Toroids Design Toroids Considerations - Ferronics

1 13 Ferrite Toroids provide an often convenient and veryeffective shape for many wide band, pulse and powertransformers and inductors. The continuous magneticpath yields the highest effective permeability and lowestflux leakage of any Considerations :The inductance may be calculated from(the units are in CGS system which is used throughoutthis catalog). Here le and Ae are the effective magneticpath length and cross sectional area of the core, is theeffective permeability of the material, and N is thenumber of turns. This formula may be used for any shapeunder all conditions provided the correct value of isused and stray reactances are given proper consider-ation.

2 In a toroidal core, this may be expressed as:where OD, ID and H are the dimensions in inches. Forlow level conditions at comparatively low frequencies theformula may be simplified by using the Inductance Index,AL, listed in this catalog. Then;The other value most frequently needed is peak fluxdensity, which may be calculated fromHere E is the RMS voltage, is a constant dependingon the wave shape (use 4 when E is symmetrical squarewave and 1 where E is a unipolar pulse), and f is thefrequency in LEVEL INDUCTORS:This section considers those applications wherenonlinearity and losses due to hysteresis are this means flux densities below a few hundredGauss.

3 The first material choice is the one having boththe highest permeability and lowest loss factor, tan / ,at the operating frequency. Considering the spaceavailable, select a core from the table and, using itsinductance index, AL, calculate the number of turnsrequired to give the desired inductance. Now select thelargest practical wire size that will fit on the core. This issomewhat difficult for a toroid, but generally the total wirecross section in the winding can be 30-60% of thewindow opening. If there are Q or loss requirementscalculate the resistance of the winding, taking intoconsideration the skin effect if the frequency is high, andadd it to the equivalent series resistance contributed bythe core losses.

4 Equation 5 shows the relationshipbetween loss factor, Q and the calculated Q is inadequate you must reduce thetotal series resistance by selecting a larger core that willallow fewer turns of larger wire, select a less lossymaterial, or use Litz wire at high frequencies to minimizethe skin effect. If losses are critical it is important to remember thathysteresis losses have been assumed to be a few 10 s of Gauss these losses are measurableand increase as approximately the power of fluxdensity. Also, remember that ferrites like other magneticmaterials show variation in inductance from part to part,with temperature and with magnetizing force.

5 Unlikepowdered metals which have air gaps between theparticles a ferrite toroid is a continuous magnetic materialwith variability effects undiluted by air gaps. This meansthat tight tolerances such as required for wave filters arenot attainable in a toroid, but will generally require agapped structure such as an E core, pot core, or INDUCTORS:In this section we consider inductors where the Design islimited by saturation or heating due to core or windinglosses. Although there is no systematic connectionbetween permeability and losses, below about 1 MHzrelatively high permeability manganese-zinc ferrites havethe most desirable combination of high saturation fluxdensity and low hysteresis losses.

6 The first step is toselect one of those materials having the desired proper-ties (usually B material) and select a core based onspace limitations. Then select a suitable operating fluxdensity. As a general rule, at room temperature materialsmay be operated to the knee of the BH loop when thefrequency is 20 kHz or less. At higher frequencieshysteresis losses produce enough heat to require thatthe flux density be decreased. As a first approximation,the product of flux density and frequency can be heldconstant above 20 kHz.

7 Knowing the voltage, frequency,flux density and area of the chosen core the minimumnumber of turns may be calculated from equation 4. Theinductance can then be estimated from equation 3 orcalculated more exactly from equations 1 or 2 by usingDesignConsiderationsToroidsToroids1 234514the appropriate value of permeability under theseoperating conditions. If this inductance is less than thedesired value, the number of turns can be adjustedupward provided there is sufficient space for the the inductance is too great it will be necessary tochoose a larger core whose cross sectional area isgreater but whose ratio of Ae/le is less, or a material withlower permeability.

8 For inductors operating above 1 MHz the materialchoice becomes more difficult since other requirementssuch as return loss may be more important. The materialchoice and Design procedure will depend on whichfactors predominate in your particular Design . Inductorshaving dc current superimposed on the ac excitationmust be given special treatment. The magnetizing forcemay be calculated using equation 6:With this information it is possible to estimate from the BHcurves how significant will be the effect of the dc dc magnetizing forces less the coercive forcewill have only a small effect on permeability, moderatevalues will depress the permeability, and magnetizingforces approaching the knee of the BH loop will consider-ably reduce the permeability and severely limit the peakflux density available for ac excitation.

9 In these cases,unless a higher inductance can be used it will be neces-sary to go to a core with a considerably longer magneticpath length or to provide an air gap such as by slottingthe core. In many power applications thermal considerationscontrol the Design . One rule of thumb that may be usefulfor first approximations is that core losses of 100 to 600mW/cm3 produce an approximate 40 C temperature exact value depends on inductor geometry andthermodynamic Considerations beyond the scope of thisguide. You must also consider the power dissipated in thewinding and its contribution to inductor heating.

10 Heatsinking or coolants may be used to remove this heat, butthe thermal conductivity of ferrite is relatively low, so theinterior core temperature will be higher. Should a largetemperature gradient develop, the core may crack fromthermal stresses. Also, where considerable temperatureexcursions occur due either to self heating or ambienttemperatures, the effect of these changes must also beconsidered with respect to changes in saturation fluxdensity and LEVEL TRANSFORMERS:The Design procedure here is essentially the same as forlow level inductors except, of course, that the windingspace must be shared between the primary and second-ary windings.