EPCOS_磁环选型计算公式_GeneralDefinitions

Data SheetData Sheet Date: September 2006  EPCOS AG 2006. Reproduction, publication and dissemination of this data sheet and the information contained therein without EPCOS’ prior express consent is prohibited. Ferrites and accessories General – Definitions 1 Hysteresis The special feature of ferromagnetic and ferrimagnetic materials is that spontaneous magnetization sets in below a material-specific temperature (Curie point). The elementary atomic magnets are then aligned in parallel within macroscopic regions. These so-called Weiss’ domains are normally oriented so that no magnetic effect is perceptible. But it is different when a ferromagnetic body is placed in a magnetic field and the flux density B as a function of the magnetic field strength H is measured with the aid of a test coil. Proceeding from H = 0 and B = 0, the so-called initial magneti- zation curve is first obtained. At low levels of field strength, those domains that are favorably oriented to the magnetic field grow at the expense of those that are not. This produces what are called wall displacements. At higher field strength, whole domains overturn magnetically – this is the steepest part of the curve – and finally the magnetic moments are moved out of the preferred states given by the crystal lattice into the direction of the field until saturation is obtained, i.e. until all elementary magnets in the material are in the direction of the field. If H is now reduced again, the B curve is completely different. The relationship shown in the hysteresis loop (figure 1) is obtained. 1.1 Hysteresis loop Magnetic field strength Figure 1 Magnetization curve (schematic) Figure 2 Hysteresis loops for different excitations and materials Initial magnetization curve Initial magnetization curves Commutation curve H I N⋅ l----------- ampere-turns length in m-----------------------------------= = A m ----- General – Definitions General Definitions 2 09/06 Please read Important notes and Cautions and warnings. Magnetic flux density Polarization J B φ A---- magnetic flux permeated area------------------------------------------= = Vs m2 ------- T(Tesla)[ ]= J B µ0H–= µ0 H⋅ J B J≈⇒« General relationship between B and H : In a vacuum, µr = 1; in ferromagnetic or ferrimagnetic materials the relation B(H) becomes nonlinear and the slope of the hysteresis loop µr » 1. 1.2 Basic parameters of the hysteresis loop 1.2.1 Initial magnetization curve The initial magnetization curve describes the relationship B = µr µ0 H for the first magnetization fol- lowing a complete demagnetization. By joining the end points of all “sub-loops”, from H = 0 to H = Hmax, (as shown in figure 1), we obtain the so-called commutation curve (also termed normal or mean magnetization curve), which, for magnetically soft ferrite materials, coincides with the initial magnetization curve. 1.2.2 Saturation magnetization BS The saturation magnetization BS is defined as the maximum flux density attainable in a material (i.e. for a very high field strength) at a given temperature; above this value BS, it is not possible to further increase B(H) by further increasing H. Technically, BS is defined as the flux density at a field strength of H = 1200 A/m. As is confirmed in the actual magnetization curves in the chapter "SIFERRIT materials”, the B(H) characteristic above 1200 A/m remains roughly constant (applies to all ferrites with high initial permeability, i.e. where µ ≥1000). 1.2.3 Remanent flux density BR(H) The remanent flux density (residual magnetization density) is a measure of the degree of residual magnetization in the ferrite after traversing a hysteresis loop. If the magnetic field H is subsequently reduced to zero, the ferrite still has a material-specific flux density BR ≠ 0 (see figure 1: intersection with the ordinate H = 0). 1.2.4 Coercive field strength HC The flux density B can be reduced to zero again by applying a specific opposing field –HC (see figure 1: intersection with the abscissa B = 0). The demagnetized state can be restored at any time by: a) traversing the hysteresis loop at a high frequency and simultaneously reducing the field strength H to H = 0. b) by exceeding the Curie temperature TC. B µ0 µr H( ) H⋅ ⋅= µ0 Magnetic field constant= µ0 1.257 10 6–⋅= Vs Am--------- µr Relative permeability= General Definitions 3 09/06 Please read Important notes and Cautions and warnings. 2 Permeability Different relative permeabilities µ are defined on the basis of the hysteresis loop for the various elec- tromagnetic applications. 