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Flyback vs half-bridge

Started by Phil Hobbs July 16, 2013
Phil Hobbs wrote:
> On 7/16/2013 8:42 PM, Joerg wrote: >> Phil Hobbs wrote: >>> On 7/16/2013 5:10 PM, Joerg wrote: >>>> Phil Hobbs wrote: >>>>> On 07/16/2013 03:52 PM, Jim Thompson wrote: >>>>>> On Tue, 16 Jul 2013 15:08:24 -0400, Phil Hobbs >>>>>> <pcdhSpamMeSenseless@electrooptical.net> wrote: >>>>>> >>>>>>> So, I'm goofing off playing with small switchers. (Well, not >>>>>>> exactly >>>>>>> goofing off, but there are somewhat more pressing tasks waiting....) >>>>>>> >>>>>>> As I said in George's thread, "Opamp w/ Vsupply > 36V", I built a >>>>>>> small >>>>>>> half-bridge supply with positive and negative voltage doublers. >>>>>>> I'm not >>>>>>> that keen on it, because (a) it uses a fair number of parts for >>>>>>> what it >>>>>>> does, and (b) it has a nasty instability. >>>>>>> >>>>>>> With a capacitively-coupled half bridge, if you let the transformer >>>>>>> saturate, it instantly discharges the coupling cap, which about >>>>>>> doubles >>>>>>> the volt-seconds on the next half-cycle and guarantee that it will >>>>>>> keep >>>>>>> saturating until the FETs cook themselves. >>>>>>> >>>>>>> The particular little ISDN transformers I'm using have really >>>>>>> amazingly >>>>>>> low leakage inductance, so I'm thinking about using a current-mode >>>>>>> flyback instead. The UCC28C45 bicmos controller chip looks pretty >>>>>>> suitable--it's about the same price as the IRS2153D, needs one less >>>>>>> FET, >>>>>>> runs up to 1 MHz, and with such a low leakage inductance I wouldn't >>>>>>> expect to need much snubbing, if any. Plus I can run the >>>>>>> transformer >>>>>>> right up to its maximum volt-seconds without worrying. >>>>>>> >>>>>>> Ideally I'd like it to give me +-45 V at about 20 mA each. >>>>>>> >>>>>>> Any words of wisdom? >>>>>>> >>>>>>> Cheers >>>>>>> >>>>>>> Phil Hobbs >>>>>> >>>>>> Do you have a decent Spice model for the ISDN transformer? >>>>>> >>>>>> ...Jim Thompson >>>>>> >>>>> >>>>> It's 2.2 mH CT : 8.8 mH CT. >>>>> >>>>> On the 9 mH side, with the 2 mH side shorted, my trusty Heathkit >>>>> HD1250 >>>>> dip meter ... >>>> >>>> >>>> Hey, I've got the same one. Since childhood. >>>> >>>> >>>>> ... shows it resonating at 2.1 MHz with 4.9 nF in parallel, which >>>>> is 1.2 uH. ... >>>> >>>> >>>> Careful. You've got tons of winding capacitance in there which can >>>> seriously fool one into believing a much too small number. You have to >>>> measure the leakage inductance at frequency-of-interest, using an >>>> impedance analyzer or do it in a more pedestrian fashion via generator >>>> and meter. >>> >>> I sort of doubt that there are nanofarads of distributed capacitance in >>> that tiny transformer, though, because otherwise its open-circuit >>> resonance would be way too low. It works as a transformer up to well >>> over 1 MHz, so at 9 mH, the winding capacitance has to be down in the >>> lowish picofarads. >>> >> >> Not nanofarads but I bet the transformer is far from a 0.99986 coupling >> factor. >> >> [...] >> > > So what's wrong with the measured values? I can do it over with e.g. > 3300 and 5000 pF, and compare the two estimated inductances. That > should be fairly diagnostic, unless I'm missing something ultra-important. > > That sort of coupling coefficient is similar to large mains > transformers, for instance. >
Ok, but I'd still measure it with the secondary sorted and then from a generator, see what remains. But for a bridge it won't matter, things won't get much better than with such transformers. For a flyback it isn't useful since it isn't air-gapped. -- Regards, Joerg http://www.analogconsultants.com/
Phil Hobbs wrote:
