4.6 Design Example for a Discontinuous-Mode
4.6.3 Using Powdered Permalloy (MPP)
These toroidal cores are widely used and made by Magnetics Inc. (data in catalog MPP303S) and by Arnold Co. (data in catalog PC104G).
After Pressman The termtransformerin the phrase flyback trans- formeris a misnomer and is very misleading. For true transformer action to take place both primary and secondaries must conduct current at the same time. We are all aware that a true transformer conserves the primary to sec- ondary voltage ratio (irrespective of current). In the flyback case the so-called transformer conserves the primary to secondary ampere-turns ratio (irrespec- tive of voltage). This means it is really a “choke”—an inductor with a DC component of current and additional windings. I find it much easier and less confusing to design my flyback “transformers” from this perspective. The reader may also find it helpful to use this approach because the inductance
becomes the dependant variable and can be easily adjusted to get the desired results. Chapter 7 deals with the design in this way.
You will see from the following that although he does not mention it, Press- man is leading you in the direction of choke design.∼K.B.
The problem in designing a core of desired inductance at a specified maximum DC current bias is to select a core geometry and material permeability, such that the core does not saturate at the maximum ampere-turns to which it is subjected. There are a limited number of core geometries, each available in permeabilities ranging from 14 to 550. Selection procedures are described in the catalogs mentioned above, but the following has been found more direct and useful.
In the Magnetics Inc. catalog, one full page (Figure 4.4) is devoted to each size toroid, and for each size, itsAlvalue (inductance in milli- henries per 1000 turns) is given for each discrete permeability. Figure 4.5, also from the Magnetics Inc. catalog, gives the falloff in permeabil- ity (or Alvalue) for increasing magnetizing force in oersteds for core materials of the various available permeabilities. (Recall the oersted–
ampere-turns relation in Eq. 2.6.)
A core geometry and permeability can be selected so that at the maximum DC current and the selected number of turns, the Aland hence inductance has fallen off by any desired percentage given in Figure 4.5. Then at zero DC current, the inductance will be greater by that percentage. Such inductors or chokes are referred to as “swing- ing chokes” and in many applications are desirable. For example, if an inductor is permitted to swing a great deal, in an output filter, it can tolerate a very low minimum DC current before it goes discon- tinuous (Section 1.3.6). But this greatly complicates the feedback-loop stability design and, most often, the inductor in an output filter or transformer in a flyback will not be permitted to “swing” or vary very much between its zero and maximum current value.
Referring to Figure 4.4, it is seen that a core of this specific size is available in permeabilities ranging from 14 to 550. Cores with perme- ability above 125 have large values ofAland hence require fewer turns for a specified inductance at zero DC current bias. But in Figure 4.5 it is seen that the higher-permeability cores saturate at increasingly lower ampere-turns of bias. Hence in power supply usage, where DC current biases are rarely under 1 A, cores of permeability greater than 125 are rarely used, and an inductance swing or change of 10% from zero to the maximum specified current is most often acceptable.
In Figure 4.5, it is seen that for a permeability dropoff or swing of 10%, core materials of permeabilities 14, 26, 60, and 125 can sustain maximum magnetizing forces of only 170, 95, 39, and 19 Oe, respec- tively. These maximum magnetizing forces in oersteds can be trans- lated into maximum ampere-turns by Eq. 2.6 (H=0.4π(NI)/lm), in
FIGURE4.4 A typical MPP core. With its large distributed air gap, it can tolerate a large DC current bias without saturating. It is available in a large range of different geometries. (Courtesy Magnetics Inc.)
FIGURE4.5 Falloff in permeability ofA1for MPP cores of various permeabilities versus DC magnetizing force in oersteds. (Courtesy Magnetics Inc.)
whichlmis the magnetic path length in centimeters, given in Figure 4.3 for this particular core geometry as 6.35 cm.
From these maximum numbers of ampere-turns (NI), beyond which inductance falls off more than 10%, the maximum number of turns (N) is calculated for any peak current. From N, the maximum inductance possible for any core at the specified peak current is cal- culated asLmax= 0.9A1(Nmax/1000)2.
Tables 4.1, 4.2, and 4.3 showNmaxandLmaxfor three often-used core geometries in permeabilities of 14, 26, 60, and 125 at peak currents of 1, 2, 3, 5, 10, 20, and 50 amperes. These tables permit core geometry and permeability selection at a glance without iterative calculations.
Table 4.1 is used in the following manner. Assume that this particu- lar core has the acceptable geometry. The table is entered horizontally to the first peak current greater than specified value. At that peak current, move down vertically until the first inductanceLmaxgreater than the desired value is reached. The core at that point is the only one which can yield the desired inductance with only a 10% swing. The number of turnsNd on that core for a desired inductanceLd within 5% is given by
Nd =1000 Ld
0.95Al
where Alis the value in column 3 in Table 4.1. If, moving vertically, no core can be found whose maximum inductance is greater than the desired value, the core with the next larger geometry (greater OD or greater height) must be used.
Switching Power Supply Design
NIMaximum Maximum permissible Magnetics Al, mH Hfor 10% ampere-turns
Inc. core Perme- per 1000 falloff in corresponding Maximum permissible turns and inductance at those turns number ability turns inductance toH for a 10% inductance falloff at indicated peak currents
Nmax/Lmax
Core μ Al H NI 1A 2A 3A 5A 10A 20A 50A Ip
55930 125 157 19 96 96 48 32 19 10 5 2 Nmax
1,382 339 145 56 15 3.5 0.6 Lmax
55894 60 75 39 197 197 99 66 39 20 10 4 Nmax
2,620 662 294 103 27 7 1 Lmax
55932 26 32 95 480 480 240 160 96 48 24 10 Nmax
6,635 1,659 737 265 66 17 3 Lmax
55933 14 18 170 859 859 430 286 172 86 43 17 Nmax
11,954 2,995 1,325 479 120 30 5 Lmax
Note:Magnetics Inc. MPP cores. All cores have outer diameter (OD)=1.060 in, inner diameter (ID)=0.58 in, height=0.44 in,lm=6.35 cm.
All inductances in microhenries.
TABLE4.1 Maximum number of turns yielding maximum inductance for various peak currentsIpat maximum inductance falloff of 10% from zero current