2.1 Initial permeability µi The initial permeability µi defines the relative permeability at very low excitation levels and constitutes the most important means of comparison for soft magnetic materials. According to IEC 60401-3, µi is defined using closed magnetic circuits (e.g. a closed ring-shaped cylindrical coil) for f ≤10 kHz, B <0.25 mT, T = 25 °C. 2.2 Effective permeability µe Most core shapes in use today do not have closed magnetic paths (only ring, double E or double- aperture cores have closed magnetic circuits), rather the circuit consists of regions where µi ≠ 1 (ferrite material) and µi = 1 (air gap). Figure 3 shows the shape of the hysteresis loop of a circuit of this type. In practice, an effective permeability µe is defined for cores with air gaps. It should be noted, for example, that the loss factor tan δ and the temperature coefficient for gapped cores reduce in the ratio µe/µi compared to ungapped cores. µi 1µ0------ ∆B ∆H--------⋅= ∆H 0→( ) µe 1µ0------ L N2 ------- l A----∑= lA----∑ Form factor= L = Inductance N = Number of turns without air gap with air gap General Definitions 4 09/06 Please read Important notes and Cautions and warnings. Figure 3 Comparison of hysteresis loops for a core with and without an air gap The following approximation applies for an air gap s « le: s = Width of air gap le = Effective magnetic path length For more precise calculation methods, see for example E.C. Snelling, “Soft ferrites”, 2nd edition. 2.3 Apparent permeability µapp The definition of µapp is particularly important for specification of the permeability for coils with tubu- lar, cylindrical and threaded cores, since an unambiguous relationship between initial permeability µi and effective permeability µe is not possible on account of the high leakage inductances. The de- sign of the winding and the spatial correlation between coil and core have a considerable influence on µapp. A precise specification of µapp requires a precise specification of the measuring coil ar- rangement. 2.4 Complex permeability µ To enable a better comparison of ferrite materials and their frequency characteristics at very low field strengths (in order to take into consideration the phase displacement between voltage and current), it is useful to introduce µ as a complex operator, i.e. a complex permeability µ, according to the following relationship: µ = µs' – j . µs" where, in terms of a series equivalent circuit, (see figure 5) µs' is the relative real (inductance) component of µ and µs" is the relative imaginary (loss) component of µ. Using the complex permeability µ, the (complex) impedance of the coil can be calculated: Z = j ω µ L0 where L0 represents the inductance of a core of permeability µr = 1, but with unchanged flux distribution. (cf. also section 4.1: information on tan δ) µe µi 1 s le ---- µi⋅+ -----------------------= µapp LL0------ inductance with core inductance without core---------------------------------------------------------------= = General Definitions 5 09/06 Please read Important notes and Cautions and warnings. Figure 4 shows the characteristic shape of the curves of µs' and µs" as functions of the frequency, using N48 material as an example. The real component µs' is constant at low frequencies, attains a maximum at higher frequencies and then drops in approximately inverse proportion to f. At the same time, µ" rises steeply from a very small value at low frequencies to attain a distinct maximum and, past this, also drops as the frequency is further increased. The region in which µ' decreases sharply and where the µ" maximum occurs is termed the cut-off frequency fcutoff. This is inversely proportional to the initial permeability of the material (Snoek’s law). 2.5 Reversible permeability µrev In order to measure the reversible permeability µrev, a small measuring alternating field is superim- posed on a DC field. In this case µrev is heavily dependent on HDC, the core geometry and the tem- perature. Figure 4 Complex permeability versus frequency (measured on R10 toroids, N48 material, measuring flux density ˆB ≤0.25 mT) µrev 1µ0------ l im ∆H 0→⋅= ∆B ∆H--------    (Permeability with superimposed DC field HDC)HDC General Definitions 6 09/06 Please read Important notes and Cautions and warnings. Important application areas for DC field-superimposed, i.e. magnetically biased coils are broadband transformer systems (feeding currents with signal superimposition) and power engineering (shifting the operating point) and the area known as “nonlinear chokes” (cf. chapter on RM cores). For the magnetic bias curves as a function of the excitation HDC see the chapter on “SIFERRIT materials”. 