# A Revised Inductance Calculator

R

#### Reg Edwards

Jan 1, 1970
0
==================================
Gary wrote -
I never heard anyone ask this question before.
The Length of the coil is the "MEASURED LENGTH of the
windings, END TO END".

=================================

Have you ever used a 12" ruler to measure the 'length' of a coil?

Wind a single layer solenoid on a cylindrical former about 1.5" in diameter.

Wind on exactly 10 spaced turns of 0.1" diameter wire.

This is a very common sort of coil used in HF radio transmitters.

Place the measuring rule along the surface of the coil in the direction of
the coil's axis.

Between which two points near the ends of the coil do you measure its
length?

Rotate the coil 180 degrees on its axis and you will find you can measure a
different length.

Or you can define the length of the coil as being the number of turns times
the winding pitch.

Which of these lengths do you insert in your inductance calculating program?

They can give you 3 inductance values differing by several percent.

As the number of turns decreases the differences increase.

As someone else has pointed out, when there is only one turn the answer can
be silly.

So length must be precisely defined. Furthermore the definition must apply
to any number of turns, perhaps excluding a single turn which can be a
special case. Single-turn coils are frequently used as radio antennas.

The above problems are solved in program SOLNOID3 which can be downloaded in
a few seconds from website below and run immediately. Or it can be run

SOLNOID3, besides inductance, calculates several other useful properties of
single layer solenoids from AF to UHF.
---
=======================
Regards from Reg, G4FGQ
go to http://www.g4fgq.com
=======================

T

#### Tom Bruhns

Jan 1, 1970
0
...
I never heard anyone ask this question before.
The Length of the coil is the "MEASURED LENGTH of the windings, END TO
END".

A lot of folk define it as the winding pitch times the number of
turns. Some have even defined it as the winding pitch times (the
number of turns plus one). It's not so different from the diameter
problem (for a single-layer uniform solenoid coil): is it inside
diameter, diameter to wire centers, or outside diameter? I don't much
care how someone defines the dimensions, so long as they are clear

Cheers,
Tom

R

#### Reg Edwards

Jan 1, 1970
0
Quite Simply, a one turn coil is equivalant to the diameter of the
wire you are using.
==============================

Indeed, if you define it as such, then just as simply stated - if you
insert coil length = wire diameter in your program you will obtain the wrong

The question arises - how will you know you have the wrong answer? And is
it too big or too small?

Sorry to be so pessimistic. It is suggested you investigate the proportions
of coil length, coil diameter,wire diameter and wire spacing such that the
formulae you use in your program become inaccurate.

On the other hand - unless you are designing coils intended for
International Standards of Inductance, an absolute accuracy of a few percent
is quite adequate for ordinary engineering equipment construction purposes.

But by far the easiest and fastest way of constructing most inductors is to
wind some turns on a some sort of former and measure it. If it's too big
then just look up at the ceiling for a few seconds and do a little
unwinding.

Incidentally, standards of reactance are defined by precision coaxial
capacitors whose values can be calculated as accurately as their few
dimensions can be measured. Parts in a million. Standards are maintained (or
used to be) in temperature-controlled, de-humidified enclosures. Frequency
is involved but that's a trivial matter of counting against a clock.

A

#### Active8

Jan 1, 1970
0
i agree with you 100%. you have to define length. and 1 turn coils? ...

i have an email to the OP in queue. i WAS going to ask if he had any
pointers on calculating mutual inductance from known core permeability
and coil geometry (some Neumann double line integral application that i
can't find on the web), but since he doesn't know how hard it would be
to calculate Q, and doesn't understand why I asked for a length
definition ...

regards,
mike

R

#### Reg Edwards

Jan 1, 1970
0
Tom sez -
I don't much care how someone defines the dimensions,
so long as they are clear about it.
===============================
Tom, I couldn't agree more.

It is our great misfortune the trouble with lengths of coils is that the
Grand Master Grover himself, failed to make himself clear. He doesn't even
mention the problem. Neither do Nagaoka, Wheeler, et al. But I confess to
have read only a small fraction of their works.

