sepic inductance is quadrupled ove induvidual coil value with other open.?

[grizedale]

In a sepic converter in continuous conduction mode with a coupled inductor (1:1) the inductance seen is 4 times what it would have been if two separate inductors had been used.

...i.e exactly the same two inductive parts, but with each one just being used as an inductor, with the other winding open.

 

[mtwieg]

Yes. Are you just wondering why? For inductors in series, the total effective inductance is L=L1 + L2 + 2Lm, where Lm is mutual inductance. If the coupling between the inductors is high, then 2Lm= L1+L2, and the total inductance will be 2*(L1+L2). If the turns ratio is 1:1 and they're on the same core, then L=4*L1.

 

[grizedale]

Thanks,

also, on SEPIC inductor datasheets they quote series and parallel inductance.

and the "parallel" inductance is actually equal to the inductance of one winding , with the other one open?

 

[FvM]

the "parallel" inductance is actually equal to the inductance of one winding , with the other one open?

parallel and single winding inductance are (almost) equal in case of ideal (high) coupling, which is in fact the usual design of a SEPIC inductor.

With coupling k < 1, parallel inductance is lower than single winding, for k = 0 (no coupling), it's only half this value.

 

[lm2577]

If the turns ratio is 1:1 and they're on the same core, then L=4*L1.

I disagree.
In magnetic-coupled inductor each coil cover the total magnetic flux generated by the two windings. With the same number of turns and the same volt-seconds applied to the windings, the total magnetic flux is equal to twice the single-coil magnetic flux.
Therefore, based on a common definition of inductance L = dPhi / dI, where dPhi - the magnetic flux covered by the turns of the winding, dI - change in current in the coil, the equivalent inductance value of each winding in magnetic-coupled inductor is equal to twice the inductance of a single coil.

 

[FvM]

I disagree.

No problem, but the the inductor physics doesn't care about. Perhaps, you have heard about the inductance of a coil being proportional to n², squared number of turns. This is due to the simple fact, that doubling the number of turns 1. doubles the magnetization B and 2. doubles the voltage induced by dB = µdH.

 

[lm2577]

... Perhaps, you have heard about the inductance of a coil being proportional to n², squared number of turns ...

In sepic there is no serially connected inductors, but only two magnetically-coupled windings (in particular the DC components of the current in the windings, in general, are different). Therefore, in practical calculations one should use the equivalent inductance value of each winding, which is half of the "total" ;-) inductance, ie 2*L. See, for example:
http://circuitprotection.eu/library/products/Inductor SEPIC App Notes.pdf

 

[FvM]

In sepic there is no serially connected inductors, but only two magnetically-coupled windings.

The previous discussion was about "series" inductance of coupled inductors, e.g in post #3, no referring to a particular circuit. The term is used e.g. in the Coilcraft Coupled Inductors datasheets. I agree, that there's no series connection of inductors in usual SEPIC configuration. This means there's neither factor four nor factor two of single windings inductance involved.

The question in the original post "in continuous conduction mode with a coupled inductor (1:1) the inductance seen is 4 times" doesn't tell which inductance is exactly measured.

 

[mtwieg]

I disagree.
In magnetic-coupled inductor each coil cover the total magnetic flux generated by the two windings. With the same number of turns and the same volt-seconds applied to the windings, the total magnetic flux is equal to twice the single-coil magnetic flux.
Therefore, based on a common definition of inductance L = dPhi / dI, where dPhi - the magnetic flux covered by the turns of the winding, dI - change in current in the coil, the equivalent inductance value of each winding in magnetic-coupled inductor is equal to twice the inductance of a single coil.

No, you're mistaken. L=Φ*N/I. You forgot turns in your equation.

The basis for self inductance is the when current is applied to a path, a flux is created that induces an EMF that opposes the applied current. The flux created per amp is proportional to N, and the emf resulting from that flux is also proportional to N. That's why inductance is proportional to N² (in the case where turns are perfectly coupled to each other).

 

[grizedale]

Basically , suppose you are doing a CCM SEPIC.

two versions as follows

1. with 2 separate uncoupled inductors of 22uH

2. A coupled inductor (1:1) where each coil, if measured with the other one open, showed an inductance of 22uH.


Would the di of the input current be 4 times less with 2) ?

..ie would input current peak to peak ripple be 4 times less with 2?

 

[lm2577]

... You forgot turns in your equation...

Ok, I absolutely agree that the total inductance of series-connected winding will be proportional to the square of the number of turns. However, the topicstarter was interested in the inductance of each of the two magnetically-coupled windings. If the current flows in only one winding (the second open) - the magnetic flux is Ф=L*N*I. When current flows in both windings, the magnetic fluxes of the two windings are added: Ф'=2*L*N*I. Consequently, the equivalent inductance of one winding is equal to L'=2*L, where L - the inductance of a single winding with the other open.
Or one can - the "total" inductance is equal to 4*L, hence the inductance of each winding is equal to half the "total", ie 2*L.

 

[FvM]

1. with 2 separate uncoupled inductors of 22uH

2. A coupled inductor (1:1) where each coil, if measured with the other one open, showed an inductance of 22uH.

Would the di of the input current be 4 times less with 2) ?

In the said circuit, the two inductors are connected in parallel, not in series. Placing two individual inductors of 22 uH results in a total inductance of 11 uH, while for the coupled inductors (k near 1), the total (parallel) inductance is equal to the inductance measured at one winding. As a result, input dI/dt is doubled for the uncoupled inductors.

In other words, in contrast to the assumption in the initial post, the effective total inductance is kept with coupled inductors but reduced by a factor two with uncoupled.