2.6 Amplitude permeability µa, AL1 value = Peak value of flux density = Peak value of field strength For frequencies well below cut-off frequency, µa is not frequency-dependent but there is a strong dependence on temperature. The amplitude permeability is an important definition quantity for pow- er ferrites. It is defined for specific core types by means of an AL1 value for f ≤10 kHz, B = 320 mT (or 200 mT), T = 100 °C. µa B ˆ µ0 Hˆ ----------= (Permeability at high excitation) B H AL1 µ0 µa⋅ l A----∑ ----------------= General Definitions 7 09/06 Please read Important notes and Cautions and warnings. 3 Magnetic core shape characteristics Permeabilities and also other magnetic parameters are generally defined as material-specific quan- tities. For a particular core shape, however, the magnetic data are influenced to a significant extent by the geometry. Thus, the inductance of a slim-line ring core coil is defined as: Due to their geometry, soft magnetic ferrite cores in the field of such a coil change the flux param- eters in such a way that it is necessary to specify a series of effective core shape parameters in each data sheet. The following are defined: le Effective magnetic length Ae Effective magnetic cross section Amin Min. magnetic cross section of the core (required to calculate the max. flux density) Ve = Ae · le Effective magnetic volume With the aid of these parameters, the calculation for ferrite cores with complicated shapes can be reduced to the considerably more simple problem of an imaginary ring core with the same magnetic properties. The basis for this is provided by the methods of calculation according to IEC 60205, which allow to calculate the effective core shape parameters of different core shapes. 3.1 Form factor The inductance L can then be calculated as follows: where µe denotes the effective permeability or another permeability µrev or µa (or µi for cores with a closed magnetic path) adapted for the B/H range in question. 3.2 Inductance factor, AL value AL is the inductance referred to number of turns = 1. Therefore, for a defined number of turns N: L µr µ0 N 2 Al----⋅ ⋅ ⋅= l A----∑ leAe------= L µe µ0 N 2⋅⋅ l A----∑ ------------------------------= AL L N 2 -------- µe µ0⋅ l A----∑ ----------------= = General Definitions 8 09/06 Please read Important notes and Cautions and warnings. L = AL · N 2 3.3 Tolerance code letters The tolerances of the AL are coded by the letters in the third block of the ordering code in conformity with IEC 62358. The tolerance values available are given in the individual data sheets. Code letter Tolerance of AL value Code letter Tolerance of AL value A ±3% L ±15% B ±4% M ±20% C ±6% Q +30/–10% D ±8% R +30/–20% E ±7% U +80/–0% H ±12% X filling letter J ±5% Y +40/–30% K ±10% General Definitions 9 09/06 Please read Important notes and Cautions and warnings. 4 Definition quantities in the small-signal range 4.1 Loss factor tan δ Losses in the small-signal range are specified by the loss factor tan δ. Based on the impedance Z (cf. also section 2.4), the loss factor of the core in conjunction with the complex permeability µ is defined as where Rs and Rp denote the series and parallel resistance and Ls and Lp the series and parallel inductance respectively. From the relationships between series and parallel circuits we obtain: 4.2 Relative loss factor tan δ/µi In gapped cores the material loss factor tan δ is reduced by the factor µe/µi. This results in the rela- tive loss factor tan δe (cf. also section 2.2): The table of material properties lists the relative loss factor tan δ/µi. This is determined to IEC 60401-3 at B = 0.25 mT, T = 25 °C. δstan µs'' µs'-------- Rs ωLs---------- = = δptan µp'' µp'-------- ω Lp⋅ Rp --------------= =and Ls Rs Rp Lp Figure 5 Lossless series inductance Ls with loss resistance Rs resulting from the core losses. Figure 6 Lossless parallel inductance Lp with loss resistance Rp resulting from the core losses. µp' µs' 1 δtan( )2+( )⋅= µp'' µs'' 1 1tan δ------------    2+  ⋅= δetan δtanµi------------- µe⋅= General Definitions 10 09/06 Please read Important notes and Cautions and warnings. 