> On 7/16/2013 8:54 PM, Joerg wrote: >> Phil Hobbs wrote: >>> On 7/16/2013 3:53 PM, Joerg wrote: >>>> Phil Hobbs wrote: >>>>> So, I'm goofing off playing with small switchers. (Well, not exactly >>>>> goofing off, but there are somewhat more pressing tasks waiting....) >>>>> >>>>> As I said in George's thread, "Opamp w/ Vsupply > 36V", I built a >>>>> small >>>>> half-bridge supply with positive and negative voltage doublers. >>>>> I'm not >>>>> that keen on it, because (a) it uses a fair number of parts for >>>>> what it >>>>> does, and (b) it has a nasty instability. >>>>> >>>> >>>> (a) ... yes. (b) ... why? What happens? Changing to another >>>> architecture >>>> while using the same kind of loop usually doesn't do much to improve >>>> stability. >>>> >>>> >>>>> With a capacitively-coupled half bridge, if you let the transformer >>>>> saturate, it instantly discharges the coupling cap, which about >>>>> doubles >>>>> the volt-seconds on the next half-cycle and guarantee that it will >>>>> keep >>>>> saturating until the FETs cook themselves. >>>>> >>>> >>>> Not sure what you mean here, but usually current mode control is the >>>> way >>>> to avoid asymmetrical runaway. >>> >>> The IRS2153D puts a square wave out of a half-bridge--no feedback, no >>> current limit, nada. If you put that into a transformer via a cap, all >>> is well until you saturate the transformer. >>> >> >> Ok, the IRS2153D is just a glorified gate driver with an oscillator in >> there. I'd use a real switcher controller chip, some are in the same >> price category. >> >> >>> Say that happens on the positive half-cycle. >>> At that moment, the voltage on the cap rapidly goes from V_DD/2 to V_DD. >>> At the next edge, the voltage across the transformer is suddenly not >>> V_DD/2 as expected, but V_DD. The transformer saturates in half the >>> time it took previously, and the voltage on the cap goes from V_DD to 0. >>> Then the cycle repeats. It's really obvious on a scope when this >>> happens, and it's far from pretty. >>> >> >> Did you use a really big cap? I've never had that happen. Usually >> ferrite saturates softly enough to just "nudge" the cap. > > 1 uF. I can probably post a scope photo tomorrow, if I have time--a > bunch of lawyering has just descended on my head. (Not that I mind very > much--expert witness work uses a different part of my brain and > generally pays somewhat better than design work.) >
That's one of the more serious problems we as a country have. Legal skirmishes usually have zero productivity from a national perspective but result in the fattest "payouts". It is the core problem why our health care system is a mess. Of course, that is never brought up by body politicus, for obvious reasons :-(
> <snip> >>>> John Larkin has recently used these tiny flyback transformers. Nothing >>>> wrong with hanging two in parallel on the primary and using the 2nd one >>>> with the secondary flipped around, for the -45V. >>>> >>>> Do you need this isolated? Else you could consider just inverting and >>>> boost. >>>> >>> >>> Doesn't have to be isolated, but it does need to be quiet, hence the >>> toroids. >>> >> >> That usually rules out flybacks. They spew a lot of noise. Then I'd use >> a half-bridge with CM control and series inductors on the output. > > Fortunately the half-bridge's worst-case condition is zero load, so it > isn't too hard to control. ...
They work ok with zero load if you can tolerate the voltage increase. That would be determined by the turns ratio. If it has to be 45.000V that's a different story. Then you'll have to let it go into a skipping mode.
> ... Of course the ungapped ferrite has a pretty > frightening tempco of mu (it goes down by half when you hit it with cold > spray), so some sort of current control is going to be required, for sure. >
Yes, needs current control but that's standard even in sub-Dollar chips. -- Regards, Joerg http://www.analogconsultants.com/
Klaus Kragelund wrote:
> On Tuesday, July 16, 2013 9:53:11 PM UTC+2, Joerg wrote: >> Phil Hobbs wrote: >>
[...]
