## Toroid Coil Calc's

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Hi everyone, my Googling thus far hasn't yielded an answer, so I'm asking here.

The general equation for calculating the inductance of a coil is:

L = (N^2 * u * A) / l

Where:

L is the inductance

N is the number of turns of wire in the coil

u = the magnetic permeability of the core material, (air, iron, etc)

A is the cross sectional area of the core

l is the length of the coil winding

So,  my question is this:  What is l, the length of the winding, for a toroidal coil, if the winding doesn't take up the full length of the toroid?

If one only has a couple turns that are not spaced out to take up the full circumference of the coil, does one use the actual length of the coil, or the length of the circumference of the toroid?

And, follow up question, if one is using the length of the circumference of the toroid, does one use the inner circumference, the outer circumference, or the middle radius circumference?

I guess one could spread the windings out to take up the full space available, but if that isn't done, what is "l" ?

Thanks,

JC

If you look up the specs for commercial toroid cores, there is an equation:

L = k * N^2

They provide the value of k for the particular core. It pretty much  does not  matter how the winding is distributed on the core.

The question of fractional turns has been around as long as toroid inductors have. The most common situation is a wire that simply passes straight through the center of the toroid. Consensus seems to be that you really use N = 1/2 in that case. Other cases are generally determined by experiment.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

you might like this toroid calculator---seems good...but please note it  is for air core, then as Jim noted you need to "k" value for your core material.  This link shows some detailed geometry considerations.

If one uses a magnetic core as a form to wind the toroid on, the inductance of the toroid can be found by calculating the value from the appropriate formula shown below for the air core inductor and then multiplying that value by the relative permeability of the magnetic core material.

http://www.nessengr.com/technical-data/toroid-inductor-formulas-and-calculator/

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Hi Jay,

The l stands for the length of the magnetic field lines, not the length of the wire. The spacing of the winding has (theoraticly) no effect on the inductance.

Nard

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ka7ehk wrote:

The most common situation is a wire that simply passes straight through the center of the toroid. Consensus seems to be that you really use N = 1/2 in that case.

Really?  Current only flows in loops so it has to make a complete trip around core section no matter how circuitous* the path may be.

*No pun intended. Well, maybe.

Letting the smoke out since 1978

Yes, really.  Welcome to the real world! How else do you imagine that an inductive current sensor works? Tek current probes used this for years. You could get more sensitivity by wrapping several wraps through the probe but they were intended to snap open and a single wire to pass through. Ditto "clamp-on" ammeters.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

Last Edited: Sat. Nov 17, 2018 - 10:12 PM

Doc,

Pulled out my magnetics book so my answers are based more on theory than experience.

So,  my question is this:  What is l, the length of the winding, for a toroidal coil, if the winding doesn't take up the full length of the toroid?

If one only has a couple turns that are not spaced out to take up the full circumference of the coil, does one use the actual length of the coil, or the length of the circumference of the toroid?

And, follow up question, if one is using the length of the circumference of the toroid, does one use the inner circumference, the outer circumference, or the middle radius circumference?

I guess one could spread the windings out to take up the full space available, but if that isn't done, what is "l" ?

As Nard said, l is the length of the magnetic path.  As far as that length, the book says that the average radius is sufficient for calculating the circumference since other factors such as permeability changes with the strength of the magnetic field.  Any calculation with a fixed permeability is not exact unless you use the B/H curve to calculate B from H.  As far coil length and spacing, since a toroid is a closed magnetic path of uniform permeability and thus uniform flux density, the position and spacing of the coil should not be important.

Alan

Added:  A more exact calculation can be found at www.phys.uri.edu/gerhard/PHY204/tsl267.pdf where "H" is height of the toroid, not magnetic field

Last Edited: Sun. Nov 18, 2018 - 01:46 PM

You missed my point entirely.  My point was there is no such thing as a 1/2 turn for a toroid.

ka7ehk wrote:

Yes, really.  Welcome to the real world! How else do you imagine that an inductive current sensor works? Tek current probes used this for years. You could get more sensitivity by wrapping several wraps through the probe but they were intended to snap open and a single wire to pass through. Ditto "clamp-on" ammeters.

Jim

You need to explain to me then why wrapping 1 turn on one of sensors you mention doubles the reading instead of multiplying it by 1.5.  I'm sure Mr. Maxwell will be interested in your answer.

Edit: Assume for the sake of argument that the concept of 1/2 turn is valid.  Then, in my example above the reading would be multiplied by 3 when adding one turn to the sensor.  Try it and see for yourself.

Letting the smoke out since 1978

Last Edited: Sun. Nov 18, 2018 - 01:33 AM

I do know that when clamp on current sensors are calibrated for one wire, straight through the "hole". making a full wrap so that the wire passes through the hole twice doubles the sensitivity.