In my opinion, after trying to fathom out how their minds worked, they did
this quite deliberately.

That excellent plagiarist Terman, whose early edition I have read,

The end-effects of a coil and a fractional number of turns, to them,
although significant when there are only a very few turns, were
incalculable, and still are. As a consequence they were unable to define
coil length. If coil length is indeterminate then so is inductance and none
of their formulae can be said to be 'exact'.

In my program SOLNOID3 I restrict myself to whole numbers of turns. The
inductance of one isolated complete turn is known exactly. So also is the
inductance of the small number of turns above which the end effects become
insignificant. It is all to do with how the mutual inductance between

So by mathematical sleight-of-hand I merged the two 'exact' formulae into
one formula which handles any number of turns from one upwards. The
resulting corrections are significant only for 2, 3 or perhaps 4 turns. But
the ONLY reason I merged the formulae into one was to make life easy for
program users. So far as they are aware there is just one magic
all-embracing formula which works for any number of turns.

Coils of two or three turns are likely to be used only by radio amateurs who
insist on making magloops out of them because they mistakenly imagine they
must be more efficient than the usual single turn versions using the same
amount of copper.

The whole of this discussion is a storm in a tea cup. Everybody ignores the
lengths of a coil's connecting wires and their mutual inductive coupling
with the coil itself. It's equivalent to a fractional increase in the number
of turns. We should all be grateful for the existence of variable tuning
capacitors.

SOLNOID3 also calculates the inductance of long coils of widely-spaced
turns, better described as coarse helicals, which if stretched out enough
become straight lengths of wire. You will notice the calculated
self-resonant frequency of a coil of wire streched out straight is the same
as that of a half-wave dipole of the same wire length. Clever program, eh?
Free to USA citizens. ;o)
----
=======================
Regards from Reg, G4FGQ
go to http://www.g4fgq.com
=======================

A

#### Active8

Jan 1, 1970
0
i agree with you 100%. you have to define length. and 1 turn coils? ...

i have an email to the OP in queue. i WAS going to ask if he had any
pointers on calculating mutual inductance from known core permeability
and coil geometry (some Neumann double line integral application that i
can't find on the web), but since he doesn't know how hard it would be
to calculate Q, and doesn't understand why I asked for a length
definition ...

maybe twocoils will do. i emailed some P haitch D re MANDK which does it
for Tesla coils. his doc says he won't wrap in in a GUI because a
winders F77 compiler cost \$500. i offered to wrap it up in a GUI in
exchange for help using the Neumann integral, etc. we'll see.

regards,
mike

A

#### Active8

Jan 1, 1970
0
I also have two other programs that I have used and trust,. One for
single layer and another for multi-layer. But they are Registered
Programs and I can't distribute them freely.

good for you. why mention it if you can't give it away. the fact adds
nothing to this discussion.

A

#### Active8

Jan 1, 1970
0
[snip]
Coils of two or three turns are likely to be used only by radio amateurs who
insist on making magloops out of them because they mistakenly imagine they
must be more efficient than the usual single turn versions using the same
amount of copper.

my understanding is that the length and diameter of Hi-Q coils are
equal. my interest in the one turn coil stems from a program from
distinti.com. the documentation shows a Faraday triple integral and
their double integral (not Neumann's - it's from their IEL or Inertial
Electrical Law), the answers of which (for M) disagree slightly, but
their method works out the same as the M calculation in MANDK which i
mentioned in my other reply to you.

anyway, the distinti program calculates M for a single turn coil which
can then be scaled by multiplying by N1 and N2 for comparison to
measured data from multi-turn coils (don't ask why they didn't just
write that in to the program), or so they'd have me beleive. i haven't
had the time to evaluate all this and i have no measurements of real
coils available.

i'm currently digging though my old physics text to try to put it all
together and may be close to a double integral solution - not sure. a
double integral would require less computing time than the Fareaday
method. I'm inscenced that the calculation of M isn't included in my
physics text, just

v1 = M(di2/dt) ... you have to measure it.

i am willing to wrap GUIs around DOS apps in exchange for help. i have a
nice platform independant GUI framework in C++.

regards,
mike

T

#### Tom Bruhns

Jan 1, 1970
0
Active8 said:
...
so can i try this program?