>> >>> With a capacitively-coupled half bridge, if you let the >>> transformer saturate, it instantly discharges the coupling cap, >>> which about doubles the volt-seconds on the next half-cycle and >>> guarantee that it will keep saturating until the FETs cook >>> themselves. >> >> >> Not sure what you mean here, but usually current mode control is >> the way >> >> to avoid asymmetrical runaway. >> >> > > You need to be careful about that. Even if you have primary current > mode peak limit, then inequalities in the secondary diodes forward > drops can let the xformer go into staircasing, saturating the > xformer. >
If the current limit works properly it'll curb in time, it normally won't let it staircase into a danger zone. Of course, all this assumes regular ferrite where the core will not saturate super-hard. I am just wondering whether all that isn't overkill for generating two 45V rails at 20mA. That's just a couple of watts. A decent gate driver should almost be able to capacitively drive that without any FETs. -- Regards, Joerg http://www.analogconsultants.com/
George Herold wrote:
> On Tuesday, July 16, 2013 6:12:17 PM UTC-4, Phil Hobbs wrote: >> On 7/16/2013 3:53 PM, Joerg wrote: >> >>> Phil Hobbs wrote: > <snip original question> >>>> Any words of wisdom? >>> ISDN transformers don't have much air gap, and you need air gap >>> for a flyback. Plus ISDN is on the way out in many areas so if >>> this has to remain in production until the cows come home I >>> wouldn't. >> So I'm discovering. The actual amount of energy I can store in >> that toroid isn't very large, so to get any power out of it I have >> to run it pretty fast. With 2.2 mH of primary inductance, that >> takes quite a bit of voltage, which makes the whole flyback thing >> sort of moot. >> > > Sorry for the diverting question, but help me out here. (I find > magnet material a bit magical.) So I thought the energy in an > inductor was 1/2*L*i^2. > > But your and Joerg's comments seem to imply the energy is mostly in > the gap. >
Yes, it is. But the gap is just called air gap, usually it's some sort of filler material. High-end plastics, phenolic or FR4, and in very cheap "solutions" ... post-consumer cardboard. One of the issues with flybacks and gapped cores is that the gap doesn't know where it is supposed to end at its sides. It extends into the surroundings and that can result in egg in the face at the EMC lab.
> Now my very limited understanding of making a gap in an inductor was > that the gap sorta sets the inductance... the actual value isn't so > dependent on the magnetic material. And doesn't the gap reduce the > inductance? >
It does, unfortunately. As in "no free lunch" :-)
> I seem to be missing something fundamental. >
Maybe something like this helps: http://www.monolithicpower.com/DesignNoteDoc/AN017_r1.0.pdf http://www.ti.com/lit/ml/slup127/slup127.pdf [...] -- Regards, Joerg http://www.analogconsultants.com/
On Wednesday, July 17, 2013 4:06:25 PM UTC+2, Joerg wrote:
> Klaus Kragelund wrote: > > > On Tuesday, July 16, 2013 9:53:11 PM UTC+2, Joerg wrote: > > >> Phil Hobbs wrote: > > >> > > > > [...] > > > > >> > > >>> With a capacitively-coupled half bridge, if you let the > > >>> transformer saturate, it instantly discharges the coupling cap, > > >>> which about doubles the volt-seconds on the next half-cycle and > > >>> guarantee that it will keep saturating until the FETs cook > > >>> themselves. > > >> > > >> > > >> Not sure what you mean here, but usually current mode control is > > >> the way > > >> > > >> to avoid asymmetrical runaway. > > >> > > >> > > > > > > You need to be careful about that. Even if you have primary current > > > mode peak limit, then inequalities in the secondary diodes forward > > > drops can let the xformer go into staircasing, saturating the > > > xformer. > > > > > > > If the current limit works properly it'll curb in time, it normally > > won't let it staircase into a danger zone. Of course, all this assumes > > regular ferrite where the core will not saturate super-hard. > > > > I am just wondering whether all that isn't overkill for generating two > > 45V rails at 20mA. That's just a couple of watts. A decent gate driver > > should almost be able to capacitively drive that without any FETs. >
In this case I think the xformer RDC and MOSFET RDC would be so high that a solution with just a forward converter capacitive coupled primary would be fine. For the flyback it needs to gapped. Non-gapped flybacks is asking for trouble Regards Klaus
