time changing magnetic field and induced voltage in a coil and a spiral

[PG1995]

Hi

Could you please help me with the **broken link removed**, and **broken link removed**? Thank you very much for your help.

Regards
PG

 

[panic mode]

Q1 and Q2 have conflicting and/or incomplete info.

doubling every second means exponential rate, which disagrees with 2Wb/s (unless 2Wb/s is value at specific time t).

figure 2 in Q3 shows no leakage flux

 

[MrAl]

Hello,


If you have something changing at the rate of 2 units per second then
the equation would be:
y=2*t+K
where
t is time and K is a constant that depends on the initial conditions.
So if when we started the initial y (ie y0) was equal to 5, then after
one second we would have:
y=2*1+5=7
After two seconds we would have:
y=2*2+5=9
and after three seconds:
y=2*3+5=11
So for each 'new' second we gain two more units of y, but you also need to
know the initial quanity K.

This is not the same as stating that y doubles ever second. For y to double
every second we would have to have:
y=a*2^t
where a is a constant and 2 is taken up to the power of t the time.

 

[PG1995]

Thank you, panic mode, MrAl.

Q1 and Q2 have conflicting and/or incomplete info.

doubling every second means exponential rate, which disagrees with 2Wb/s (unless 2Wb/s is value at specific time t).

figure 2 in Q3 shows no leakage flux

Q1 and Q2: Let's assume 2 Wb/s is value at some specific time t.

Q3: What does it have to do with leakage flux? Okay, in the primary turn there would be leakage flux because the turns carry currents but to have leakage flux in the secondary turns first you have to have current in the secondary turns which means there should be induced voltage and to have induced voltage there must be interaction between the flux (generated by the primary turns) and the secondary turns. Less interaction means less induced voltage. In my humble opinion, there would be less interaction because the secondary turns are not 'immersed' in the flux. I hope I make some sense.

Thanks a lot for the help.

Best wishes
PG

 

[MrAl]

Hi,

Leakage flux is a funny thing. Even though two coils are on the same core and there is no fringing there is still something called leakage inductance which means the coupling between the two coils is not one hundred percent. For the best coupling, the one coil has to be wound one on top of the other so the turns are close to each other. To introduce leakage inductance the two coils are wound next to each other instead of on top of each other. So for a center core length of say 2 inches we would normally make a transformer by winding the secondary first and then the primary second, one on top of the other, where the secondary takes up the full 2 inch span and so does the primary. But to get leakage inductance we would wind the primary on only (say) half of the span covering only 1 inch of the total length of the center leg of the core, and the secondary on the other half (the other 1 inch length) of the center core leg. That would give us a certain leakage inductance, but if we wound the primary on only 3/4 inch near the top of the core and the secondary on the bottom 3/4 inch span then we would have two coils separated by a distance of 1/2 inch along the magnetic path, and this would make the leakage inductance higher than when they were almost touching.

Sometimes we do this on purpose, but sometimes it comes sort of as a secondary effect which may or may not be good for the application. For a good example take those DC wall warts. To achieve a certain safety class the two coils are not allowed to touch each other even though there is insulation between the layers and of course wire insulation. They have to be separated by some distance on the core where the primary is wound on one part of the core and the secondary is wound on another part of the core so there is some minimum distance between any two wires in the two coils which could be 1/8 inch or so. What happens is we achieve a good safety class, but we introduce leakage inductance. The leakage inductance for a DC wall wart causes a drop in voltage due to imperfect coupling, and this drop is more with load so we get more voltage drop with load. We'll also get a little filtering action so this helps a little.

You're question about the core and the turns seemingly not inside the field is an interesting one. The main calculations dont really address this issue and only consider things like area. If the field is 'contained' wholly within the core then how do the wires get exposed to the field. But after all the wires can 'generate' the field so why not also be affected by the field. It's almost like the core is only limiting the speed at which the wires interact. The energy is stored in the core however, so that means there has to be interaction between the core and the wires. But it's also interesting that when the coils are wrapped around the core in different places, we see less coupling. But the question is, if we removed the core and used a higher frequency and neglected other effects like the skin effect, would we see the same coupling.

When we say the field is confined to the core however, i think what we mean is that the relative field strength is highest inside the core. It's usually so much higher however (100 to 10000 times higher) that we probably cant measure the field outside because it looks much lower. But we know that a wire all by itself generates a field, with or without a core, and the core cant magically suck in all of the field that the wires generate because that doesnt stand the test of simple calculation of the field just outside the wire. But the closeness of the wires do play a big part in the couple as close wires couple well even without a core. More to think about i guess

If i did calculations for this kind of thing, i would start by calculating the effect of the H from the wires on the core and B in the vicinity of the wires. Now for a core very close to a wire when the wire is energized the core will become magnetized. The core is able to becomes magnetized because of the current in the wire and the fact that the H field radiates out from the wire and affects the sore, and the core reacts by having more of it's magnetic moments aligned and those moments create a B field. But if the current was stopped then some of those moments would tend to go back to their original positions, and that changing B field would influence the wires. It would seem hard to believe that the wires could influence the core but the core could not influence the wires or we would end up having a 'diode' for magnetic fields. If the field could get inside the core, then how could it not get outside the core too. So it appears that we have to consider the wire to be part of the total core construction if we want to think of the field as being confined within the core.