Um, perhaps not. It seems to no longer be offered. You could try the
contact info on www.saratogasoftware.com and see if he still sells it.
can we get it to calculate mutual inductance
between coils? how about the source code?

Probably neither...

Cheers,
Tom

W

#### Watson A.Name - 'Watt Sun'

Jan 1, 1970
0
Hi Mike, Pretty Small Coil. Yes, this is due to Rounding. I can fix
this, but even if I change this, the next person will come up with a
.003 uH coil, or even smaller. How small should I go?

From what I've read, maybe here, a one inch piece of wire has about 10
nanohenrys. So if it goes down to that little, just put a lower limit
on the value that can be entered, and do a fair calculation of
anything above it.

Take care.......Gary

--
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###Got a Question about ELECTRONICS? Check HERE First:###
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My email address is whitelisted. *All* email sent to it
goes directly to the trash unless you add NOSPAM in the
Subject: line with other stuff. alondra101 <at> hotmail.com
Don't be ripped off by the big book dealers. Go to the URL
that will give you a choice and save you money(up to half).
http://www.everybookstore.com You'll be glad you did!
Just when you thought you had all this figured out, the gov't
changed it: http://physics.nist.gov/cuu/Units/binary.html
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W

#### Watson A.Name - 'Watt Sun'

Jan 1, 1970
0
I also have two other programs that I have used and trust,. One for
single layer and another for multi-layer. But they are Registered
Programs and I can't distribute them freely.

Yes, I could add tons of other stuff, but not now.
I believe self resonance is only accurate on a pure air core, not
wound on a bobbin.
Also, Not sure how difficult it would be to calculate Q.

The absolute maximum Q at a freq is the reactance of the coil at that
freq divided by the DC resistance. But the Q will always be lower
than that because the actual AC resistance will be higher because of
skin effect, when much of the inner copper wire has no current.
So you could do a simple calc based on reactance / DC res and say that
the max Q is that value, but expect less due to skin effect.
Take care.....Gary

--
@@[email protected]@[email protected]@@[email protected]@[email protected]@[email protected]@@[email protected]@[email protected]@[email protected]@,@@[email protected]@[email protected],@@[email protected]@[email protected]@[email protected]@
###Got a Question about ELECTRONICS? Check HERE First:###
http://users.pandora.be/educypedia/electronics/databank.htm
My email address is whitelisted. *All* email sent to it
goes directly to the trash unless you add NOSPAM in the
Subject: line with other stuff. alondra101 <at> hotmail.com
Don't be ripped off by the big book dealers. Go to the URL
that will give you a choice and save you money(up to half).
http://www.everybookstore.com You'll be glad you did!
Just when you thought you had all this figured out, the gov't
changed it: http://physics.nist.gov/cuu/Units/binary.html
@@[email protected]@[email protected]@[email protected]@[email protected]@[email protected]@[email protected]@@[email protected]@[email protected]@@[email protected]@[email protected]@[email protected]@[email protected]@[email protected]@[email protected]@@

M

#### Mark Fergerson

Jan 1, 1970
0
Gary said:
Hi All, I have revised my Java Script Inductance Calculator. It now
covers the wire ranges from 1 to 45 Awg, including the half gauges
from 10 1/2 Awg to 25 1/2 Awg. Most people aren't even aware these
exist.

Does it do flat spirals?

Mark L. Fergerson

G

#### Gary Lecomte

Jan 1, 1970
0
Active8 said:
i agree with you 100%. you have to define length. and 1 turn coils? ...

i have an email to the OP in queue. i WAS going to ask if he had any
pointers on calculating mutual inductance from known core permeability
and coil geometry (some Neumann double line integral application that i
can't find on the web), but since he doesn't know how hard it would be
to calculate Q, and doesn't understand why I asked for a length
definition ...

regards,
mike

I do know how hard it is to measue Q, I just didn't have a formula
handy as I was writing.

