Flux density

• posted

Reviewing stuff I forgot during lockdown, this is one thing I never got.

H is amp-turns/meter, and having distance in the denominator suggests that it is also a measure of flux density (but without the core influences). So why is B defined as flux density, as if that distinguishes it from H?

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"Tom Del Rosso" wrote in news:racu90\$svq\$ snipped-for-privacy@dont-email.me:

90 degrees of other than Kevin Bacon?
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It's just a definition. In Gaussian units (rationalized CGS-ESU), B is quoted in gauss and H in oersted, but there's no actual dimensional difference, i.e. mu is dimensionless.

Cheers

Phil Hobbs

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Dr Philip C D Hobbs
Principal Consultant ```
• posted

B is flux density: wrap a loop of wire around a given cross-sectional area, of uniform flux density B, and you get B*A flux in that loop (which if the flux is changing, you can do Faraday's law, etc.). Who knows what current flows in the wire.

Conversely, put some current into a loop of a given perimeter, and you have some magnetic field intensity H within it (give or take geometry, of course). Who knows how much flux that took.

In space, the ratio of these two happens to be mu_0. Or at the terminals of the loop, its inductance: H == V.s / A. For general materials, use mu = mu_0 * mu_r, and the effective cross sectional area A_e and effective path length l_e.

Tim

```--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design ```
• posted

I think Phil understood best what I meant, but all the answers (except Kevin Bacon) contributed something helpful. Thanks so much.

A few things.

Where do you measure l_e?

What is V_s?

And you seem to be relating inductance H to mu, but isn't that a whole different H? Inductance doesn't depend on current for one thing.

• posted

"Tom Del Rosso" wrote in message news:raf445\$1vt\$ snipped-for-privacy@dont-email.me...

In general, you'd calculate it by integrating over space, in such a way that you get the average of magnetic path lengths, weighted by their contributions to total flux. I guess that's a ratio between some Maxwell equations but I can't think which ones at a glance.

When mu_r >> 1, the path is essentially all in the core (or gaps between core pieces), so is the mean circumference of the core. l_e is almost exclusively used with cores, since it isn't very meaningful elsewhere...

Same for A_e, the effective area is the core cross section. You can define it easily enough for helical geometries (solenoid, toroid, whatever) as well, but you'll always get an inductance greater than calculated because there's leakage between turns as well as the main (intended?) field.

V.s is the product of volts and time, flux (webers). (Notice I consistently used underscore to denote subscript.)

I bring up inductance because we're often concerned with circuit parameters (volts, amps, winding flux, inductance), or what makes them up (inductivity (inductance / turn^2), flux per turn, amp-turns), as well as the fields and other bulk properties (flux density, magnetization, permeability).

I like to treat turns as their own unit, to keep track of whether I'm talking about circuit values (turns cancel out), core values, or fields.

The thing about dimensional analysis is, you can always add dummy units and track them through the operation -- a helpful tip just for hand-working algebra -- but it's a lot harder to remove units, and doing so may invite confusion (I would perhaps suggest avoiding the cgs system until one is very comfortable with fields).

Yes, magnetization symbol is H (bold H if you're talking about vectors), and the henry unit is H, one must be careful not to confuse the two. I usually use "==" to denote unit equivalence, and a regular "=" to denote mathematical equivalence.

Also I tend to refer to H as magnetization, even though that's the built-in magnetization M (i.e., a permanent magnet). What I mean is "magnetic field intensity" but ain't no one got time fo' dat.

Also also, inductance does vary with current, for practical ferromagnetic cores -- that's one reason why we're interested in tracking the total flux (circuit flux * turns / A_e = B), or sometimes magnetization (circuit amperes * turns / l_e = H), in magnetic component design.

If you're more interested in fields in general, than component design, you can ignore much of the circuit-oriented values.

Tim

```--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design ```
• posted

"Tom Del Rosso" wrote in news:racu90\$svq\$ snipped-for-privacy@dont-email.me:

Here is a good start, though it begins much earlier than the info you want. Still a pretty good instructor.

• posted

And for the same reason you read it from the datasheet of the core, not measure. One can also resort to FEM sims, but I believe it is pretty rare outside of academia.

Best regards, Piotr

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In my experience, l_e and A_e are very close to the expected mechanical dimensions -- i.e., cross section of the wound limb(s), mean circumference of expected path. I don't think that's necessary, and is in part a consequence of conventional shapes being well behaved -- compact, symmetrical, optimized for cost and performance.

Also, v_e ~= l_e * A_e, which I'm not sure has to necessarily be true. (There could be vestigial core features that don't magnetize, so the core volume is greater than the active volume; but then, it's _effective_ volume, so that wouldn't be counted anyway?).

And when you bring nonlinearity into things... As magnetization rises: mu_eff falls, A_e rises some (fringing fields), l_e rises some (because the inside track saturates first, especially inside corners, pushing the active volume outwards).

The changes in mu_eff and A_e partially oppose, so it's not immediately obvious how to separate them; since they're both effective parameters, we might just assume one or the other remains constant instead, and measure the other as the combination.

These are hopefully effects we can ignore... which for power application, yep, no problem. For signals, well obviously you want to keep the magnetization low to avoid distortion, frequency shift, etc. Some airgap helps ballast changes in core mu, which would otherwise be rather sensitive (not to mention, to temperature as well as signal level).

Tim

```--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design ```

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