On 07/17/2013 10:00 AM, Joerg wrote:
> Phil Hobbs wrote: >> On 7/16/2013 8:54 PM, Joerg wrote: >>> Phil Hobbs wrote: >>>> On 7/16/2013 3:53 PM, Joerg wrote: >>>>> Phil Hobbs wrote: >>>>>> So, I'm goofing off playing with small switchers. (Well, not exactly >>>>>> goofing off, but there are somewhat more pressing tasks waiting....) >>>>>> >>>>>> As I said in George's thread, "Opamp w/ Vsupply > 36V", I built a >>>>>> small >>>>>> half-bridge supply with positive and negative voltage doublers. >>>>>> I'm not >>>>>> that keen on it, because (a) it uses a fair number of parts for >>>>>> what it >>>>>> does, and (b) it has a nasty instability. >>>>>> >>>>> >>>>> (a) ... yes. (b) ... why? What happens? Changing to another >>>>> architecture >>>>> while using the same kind of loop usually doesn't do much to improve >>>>> stability. >>>>> >>>>> >>>>>> With a capacitively-coupled half bridge, if you let the transformer >>>>>> saturate, it instantly discharges the coupling cap, which about >>>>>> doubles >>>>>> the volt-seconds on the next half-cycle and guarantee that it will >>>>>> keep >>>>>> saturating until the FETs cook themselves. >>>>>> >>>>> >>>>> Not sure what you mean here, but usually current mode control is the >>>>> way >>>>> to avoid asymmetrical runaway. >>>> >>>> The IRS2153D puts a square wave out of a half-bridge--no feedback, no >>>> current limit, nada. If you put that into a transformer via a cap, all >>>> is well until you saturate the transformer. >>>> >>> >>> Ok, the IRS2153D is just a glorified gate driver with an oscillator in >>> there. I'd use a real switcher controller chip, some are in the same >>> price category. >>> >>> >>>> Say that happens on the positive half-cycle. >>>> At that moment, the voltage on the cap rapidly goes from V_DD/2 to V_DD. >>>> At the next edge, the voltage across the transformer is suddenly not >>>> V_DD/2 as expected, but V_DD. The transformer saturates in half the >>>> time it took previously, and the voltage on the cap goes from V_DD to 0. >>>> Then the cycle repeats. It's really obvious on a scope when this >>>> happens, and it's far from pretty. >>>> >>> >>> Did you use a really big cap? I've never had that happen. Usually >>> ferrite saturates softly enough to just "nudge" the cap. >> >> 1 uF. I can probably post a scope photo tomorrow, if I have time--a >> bunch of lawyering has just descended on my head. (Not that I mind very >> much--expert witness work uses a different part of my brain and >> generally pays somewhat better than design work.) >> > > That's one of the more serious problems we as a country have. Legal > skirmishes usually have zero productivity from a national perspective > but result in the fattest "payouts". It is the core problem why our > health care system is a mess. Of course, that is never brought up by > body politicus, for obvious reasons :-(
You could say much the same thing about the army, but once the shooting starts, you're glad they're there. The case I'm working on today concerns an alleged misappropriation of trade secrets by a big semiconductor company. There's a lot of money at stake, so I'm pretty much in the noise. Designing stuff for start-ups is a bit different.
> > >> <snip> >>>>> John Larkin has recently used these tiny flyback transformers. Nothing >>>>> wrong with hanging two in parallel on the primary and using the 2nd one >>>>> with the secondary flipped around, for the -45V. >>>>> >>>>> Do you need this isolated? Else you could consider just inverting and >>>>> boost. >>>>> >>>> >>>> Doesn't have to be isolated, but it does need to be quiet, hence the >>>> toroids. >>>> >>> >>> That usually rules out flybacks. They spew a lot of noise. Then I'd use >>> a half-bridge with CM control and series inductors on the output. >> >> Fortunately the half-bridge's worst-case condition is zero load, so it >> isn't too hard to control. ... > > > They work ok with zero load if you can tolerate the voltage increase. > That would be determined by the turns ratio. If it has to be 45.000V > that's a different story. Then you'll have to let it go into a skipping > mode. > > >> ... Of course the ungapped ferrite has a pretty >> frightening tempco of mu (it goes down by half when you hit it with cold >> spray), so some sort of current control is going to be required, for sure. >> > > Yes, needs current control but that's standard even in sub-Dollar chips.