As to a single turn coil with a pitch, what is the point of it? The
purpose of Pitch is to reduce inter-wire capacitance and raise the Q.
This is almost non-existant on a single turn coil with even no pitch.
Wire leads and parts close to the coil will be more of a problem. And
No Formula can account for those errors.

Length of a coil simply put is the parallel distance, end to end.

Between all the e-mails I have recieved, there isn't much time to
reply here, and currently there is a Forest Fire, Guessing within
about 2 miles of my town. Can't see it for the surrounding mountains
and currently were down wind from it, but I have posted pictures on my
site of the Hellicopters hauling water to fight the fire. There return
time is about every 3 minutes.

So I'm busy with this.

Take care......Gary

A

#### Active8

Jan 1, 1970
0
alondra101 said:
The absolute maximum Q at a freq is the reactance of the coil at that
freq divided by the DC resistance. But the Q will always be lower
than that because the actual AC resistance will be higher because of
skin effect, when much of the inner copper wire has no current.
So you could do a simple calc based on reactance / DC res and say that
the max Q is that value, but expect less due to skin effect.

if you've got Xc, you have freq and can calculate skin depth. do a
resistivity calc and you have ac resistance, no?

mike

A

#### Active8

Jan 1, 1970
0
Does it do flat spirals?

Mark L. Fergerson

mike

J

#### Jack Smith

Jan 1, 1970
0
if you've got Xc, you have freq and can calculate skin depth. do a
resistivity calc and you have ac resistance, no?

Not quite. The current distribution in a solenoid coil is not uniform
due to proximity effects. (Terman describes this well in Radio
Engineering.) The current is forced to flow in a smaller cross
sectional area than predicted by a simple skin depth calculation.
Thus, the proximity effect increases the loss over that predicted by
the simply calculating the increased resistance due to skin effect, as
the standard skin effect formula assumes the conductor is in free
space.

There are, of course, other loss factors that are usually considered
to be part of a single "loss resistance" when one measures the Q of an
inductor. For example, if the inductor is wound on a former, there
will be some loss in the coil form. If the coil is not some distance
from nearby conductors, there will be some induced eddy current loss.

The Radiotron Designer's Handbook (4th ed) has some graphical
calculation procedures, as well as some emperical equations for
estimating coil Q. I've found these to be reasonable estimations, in
the +/- 10% range.

Jack

D

#### DarkMatter

Jan 1, 1970
0
That sinking feeling you get when you realize that you have just farted in
public

No. You don't get that feeling unless you fart in public, and are
noticed as the culprit. Silent and deadly doesn't count unless you
are stupid and admit to it.

D

#### DarkMatter

Jan 1, 1970
0
i agree with you 100%. you have to define length. and 1 turn coils? ...

i have an email to the OP in queue. i WAS going to ask if he had any
pointers on calculating mutual inductance from known core permeability
and coil geometry (some Neumann double line integral application that i
can't find on the web), but since he doesn't know how hard it would be
to calculate Q, and doesn't understand why I asked for a length
definition ...

regards,
mike

It is simple. The ideal turn is one with a zero diameter, and
inductance is at maximum for that turn. Such items are not really
feasible.

A quarter inch diameter coil of any given size wire will yield more
inductance than a 1/2 inch diameter coil of the same wire. Not
because the wire length differs, but because the coil turn diameter
differs. The only difference the wire length causes is the ESR value,
which does affect other inductor parameters. Frequency is also a
factor. An inductor will not read the same at 100kHz as it will when
tested at 1kHz or 10kHz.

D

#### DarkMatter

Jan 1, 1970
0
good for you. why mention it if you can't give it away. the fact adds
nothing to this discussion.

Piss and moan a little, why doncha?

You were smart, up until that moment.

Sheesh, just get online at any wire manufacturer, and use their
online calculators. They are much more comprehensive, and have
compensations built in, I'm sure.

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