Transformers, inductors, chokes

 

(SIMPLIFIED CALCULATION)

       1. MAGNETIC MATERIALS AND THEIR PROPERTIES
   Of all the variety of magnetic materials, we will focus on soft magnetic ferrites, since they are capable of operating in a wide range of both frequencies (from hundreds of Hz to hundreds of kHz) and temperatures (from -60 ° С to + 155 ° С no more).
It should be noted that at frequencies below 10 kHz, the dimensions of the electromagnetic elements turn out to be overestimated, which determines the limitation of the application.     
Ferrites have high resistivity, hence negligible eddy current losses. However, the losses due to magnetization reversal associated with the "viscosity" of the material are significant and reach 3 ... 5%. Therefore, the efficiency of transformers is usually within 0.95. .0.97.
     Of the latest developments, the most promising are ferrites of grades 2500НМС1 and 2500НМС2, which, unlike other brands, have a negative temperature dependence of losses. The use of ferrite grade М2500НМС2 allows to reduce weight by 8% and dimensions by 15%, and while maintaining the previous standard sizes - increase power by 20%.
Ferrites 2500НМС1 and 3000НМС have low values of losses in strong magnetic fields in the frequency range adopted in television technology, increased magnetic induction at high ambient temperatures and during magnetization. Ferrite cores are used, as a rule, in relatively weak magnetic fields with an intensity of no more than 10 A / cm. In the region of medium fields (up to Hm inclusive), with an increase in induction, the permeability also grows, which causes a slow increase in losses. When passing to the region of strong fields, the permeability begins to decrease and no longer compensates for the increase in induction, as a result of which the losses increase sharply. It follows from this that the value of W is the maximum permissible induction for any ferrite.
Residual induction Bg in strong fields (over W) can be 0.3 ... 0.6 saturation induction Bs.
     Saturation induction, operating frequency range and ambient temperature for some grades of ferrite are given in table. 1.
The Curie point of the selected ferrite must exceed the Maximum operating temperature by at least 30 ... 40 0 С. Induction W is the maximum allowable, because the transition to the region of stronger fields leads to a sharp increase in losses. In fig. 1 shows the dependence of magnetic inductions for material 2500NMS on tension and temperature. A similar dependence for material 1500NMZ is shown in Fig. 2
     The dependence of the magnetic permeability on the strength of the magnetic field caused by DC magnetization for different materials is shown in Fig. 3 [1].
     The effect of the air gap on the magnetic permeability is shown in Fig. 4.
     The magnetic field strength of a DC bias transformer is determined by:
     Н = Iо * n / Lm, A / cm (1)
     where Io is the direct current strength, A;
     n is the number of turns;
    LmIs the effective value of the length of the mean line of force, see.                        материалы для трансформаторов и дросселей                                               

                
                                                                                                                                                                                           

          2. CORE SIZES AND THEIR CHARACTERISTICS
Of all the variety, we will focus on three main types: ring, armored and W-shaped, which are shown in Fig. 5 ... 7.
The implementation of miniaturization of secondary power supplies (IVEP) goes along the path of increasing the conversion frequency. This makes it possible to significantly reduce the dimensions of wired products - transformers and chokes. For this purpose, ring and armor cores are best suited. Ring cores have the advantage of being have a larger winding space. For transformers with energy storage (for example, ONPSh, see below) and for chokes with magnetized bias (PHI ... PHIII), an armored core is preferable due to the possibility of creating a non-magnetic gap.
The armored core is a good magnetic shield for the winding inside it, since the maximum value of the induction W is achieved only in the central section, and in the rest of the core it is small. In this case, the magnetic properties of ferrite (primarily magnetic permeability) are quite high, since the core has a large volume reserve of the magnetic material. Due to this, the core has a smoother transition from the linear region to the saturation region. Sometimes the gap is not made over the entire section of the core, which makes it possible to improve the properties of ferrite in a wider range of loads. In addition, cores of this type can be conveniently attached to the radiator.
A ring core can generate less electromagnetic radiation than an armored core, but due to asymmetric winding, it may need to be shielded. 
When performing transformers and chokes on circular magnetic circuits, the greatest magnetic permeability is ensured, interference is reduced and electromagnetic properties are improved, because the magnetic field is contained in the space bounded by the windings. As the conversion frequency increases, so does the advantage of toroidal cores. With the same ampere turns, the induction in the ring magnetic circuits is greater than in the armored ones, which makes it possible to reduce the weight and dimensions of the transformer.
W-shaped cores are also inferior to ring ones, since the latter have better heat-dissipating properties due to the larger cooling surface of the windings.

Armored magnetic conductors are used in cases where it is required:

  • high quality factor in a given band;
  • the ability to adjust the inductance;
  • ensuring a low coefficient of introduced nonlinear distortion;
  • high resistance to mechanical and climatic influences;
  • no stray fields.

