4
\$\begingroup\$

I have a slight confusion regarding the saturation rating of transformers. I often find this value stated in Volt-Seconds, which is a unit for the saturation flux, i.e. the maximum flux that the core can hold. After all, the saturation flux density \$B_\text{sat}\$ and the cross section of the core \$A\$ are both independent of its windings. So their product \$\Phi_\text{sat}=B_\text{sat}\cdot A\$, which happens to have units of Volt-Seconds, has to be independent of the windings, too.

Therefore, I regarded the saturation Volt-Second rating to be a property of the transformer core.

But then I thought about what happens in a 2:1 transformer when I apply the same Vs to one or the other winding (with no load on the second winding):

  • The inductance of the shorter winding is 1/4th of the inductance of the longer winding
  • So the current through the shorter winding will rise 4x as fast
  • So for the same Vs applied to each winding, the shorter winding will have developed twice as many Ampere-Turns
  • So the shorter winding would have generated twice the flux for the same Vs (and would thus saturate at a lower Volt-Second rating)

Now I was confused, because the latter consideration would indicate that the Volt-Second saturation does in fact depend on the winding properties and is not a property of the core.

Where did I go wrong?

\$\endgroup\$
20
  • 1
    \$\begingroup\$ @Andyaka my version of this is: My edit merely pours the argument that has already been there, into mathematical terms. It is the same argument, that I explained in the first comment to your answer. \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:28
  • 1
    \$\begingroup\$ @Andyaka I don't see how the minor edit to the question is "widening the goalposts". It does not seem to have invalidated your answer since the part of the question you quoted did not change. \$\endgroup\$
    – Null
    Nov 10, 2023 at 14:14
  • 2
    \$\begingroup\$ @Andyaka If you don't want to "go to all the trouble" of expanding your answer then don't. The OP and other users will vote accordingly. \$\endgroup\$
    – Null
    Nov 10, 2023 at 14:34
  • 1
    \$\begingroup\$ @Andyaka Regardless of whatever point you are trying to make, it was a legitimate edit to the question and you'll just need to deal with it as you see fit. \$\endgroup\$
    – Null
    Nov 10, 2023 at 15:52
  • 1
    \$\begingroup\$ @Andyaka The addition of one sentence does not make it a chameleon question. \$\endgroup\$
    – Null
    Nov 10, 2023 at 16:23

4 Answers 4

7
\$\begingroup\$

The transformer/inductor core saturation parameter is not a Volt.Second product, though it is frequently pronounced like that, perhaps to save syllables, assuming a single turn. It is a Volts_Per_Turn.Second product.

If you have a winding with twice as many turns, you can apply twice as many volts.

Consider an inductor wound with two separate identical windings. The core flux does not care whether you connect these windings in parallel, to get V at twice the I, or in series, to get twice the V at only one I.

If you have some windings on a core, you can easily scale the core Vs/turn property by the actual number of turns on a particular winding, to give you a Vs product specific to that winding.

\$\endgroup\$
3
  • 1
    \$\begingroup\$ So when I apply 1 Vs to a winding, I don't actually cause 1 Vs of flux, but only 1 Vs/N (with N being number of turns in said winding) ? Ok this explains, why the winding-specific would not match the core's Vs saturation rating. Thank you! \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:45
  • 1
    \$\begingroup\$ To all other people who answered this (seemingly obvious ?) question: Perhaps, Neil's answer isn't the neatest, but it's what made me see where my confusion lied. I now recognize, that you all essentially brought up the same argument about Faraday's law of induction and the \$N\$ in it. So to future reader's of this question: Please read the other answers, too. \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 14:05
  • \$\begingroup\$ @tobalt I just dropped into this and see all the writing. I pulled up these snips from some old document I'd written on designing an inductor for the Joule Thief. Anyway, I agree with you that Neil said it very well. \$\endgroup\$ Nov 10, 2023 at 14:30
2
\$\begingroup\$

Now I was confused, because the latter consideration would indicate that the Volt-Second saturation does in fact depend on the winding properties and is not a property of the core.

Core permeability, current and number of turns dictate the saturation point. For convenience that can be equated to volt.seconds but, it will be a different value for a different number of turns.

We probably all know this: -

$$V = N\dfrac{d\Phi}{dt}$$

So, if we rearrange we get this: -

$$V\cdot dt = N\cdot d\Phi$$

Or, volt.seconds yields flux multiplied by the number of turns.

