotten) by Philip Geffe
(*the* Geffe) on the design of single-layer solenoids for RF filters in
Microwave Journal, Dec 96. PG writes software to do a lot of circuit
things and he's collected together the relevant equations and some
polynomial approximations in a way which should help one produce a nice
program for automating this.
Kendall Castor-Perry
If there's a NOSPAM in the reply-to, remove it...
my employer pays for my net connection but I speak for myself.
John Woodgate
In article <61icr7$6mu$2...@wnnews.sci.kun.nl>, Bill Sloman
<slo...@sci.kun.nl> writes
Now who's applying for Official Newsgroup Comedian?
Alan Fowler
slo...@sci.kun.nl (Bill Sloman) wrote:
> <snipped content>
>> Now about those syndication rights, I think first we have to come up
>> with a decent plot!
>What is wrong with the traditional - capacitor sees inductor, capacitor falls for inductor,
>capacitor's family forces rejection of inductor due to inductor's low Q,
>inductor is rewound with Litz wire, capacitor runs into rewound inductor at otherwise
>boring symposium...
>Kept Hollywood going for years.
> Bill Sloman, Nijmegen
Hollywood? Perhaps. It sounds more like Mills and Boon. The
old type, not the new SEX, SEX, SEX books they are reputed to be
releasing.
regards, Alan.
.
,-._|\ Alan Fowler. (Alan M. Fowler FIEAust CPEng)
/ Oz \ Mail Address: PO Box 1008G, North Balwyn 3104 Vic, AUSTRALIA.
\_,--.x/ Phone: +613-9857-7128 Member, Melbourne PC User Group.
v +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Winfield Hill
John Woodgate, <j...@jmwa.demon.co.uk> said...
>
> Bill Sloman <slo...@sci.kun.nl> writes
>> hi...@rowland.org (Winfield Hill) wrote:
>>
>>> Now about those syndication rights, I think first we have to come up
>>> with a decent plot!
>>
>> What is wrong with the traditional - capacitor sees inductor, capacitor
>> falls for inductor, capacitor's family forces rejection of inductor due
>> to inductor's low Q, inductor is rewound with Litz wire, capacitor runs
>> into rewound inductor at otherwise boring symposium...
>>
>> Kept Hollywood going for years.
>>
>> Bill Sloman, Nijmegen
>
I see the discussion of high-Q high-voltage inductor design is getting
a little boring... Yawn.
Winfield Hill
James P. Meyer, <jim...@acpub.duke.edu> said...
>
>On Sat, 4 Oct 1997 ma...@global.california.com wrote:
>
>> Be aware that Litz wire works great as long as *every* wire in the bundle
>> is in the exact same field over its length! If not, you then have shorted
>> turns of a transformer with their loops of currents flying around, all
>> clouding the issue for you, too.
>
> magnetic fields. Any inequality of external field that tried to set up a
> "loop of current" within the strands of a piece of Litz wire would be
> equalized by the very same phenomenon.
Looking at a length of litz wire, with its very regular construction and
wind, it's hard to imagine any wires of significantly differing length...
ma...@global.california.com
On 12 Oct 1997, Winfield Hill wrote:
> James P. Meyer, <jim...@acpub.duke.edu> said...
> >
> >On Sat, 4 Oct 1997 ma...@global.california.com wrote:
> >
> >> Be aware that Litz wire works great as long as *every* wire in the bundle
> >> is in the exact same field over its length! If not, you then have shorted
> >> turns of a transformer with their loops of currents flying around, all
> >> clouding the issue for you, too.
> >
> > You can't have "loops of currents" that don't generate their own
> > magnetic fields. Any inequality of external field that tried to set up a
> > "loop of current" within the strands of a piece of Litz wire would be
> > equalized by the very same phenomenon.
>
> Looking at a length of litz wire, with its very regular construction and
> wind, it's hard to imagine any wires of significantly differing length...
>
I didn't say "length" difference, I said difference of the "field" that
each wire is in. Every length can be identical, but each wire may not sit
in *exactly* the same field. That's what causes the loops and "shorted
turn" effects.
- Robert -
Winfield Hill
ma...@global.california.com, <ma...@global.california.com> said...
>
>
>
>On 12 Oct 1997, Winfield Hill wrote:
>
>>>On Sat, 4 Oct 1997 ma...@global.california.com wrote:
>>>
>>>> Be aware that Litz wire works great as long as *every* wire in the bundle
>>>> is in the exact same field over its length! If not, you then have shorted
>>>> turns of a transformer with their loops of currents flying around, all
>>>> clouding the issue for you, too.
>>
>> wind, it's hard to imagine any wires of significantly differing length...
>
> I didn't say "length" difference, I said difference of the "field" that
> each wire is in. Every length can be identical, but each wire may not sit
> in *exactly* the same field. That's what causes the loops and "shorted
> turn" effects.
I'm having some difficulty picturing such a situation. Could you be
more specific with an example? Maybe a very small coil with a large litz?
Alan Fowler
hi...@rowland.org (Winfield Hill) wrote:
>James P. Meyer, <jim...@acpub.duke.edu> said...
>>
>>On Sat, 4 Oct 1997 ma...@global.california.com wrote:
>>
>>> Be aware that Litz wire works great as long as *every* wire in the bundle
>>> is in the exact same field over its length!
>>
[snip]
> Looking at a length of litz wire, with its very regular construction and
> wind, it's hard to imagine any wires of significantly differing length...
I wonder whether the "problem" is more likely to be that all
wires haven't the same length in each position in the
cross-section. Suppose the pattern repeats every 3 metres, and
your piece of litz wire is 4.5 metres, i.e. one and a half
pattern lengths. But I would expect the result to be a small
variation.