The main geometric parameters of some cores of magnetic circuits are given in table. 2 [2], where:
Sm is the effective value of the cross-sectional area of the magnetic conductor;
So is the area of the magnetic conductor window;
Vm = Lm * Sm - effective volume of the magnetic conductor.

  3. INDUCTIVITY
The values of the initial inductance Al for some standard sizes of magnetic circuits are given in table. 3.
The values of the initial inductance Al and the effective magnetic permeability, depending on the size of the gap for the W-shaped cores are given in table. 4.  
Coil inductance is L = AL* n2 (2),
whence n = (L / AL)-2  (3).
Calculation example 1:
Core Ml 500НМ К10x6x3
n = 300
L =?
Coil inductance according to the formula (2)
L = AL* n2= 440 * ZOO2 = 40 • 106 nH = 40 mg
Calculation example 2:
Core М2000НМ Ш7х7
n = 10
L =?
L = 1840 * 102 = 184*103nH = 184 μH.
For any other magnetic circuit ^ not listed in the table, the inductance of a coil with a ferromagnetic core, in which almost all the flux is closed through the core, can be calculated using the formula:
  (4),
whence n = 8920 * where = 4*3,14*10-9 H / cm - magnetic permeability of vacuum;  Is the effective value of the initial magnetic permeability.
Note At weak alternating magnetic fields (Vm <0.05 T) and no DC bias, effective magnetic permeability equal to the initial, which is given in the reference books for each standard size of the core (for circular magnetic circuits it is included in the ferrite grade) and is measured at a frequency of no more than 10 kHz with a field strength H of no more than 0.4 A / cm.
From the expression it follows that the inductance of the coil for the same number of turns depends on the ratio Sm / Lm, and since with an increase in the core, both Sm and Lm, their ratio remains approximately constant. Therefore, with the same number of turns, the inductances of the coils wound on small and large rings with the same magnetic permeability are approximately the same. A large ring is advantageous when a high Q-factor of the coil is needed.
The cutoff frequency of the magnetic core material, starting from which the sectioning of the windings is necessary:                             
frp = 1000 /, MHz.
Calculation example 3:
Core Ml 500НМ К10x6x3                                                                                                                                                             
n = 300                                                                                                                                                                                                    
L =? '
Coil inductance according to the formula (4)
L = 1.26 * 10-8 *1500 *3002* 0.06 / 2.45 = 0.04 H = 40 mH.
Calculation example 4:
Core М2000НМ Ш7 × 7
n = 10
L =?
L = 1.26 * 10-8 *1490 *102 0.62 / 6.29 = 184 • 10-6H = 184 μH.
As you can see from examples 1,3 and 2,4, the results are the same.
With an increase in the amplitude of the alternating current, the effective magnetic permeability , and consequently, the inductance of the coil increases by about 1.5 ... 2 times (depending on the ferrite grade and the magnitude of the current). With an increase in the constant component of the current, , and hence the inductance of the coil, fall. The dependence of the dynamic magnetic permeability on bias is shown in Fig. 8.
The introduction of an air gap is equivalent to the parallel connection of the inductance due to the magnetic flux in the magi-conductor (with a nonlinear Weber-ampere characteristic - Fig. 9, curve 1), and the flow in the gap (with a linear characteristic - Fig. 9, curve 2). As shown in Fig. 9, curve 3 is the most effective approximation of the L (i) dependence to linear when operating with a varying bias current.
where- the size of the gap, see. In amateur conditions, this is achieved by breaking the ring into two parts, followed by gluing them.
Most often, inductors should be adjustable. Armored cores are most suitable for this purpose. The initial inductance depending on the size of the gap, the types of trimming cores and the overlap coefficient (range of inductance variation) for cores made of 1500NM material are given in Table 5.
To obtain time-stable parameters of inductances, the cores are subjected to aging (exposure to a temperature of 10 ... 15 ° C above the upper operating temperature for 48 hours), after which the assembled coils are subjected to a cyclic effect of increased (+ 85 ° C) and reduced (-60 ° C) ) temperatures - at least five cycles.         

           4. TRANSFORMERS. OVERALL POWER OF THE MAGNETIC CONDUCTOR    

The core of the transformer magnetic circuit is selected based on the required overall power:where Pi = Ui * Ii is the power of the i-th winding. As you can see, the overall power of the transformer is equal to the half-sum of the powers of all windings (both primary and secondary). Usually it is taken to be equal to the sum of the capacities of all loads. Since the choke has only one winding, the overall power of the choke is twice the power of the transformer, i.e. the mass of the choke is half the mass of the transformer with the same electromagnetic power. Suppose we have a simple transformer with one primary and one secondary winding. We use the well-known formula for the EMF of induction: U = 4.44 * f Bm* Sm * n * 10-4 , B (8) and the expression for the winding current:

 I = jSMKM102/ 2n, A (9),

 

where Km = Sn n / So = (0.1 ... 0.35) - coefficient of filling the window with copper;                                                                                  Sn is the cross-sectional area of the wire, mm2; n is the number of turns. Multiplying U by I, we obtain an expression for the overall power: Рgab = UI = 4.44f BmSmSo njKM10-2 / 2n = 2.2SMSofBmjKM10-2, Wt (10) Since the range of induction change with symmetric magnetization reversal is 2W, expression (10) can be rewritten as follows: Pgab = SmSo f jKm10-2 , W (11) From the formula it follows that, other things being equal, the higher Km, the higher the utilization factor of this magnetic circuit in terms of power. For this purpose, a rectangular wire is sometimes used, and the coils are frameless, which makes it possible to bring Km to 0.7 against the usual 0.5. In addition, flat wires have less surface effect (current displacement effect). To select a magnetic core, it is convenient to use the SoSm product, which characterizes the electromagnetic power:  (12), where - the range of changes in the magnetic induction in the core during the duration of the pulse tn. T (Fig. 10); = 2Bm <l,2Bs — для двухтактного преобразователя;

  = (0.5 ... 0.75) W - for magnetic circuits of one-cycle voltage converters (SPD) and chokes with a gap;           

= Bm-Br = 0.25Bm - for chokes of LC filters without a gap and without a reverse connected diode;

 Km = 0.15 for an annular magnetic circuit;

 Km = 0.25 ... 0.35 for the rest of the magnetic cores (Km for chokes is twice as high, since the entire window is occupied by one winding);     

 = 0.095 ... 0.97-efficiency of the transformer.     

 Single-ended converters with "direct" diode switching can work with approaching 2Vm, if you introduce forced magnetization reversal of the magnetic circuit. From formulas (11) and (12) it follows that from the same core in a push-pull converter it is possible to remove power 3 ... 4 times more than in a single-cycle, because, firstly, the value and secondly, the introduction of a gap due to a decrease in magnetic permeability requires a larger number of turns of the windings in the same winding space. Therefore, single-ended converters with "reverse" diode switching are used in relatively simple and low-power stabilized IWEP (up to 100 W), when good filtering of the voltage ripple of the primary source is required, and the load is of varying nature.                                                                                                                                                      Single-ended converters with "direct" diode switching, although they allow operation with a large , are used at a load power, as a rule, no more than 350 W. A two-stroke converter with an output of the midpoint of the primary winding of the transformer (Roer circuit and the like) is used up to 300 W. A push-pull half-bridge circuit is usually used up to 700 W, over 700 W - a push-pull bridge. Recommended value taking into account the change in the magnetization reversal loop in the single-cycle mode is given in table. 6. Cross-sectional area of the wire Sn = Ie / jN mm2 (13) Along with this, Sn = 3.14d2/ 4 (14) Solving equations 13 and 14 with respect to d, we obtain d = 1.13 * (Ie / jN)-2 (15) where Ie is the effective value of the current, A; j is the current density, A / mm2; N is the number of parallel-connected wires; d - wire diameter, mm. The current density j in the transformer windings is selected in accordance with table. 7 or 8. To simplify the choice of a ring magnetic conductor made of M2000NM material, it is convenient to use the approximate data given in table. 9. One of the main requirements for the electrical parameters of transformers is to reduce to a certain level the leakage inductance Ls, which determines the coefficient of magnetic coupling between the windings and, accordingly, the transfer coefficient and efficiency of the transformer. Kmc = (L1 * Ls) / L1 .Ensuring a good magnetic coupling between the primary and secondary windings of transformers at low levels of output voltages is difficult due to the significant difference in the number of winding turns. The leakage inductance can be reduced by dividing the primary winding into two parts, one of which is wound in the lower layer, and the second in the upper, after the secondary. Even better results can be obtained if the primary and secondary windings are wound together, for which the primary winding is divided into several windings with the number of turns equal to the number of turns of the secondary winding, which are then connected in series. shorting the windings to the core, the sharp edges of the magnetic circuit should be blunt. To increase the flux linkage, the windings should be placed in one row, close to each other. The windings, between which it is necessary to obtain good flux linkage, must be separated from each other by the minimum necessary insulation and the turns of one must be located above the turns of the other in the same section of the winding. If the windings differ significantly in the number of turns, it is advisable to wind the small winding with two or more parallel wires. The primary winding is divided into three sections, wound by a frameless method and insulated with fluoroplastic tape. The secondary winding consists of four volumetric two-turn sections, stamped from sheet copper with a thickness of 0.5 mm in the form of rings, cut and soldered to each other and also insulated with fluoroplastic tape. The sections of the primary winding are placed between the sections of the secondary, and ring electrostatic screens made of thin copper foil are inserted between them. The core of the SB48 transformer is sandwiched between two radiators. The use of this method of making the windings made it possible to obtain a leakage inductance that is only 5% from the inductance of the primary winding.

 A.Petrov Mogilev

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