I would also consider a wire passing straight though the hole in a core to be 1/2 turn and the case where it wraps around the outside of the core to pass through the hole twice to be a full turn.

I have seen these cases in practice more times than I can count.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

So you're saying 1/2 turn produces reading x and 1.5 turns produces reading 2x? If that's really what you're saying then I humbly suggest you revisit your undergrad text books.

Letting the smoke out since 1978

I would also consider a wire passing straight though the hole in a core to be 1/2 turn

Yep, you can pass the wire through a hole drilled in the core so it picks up half the flux, (effectively forming a half turn).  You can also double up on the cores  (each turn going through both & one turn going through only one core if a half turn is needed).

taken from page 126

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Last Edited: Sun. Nov 18, 2018 - 05:44 AM

My definition of 1/2 turn is ONE pass though the center hole of the core. One turn is when the wire passes through twice. Not the same as avrcandies' illustration; both sides to the drawing show only 1/2 turn because the wire goes through the center hole only once.

Jim

Jim Wagner Oregon Research Electronics, Consulting Div. Tangent, OR, USA http://www.orelectronics.net

Last Edited: Sun. Nov 18, 2018 - 07:06 AM

One turn is when the wire passes through twice

well....perhaps that might be semantics, however a simplest current sensing transformer (a wire just going straight through the core) is usually considered to have 1 turn (the rest of the connecting circuitry finishes the loop).   So any actual (additional) "turn" is considered turn number 2.   Maybe these are sometimes spec'd (Iout/Imon) with one physical loop (middle pic).

This type of current transformer uses the actual cable or bus-bar of the main circuit as the primary winding, which is equivalent to a single turn.

https://www.electronics-tutorials.ws/transformer/current-transformer.html

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Aren't you all talking about two different things here: transformers and inductors?

#1 This forum helps those that help themselves

#2 All grounds are not created equal

#3 How have you proved that your chip is running at xxMHz?

#4 "If you think you need floating point to solve the problem then you don't understand the problem. If you really do need floating point then you have a problem you do not understand." - Heater's ex-boss

Wow, I appreciate all of the input, and everyone's insight!

It makes sense that the mag field is essentially uniform, (approximation) within the core, so the distance over which one spreads out the coil shouldn't matter.

I think I'll use the average radius, as it has been far too many years since I did the maths needed to integrate the B field as a function of the radius!

Nard, good to hear from you.  If I recall correctly one of your projects from the past was a coil winder!

I guess this question was right up your alley.

The source of the question was that one of my sons lives at home and is studying engineering.

They recently studied RC and RL circuits, this week they will tackle RLC circuits and resonance.

Anyway, they had an extra credit project: Create a 5 mH coil, wirte up your report, and bring the coil in to demonstrate it to an instructor, showing that it is 5 mH.

I'll post some photos of his/our trial coils tomorrow.

It was MUCH harder and more involved than expected to make a simple inductor of 5 mH!

(Now I know why I just order stuff from Mouser!!!)

To cut a long story short the first several coils made were in the uH range, off by a factor of 1000!

These were wound on large bolts, we even drove to the hardware store and bought a new, huge, bolt.

I think these were likely stainless steel, (carbon steel ?), and their permeability was in the 10^-3 range.

When he wasn't getting anywhere I ordered a three iron core toroids from Amazon, and the smaller one hit 1/3 mH, wow, getting into the right range.

Now only off by a factor of 15, not 1000.

He then wound his final coil over the other two, slightly larger, toroids, stacked on top of each other, (to double the area of the core).

After two full layers he measured it and had 20+ mH's Whow!  Success, overshot the goal, (finally).

Winding a really long wire for 150+ turns through a toroid is itself a challenging project as the wire keeps kinking and getting tangled...

My question was because I wanted to calculate the expected inductance vs what he actually built.

Photos to follow, it was a fun project to watch him work on.

I appreciate everyone's insight and guidance!

JC

Nope.  Transformers work because of mutual inductance between the windings.  It's all about current loops and magnetic flux.

Letting the smoke out since 1978

avrcandies wrote:
well....perhaps that might be semantics, however a simplest current sensing transformer (a wire just going straight through the core) is usually considered to have 1 turn (the rest of the connecting circuitry finishes the loop).

Hence my bad pun in #5 above.

Letting the smoke out since 1978

a good ref:

https://owenduffy.net/balun/concept/tt.htm

Also, For toroids, no fractional turn per se:

When in the dark remember-the future looks brighter than ever.   I look forward to being able to predict the future!

Last Edited: Sun. Nov 18, 2018 - 04:04 PM