\$\endgroup\$
12
  • \$\begingroup\$ When I add more turns, and thus increase the volt-second saturation point of the winding: How does this relate to the core having a fixed crosssectional area, fixed saturation flux density, and thus fixed saturation flux (which is the product of saturation flux density and crosssectional area), which can be also equated to a fixed volt-second saturation point of the core ? In this argument I am talking about the magnetic circuit only, and use Vs only as units for the flux. I am confused why they don't match the winding-specific Vs number. \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 12:53
  • \$\begingroup\$ I'm sorry but I answered your question i.e. your initial assumption about V.s being related only to the core is incorrect. In other words if you have a 2:1 step down transformer, the core will see the same flux when half the voltage is applied to the secondary \$\endgroup\$
    – Andy aka
    Nov 10, 2023 at 12:58
  • 2
    \$\begingroup\$ If you insist...仄 In my opinion, you only re-stated the second side of my confusion. You did not indicate what is flawed with the argument that led me to the first side of my confusion. \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:00
  • 1
    \$\begingroup\$ You haven't provided an argument for V.s being a core property. \$\endgroup\$
    – Andy aka
    Nov 10, 2023 at 13:01
  • \$\begingroup\$ What? lol.. ok nvm then. If you do mind, re-read the second sentence of my question, or first comment to your answer. \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:01
2
\$\begingroup\$

Correct, you need to know the winding reference. Usually it's labeled "primary", but datasheets are often vague about this, and one may wish to ask the manufacturer.

There's also the matter of whether it's peak, peak-to-peak, sine wave, RMS, or what flux. Peak should be the most common, but you never know unless specified.

Regarding the confusion between cores and windings, consider that there are two fluxes in play here: the free field flux \$B A_e\$, and the electrical or in-circuit flux \$B A_e N\$. When I present calculations on these, I include a fake unit of "turns" (t) (usually arising from \$\mu_0\$ or \$A_e\$), to make it explicit that the field flux is per-turn, while the electrical flux is at given turns. (Inserted on the proper constant, we automatically get \$A_L\$ in units of H/t2, for example. Oh hm, it's both then isn't it? :) )

Alternately, one might carefully label the variables, like using capital \$\Phi\$ for field flux, and lowercase \$\phi = \Phi N\$ for circuit flux.

\$\endgroup\$
2
  • 1
    \$\begingroup\$ Not my downvote. Just for clarification: if the apparent in-circuit saturation flux is \$B\cdot A\cdot N\$, then that means, that applying 1 Vs to a winding of \$N\$ turns, only causes 1 Vs/N of flux in the core? \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:54
  • 1
    \$\begingroup\$ That is correct. \$\endgroup\$ Nov 10, 2023 at 14:05
2
\$\begingroup\$

I often find this value stated in Volt-Seconds

Volt-seconds i.e. flux, along with core properties including saturation flux density, becomes a transformer parameter. Volt-seconds also equals to Ampere-Henries.

$$ V_L \ \Delta t = L \ \Delta i $$

So, for an inductor (can also be a transformer's one of the windings) with an inductance of L with a number of turns of N, by applying either of the following, you shouldn't exceed the Volt-seconds product which corresponds to, as you said, \$\Phi_{sat} = B_{sat} \ A_e\$:

  • a voltage of V across the terminals, for a time duration of t, or
  • a current change of i

But then I thought about what happens in a 2:1 transformer when I apply the same Vs to one or the other winding

We can model a transformer like this:

schematic

simulate this circuit – Schematic created using CircuitLab

I'll not explain what is what, as you already know.

The above model shows that only the primary winding has a "magnetising" inductance which is a result of an assumption like "This winding will magnetise the core" (The rest is an ideal transformer which has infinite magnetising inductance and therefore isn't mentioned). We often don't think about magnetisation using any other windings. As a result, when we design a transformer, after determining the turns ratio, we calculate the number of turns of the "primary" or "magnetising winding" using Faraday's equation:

$$ V_t = N \ A_e \ \frac{dB}{dt} $$

So we define the Volt-seconds for primary (or whichever winding is assumed to be magnetising the core). So if you apply the same Volt-seconds to another winding, specifically to one having a lower number of turns, the flux swing will be higher and maybe closer to (or even beyond) the saturation level.

As a result, if we define Volt-seconds for a transformer, we should also define its "primary winding". Or in other words, Volt-seconds per turn. We don't often use the latter because we know that one specific winding will be used as a primary i.e. the winding that magnetises the core.

Also, as I mentioned above as Ampere-Henries, if you apply the same Volt-seconds to a lower inductance (which is a result of a lower number of turns) you'll cause a larger current change which in turn will cause a higher H-field change. Because of the relation between B and H, the B swing will be higher and closer to the saturation point.

\$\endgroup\$
3
  • \$\begingroup\$ Aha! So is it, that applying Vs to an actual winding, we also cause a current. And this current times inductance adds additional flux to the "pure" volt-second flux ? \$\endgroup\$
    – tobalt
    Nov 10, 2023 at 13:31
  • \$\begingroup\$ @tobalt sorry, my answer was unfinished, I accidentally posted. Wait for the update. \$\endgroup\$ Nov 10, 2023 at 13:34
  • 1
    \$\begingroup\$ @tobalt Please see the edit. \$\endgroup\$ Nov 10, 2023 at 13:45

Your Answer

By clicking Post Your Answer, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.