Piece of Wire Through a Toroid

Correction.. (Huhhh.. )

H includes uo

when

0.4*pi*N*I H= ---------- le

le in cm

When you went to the Christmas party and entered saying "I come baering gifts..." they knew it was you... The stripper almost said the same thing... "I come baring gifts..." The knew it was her too... and her little jugs too...

You want turns count on a toroid, count the wires INSIDE the center. THAT is the right turns count.

YUP!

Is that exactly true? I've actually cracked black (high mu) ferrite toroids by saturating them. My crazy guess is, field is slightly higher around the inner annulus, saturating it first and causing magnetostriction that expands it, uniformly cracking it into about fifteen pieces. If it saturated evenly, it would expand evenly.

Magnetic path length is always a factor in calculations, so I'm guessing the ratio of B across the toroid goes something like ln(R/ r)? Logs always seem to show up in concentric things...

Tim

A straight-wire power inductor wastes space and core material compared to a wound toroid. As you have seen, the field within a toroid on a straight wire is not uniform so you'll have to choose your operating point to avoid core saturation near the wire while wasting capacity near the outside. This can be mitigated by using a bigger toroid, but then you need even more space. A wound toroid has a nearly uniform field inside, so its size can be optimized. Furthermore, inductance in a wound coil is proportional to the SQUARE of the number of turns, not just the length of the core. Core loss increases with maximum flux density, so again, the wound toroid would be the way to go.

80 cm??? I rest my case.

-- Joe

on:

Yup.. It's a SuperBead.. :) A crazy 80cm long power inductor if the ur stays constant. It's a chunky inductor but can still fit in a very long box.. :) And still shorter than the power cord :)

I'll guess at some cored straight wire advantages:

-----------------------------

*) Lowest interwinding capacitance for high frequency. *) 100% shielded for low EMI (No stray field) *) High surface area for cooling. *) Very easy construction. *) Low profile *) I can order factory direct cause so many cores are needed.. (Ok just joking with that last one.)

Consider:

B = (ur*uo*I)/(2*pi*r)

Say Bsat. ~= 0.4Telsa Say I = 1A Say wire diameter = 1mm

Since ferrite ur drops on creep to saturation. Solving for ur at surface of wire.

ur = 0.4T*2*pi*0.5E-3/(uo*I )

ur = 1000

So..If I haven't messed up the physics and math, this means:

If the core ur drops to 1000, the surface of the core can handle the

4000 gauss flux density at the surface of the wire. The core surface contributes to inductance and is not totally saturated. More core radius yeilds more ur yeilds more L. That gives me a hint about deltaB and core loss.

So you say a straight wire in a core would have more core loss than a coiled design..??

Is it worth trying an experiment??

D from BC myrealaddress(at)comic(dot)com British Columbia Canada

It's definitely worth experimenting when someone tells you it cannot work :-).

-- Joe

,snip>

How about this test setup?

Objective: Just how lossy is a straight wire ferrite inductor using the highest permeability material at 800Khz.

Say 50 toroids =================

--------------------------

Ooops.. I just noticed on a data sheet that ui of materials like W (ui =10000) drop to ~2000 @800khz.

AFAIK there's no material with ui = 10000 at 800khz. Looks like a straight wire inductor at 400uH will be much longer than

80cm. More like 270cm with u=3000 Using calculator on:

So no experiment.. Oh well.. Coils are good. :)

D from BC myrealaddress(at)comic(dot)com British Columbia Canada

Not so fast, D.

The inductance calculator you are using above is for a straight wire made of a conductor with a particular permeability. That's not the same as having a surrounding core.

It's easy to find the inductance of a toroid on a straight wire. First, inductance is just the derivative of flux with respect to current:

L=3Ddp/di

We already know the flux in a toroid on a straight wire: p =3D uo*ur*i*d*ln(ro/ri)/2*pi

Differentiating, we have:

L=3Ddp/di =3D uo*ur*d*ln(ro/ri)/2*pi

For d=3D100cm, ri=3D1.5mm, ro=3D2.5mm, ur =3D3000 =3D 4pi*10^-7*3000*1m*ln(.0025/.0015)/2pi =3D 2*10^-7*3000*1*ln(.0025/.0015) =3D 306 uH

Getting closer, no?

-- Joe

I think you'll find the permeability drops considerably, for any DC filtering application when you're using ungapped ferrite.

Your recent foray into marix (flat) transformers should have provided some insight into single-turn multi-core structures.

RL

Yup... Geez...I suck at magnetics.. :P

Since it's just a ratio in ln and if I use a stack of production toroids:

OD 9.53 mm ln ------- ID 4.75 mm

L = 418uH

I was just curious of the alternative if I didn't coil to get away from interwinding capacitance, leakage flux and EMI. Also, I thought it would be a nice start to learn some magnetics theory...

I'll be getting back into researching matrix transformers after research on planar mag and EFD cores.

I'm still a newbie at magnetics and I find it a pita.. flux flux density Al current density hysteresis loss skin effect core sizes wire diameters layering resonance heat sinking heat rise EMI fringing leakage flux gaps complex permeability initial permeability relative permeability amplitude permaeability

• more

...huhhh :P

I believe some understanding of all that is still needed to utilize the magnetics development software.. :( The program from EPCOS for example..

D from BC myrealaddress(at)comic(dot)com British Columbia Canada

Yes, they are approximately the same because the most of the flux follows paths entirely within the cores. Flux that passes partly through air and partly through core has roughly the same relative density as flux that passes entirely through air - i.e. a small fraction, on the order of 1/ur.