I may just make a boost with a two-winding toroid, and return the other end of the second winding to the raw -15V supply. (A lot of the Murata toroids are actually dual-winding, but they expect you to wire them in parallel to get the current handling capacity.) There are some PoE things that look like they could usefully be run backwards, but the coupling coefficients are low enough that they must have gaps. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
On 07/17/2013 09:42 AM, George Herold wrote:
> On Tuesday, July 16, 2013 6:12:17 PM UTC-4, Phil Hobbs wrote: >> On 7/16/2013 3:53 PM, Joerg wrote: >> >>> Phil Hobbs wrote: > <snip original question> >>>> Any words of wisdom? >> >>>> >> >>> >> >>> ISDN transformers don't have much air gap, and you need air gap >>> for a flyback. Plus ISDN is on the way out in many areas so if >>> this has to remain in production until the cows come home I >>> wouldn't. >> >> So I'm discovering. The actual amount of energy I can store in >> that toroid isn't very large, so to get any power out of it I have >> to run it pretty fast. With 2.2 mH of primary inductance, that >> takes quite a bit of voltage, which makes the whole flyback thing >> sort of moot. >> > > Sorry for the diverting question, but help me out here. (I find > magnet material a bit magical.) So I thought the energy in an > inductor was 1/2*L*i^2. > > But your and Joerg's comments seem to imply the energy is mostly in > the gap. > > Now my very limited understanding of making a gap in an inductor was > that the gap sorta sets the inductance... the actual value isn't so > dependent on the magnetic material. And doesn't the gap reduce the > inductance? > > I seem to be missing something fundamental. > > Thanks, George H.
Yes, the energy is mostly in the gap, and yes, the gap reduces the inductance. If you have a gap amounting to 1% of the average magnetic path length, you have an effective mu of 100. The perpendicular component of B is continuous across the air/core interface, but perpendicular H jumps up by a factor of the mu of the core, i.e. about 2000 or so. The magnetic energy density is proportional to B*H, so the energy stored in the gap is 1% x 2000 = 20 times the energy stored in the core. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
On 2013-07-17 15:42, George Herold wrote:
> > Sorry for the diverting question, but help me out here. (I find > magnet material a bit magical.) So I thought the energy in an > inductor was 1/2*L*i^2. > > But your and Joerg's comments seem to imply the energy is mostly in > the gap. > > Now my very limited understanding of making a gap in an inductor was > that the gap sorta sets the inductance... the actual value isn't so > dependent on the magnetic material. And doesn't the gap reduce the > inductance? > > I seem to be missing something fundamental. > > Thanks, George H.
Hi George, The magnetic energy in a given volume is E=1/2 VB^2 / (u_0 u_r), so for a given B, the energy in a given volume of ferrite is u_r times less than in the same volume of air. For a ferrite magnetic circuit with an air gap, the total magnetic energy works out as E=1/2 B^2 (A l_f/(u_0 u_r) + A l_a/u0), where A is the cross section area of the magnetic circuit, and l_f and l_a are the path length in ferrite and air, respectively. (I neglect fringing. That's good enough, usually.) You can work this out from just two of Maxwell's four laws. Cheers, Jeroen Belleman
On Wednesday, July 17, 2013 10:14:40 AM UTC-4, Joerg wrote:
> George Herold wrote: >=20 > > On Tuesday, July 16, 2013 6:12:17 PM UTC-4, Phil Hobbs wrote: >=20 > >> On 7/16/2013 3:53 PM, Joerg wrote: >=20 > >>=20 >=20 > >>> Phil Hobbs wrote: >=20 > > <snip original question> >=20 > >>>> Any words of wisdom? >=20 > >>> ISDN transformers don't have much air gap, and you need air gap >=20 > >>> for a flyback. Plus ISDN is on the way out in many areas so if >=20 > >>> this has to remain in production until the cows come home I >=20 > >>> wouldn't. >=20 > >> So I'm discovering. The actual amount of energy I can store in >=20 > >> that toroid isn't very large, so to get any power out of it I have >=20 > >> to run it pretty fast. With 2.2 mH of primary inductance, that >=20 > >> takes quite a bit of voltage, which makes the whole flyback thing >=20 > >> sort of moot. >=20 > >>=20 >=20 > >=20 >=20 > > Sorry for the diverting question, but help me out here. (I find >=20 > > magnet material a bit magical.) So I thought the energy in an >=20 > > inductor was 1/2*L*i^2. >=20 > >=20 >=20 > > But your and Joerg's comments seem to imply the energy is mostly in >=20 > > the gap. >=20 > >=20 >=20 >=20 >=20 > Yes, it is. But the gap is just called air gap, usually it's some sort >=20 > of filler material. High-end plastics, phenolic or FR4, and in very >=20 > cheap "solutions" ... post-consumer cardboard. >=20 >=20 >=20 > One of the issues with flybacks and gapped cores is that the gap doesn't >=20 > know where it is supposed to end at its sides. It extends into the >=20 > surroundings and that can result in egg in the face at the EMC lab. >=20 >=20 >=20 >=20 >=20 > > Now my very limited understanding of making a gap in an inductor was >=20 > > that the gap sorta sets the inductance... the actual value isn't so >=20 > > dependent on the magnetic material. And doesn't the gap reduce the >=20 > > inductance? >=20 > >=20 >=20 >=20 >=20 > It does, unfortunately. As in "no free lunch" :-) >=20 >=20 >=20 >=20 >=20 > > I seem to be missing something fundamental. >=20 > >=20 >=20 >=20 >=20 > Maybe something like this helps: >=20 >=20 >=20 > http://www.monolithicpower.com/DesignNoteDoc/AN017_r1.0.pdf >=20 > http://www.ti.com/lit/ml/slup127/slup127.pdf
Wow, great! (lunch time reading material.) Thanks Joerg. =20 I think I see my problem. Without the gap the B field in the material is m= uch higher (for a given current) and it's that much closer to saturation. (= Maybe a lot closer!) So I guess I can believe that for a gapped inductor y= ou can get more energy storage... you just have to run it at a higher curre= nt. (I'll have to try putting in some numbers.) Say are there any good books about transformers/ inductors/ magnetic materi= als? The subject seems to go from the trivial freshman physics transformer. To = the "full hair ball" real world situation, with nothing in between. George H.
>=20 >=20 >=20 > [...] >=20 >=20 >=20 > --=20 >=20 > Regards, Joerg >=20 >=20 >=20 > http://www.analogconsultants.com/
On Wednesday, July 17, 2013 11:23:57 AM UTC-4, Phil Hobbs wrote:
> On 07/17/2013 09:42 AM, George Herold wrote: > > > On Tuesday, July 16, 2013 6:12:17 PM UTC-4, Phil Hobbs wrote: > > >> On 7/16/2013 3:53 PM, Joerg wrote: > > >> > > >>> Phil Hobbs wrote: > > > <snip original question> > > >>>> Any words of wisdom? > > >> > > >>>> > > >> > > >>> > > >> > > >>> ISDN transformers don't have much air gap, and you need air gap > > >>> for a flyback. Plus ISDN is on the way out in many areas so if > > >>> this has to remain in production until the cows come home I > > >>> wouldn't. > > >> > > >> So I'm discovering. The actual amount of energy I can store in > > >> that toroid isn't very large, so to get any power out of it I have > > >> to run it pretty fast. With 2.2 mH of primary inductance, that > > >> takes quite a bit of voltage, which makes the whole flyback thing > > >> sort of moot. > > >> > > > > > > Sorry for the diverting question, but help me out here. (I find > > > magnet material a bit magical.) So I thought the energy in an > > > inductor was 1/2*L*i^2. > > > > > > But your and Joerg's comments seem to imply the energy is mostly in > > > the gap. > > > > > > Now my very limited understanding of making a gap in an inductor was > > > that the gap sorta sets the inductance... the actual value isn't so > > > dependent on the magnetic material. And doesn't the gap reduce the > > > inductance? > > > > > > I seem to be missing something fundamental. > > > > > > Thanks, George H. > > > > Yes, the energy is mostly in the gap, and yes, the gap reduces the > > inductance. If you have a gap amounting to 1% of the average magnetic > > path length, you have an effective mu of 100. The perpendicular > > component of B is continuous across the air/core interface, but > > perpendicular H jumps up by a factor of the mu of the core, i.e. about > > 2000 or so. > > > > The magnetic energy density is proportional to B*H, so the energy stored > > in the gap is 1% x 2000 = 20 times the energy stored in the core. >
Thanks Phil, (I'll have to go work it out for myself now.) I just remembered the one place that I finally 'got' air gap electro-magnetics was in the second volume of the Feynman lectures. George H.
> > Cheers > > > > Phil Hobbs > > > > > > -- > > Dr Philip C D Hobbs > > Principal Consultant > > ElectroOptical Innovations LLC > > Optics, Electro-optics, Photonics, Analog Electronics > > > > 160 North State Road #203 > > Briarcliff Manor NY 10510 > > > > hobbs at electrooptical dot net > > http://electrooptical.net