4.3 Quality factor Q The ratio of reactance to total resistance of an induction coil is known as the quality factor Q. The total quality factor Q is the reciprocal of the total loss factor tan δ of the coil; it is dependent on the frequency, inductance, temperature, winding wire and permeability of the core. 4.4 Hysteresis loss resistance Rh and hysteresis material constant ηB In transformers, in particular, the user cannot always be content with very low saturation. The user requires details of the losses which occur at higher saturation, e.g. where the hysteresis loop begins to open. Since this hysteresis loss resistance Rh can rise sharply in different flux density ranges and at different frequencies, it is measured to IEC 60401-3 for µi values greater than 500 at B1 = 1.5 and B2 = 3 mT (∆B = 1.5 mT), a frequency of 10 kHz and a temperature of 25 °C (for µi < 500: f = 100 kHz, B1 = 0.3 mT, B2 = 1.2 mT). The hysteresis loss factor tan δh can then be calculated from this. For the hysteresis material constant ηB we obtain: The hysteresis material constant, ηB, characterizes the material-specific hysteresis losses and is a quantity independent of the air gap in a magnetic circuit. The hysteresis loss factor of an inductor can be reduced, at a constant flux density, by means of an (additional) air gap For further details on the measurement techniques see IEC 62044-2. Q ωL RL ------- reactance total resistance---------------------------------------- = = δtan h Rh ω L⋅----------- δ B2( )tan δ B1( )tan–= = ηB δhtan µe ∆Bˆ⋅ -------------------= δhtan ηB ∆Bˆ µe⋅⋅= General Definitions 11 09/06 Please read Important notes and Cautions and warnings. 5 Definition quantities in the high-excitation range While in the small-signal range (H ≤ Hc), i.e. in filter and broadband applications, the hysteresis loop is generally traversed only in lancet form (figure 2), for power applications the hysteresis loop is driv- en partly into saturation. The defining quantities are then µrev = reversible permeability in the case of superimposition with a DC signal (operating point for power transformers) µa = amplitude permeability and PV = core losses. 5.1 Core losses PV The losses of a ferrite core or core set PV is proportional to the area of the hysteresis loop in ques- tion. It can be divided into three components: Owing to the high specific resistance of ferrite materials, the eddy current losses in the frequency range common today (1 kHz to 2 MHz) may be practically disregarded except in the case of core shapes having a large cross-sectional area. The power loss PV is a function of the temperature T, the frequency f, the flux density B and is of course dependent on ferrite material and core shape. The temperature dependence can generally be approximated by means of a third-order polynomial, while applies for the frequency dependence and for the flux density dependence. The coefficients x and y are dependent on core shape and mate- rial, and there is a mutual dependence between the coefficients of the definition quantity (e.g. T) and the relevant parameter set (e.g. f, B). In the case of cores which are suitable for power applications, the total core losses PV are given explicitly for a specific frequency f, flux density B and temperature T in the relevant data sheets. When determining the total power loss for an inductive component, the winding losses must also be taken into consideration in addition to the core-specific losses. where, in addition to insulation conditions in the given frequency range, skin effect and proximity effect must also be taken into consideration for the winding. PV PV, hysteresis PV, eddycurrent PV, residual+ += PV f( ) f 1 x+( )∼ 0 x 1≤ ≤ PV B( ) B 2 y+( )∼ 0 y 1≤ ≤ PV, tot PV, core PV, winding+= General Definitions 12 09/06 Please read Important notes and Cautions and warnings. 5.2 Performance factor (PF = f · Bmax) The performance factor is a measure of the maximum power which a ferrite can transmit, whereby it is generally assumed that the loss does not exceed 300 kW/m3. Heat dissipation values of this order are usually assumed when designing small and medium-sized transformers. Increasing the performance factor will either enable an increase of the power that can be transformed by a core of identical design, or a reduction in component size if the transformed power is not increased. If the performance factors of different power transformer materials are plotted as a function of fre- quency, only slight differences are observed at low frequencies (< 300 kHz), but these differences become more pronounced with increasing frequency. This diagram can be used to determine the optimum material for a given frequency range (for diagram see page 16). General Definitions 13 09/06 Please read Important notes and Cautions and warnings. 6 Influence of temperature 6.1 µ(T) curve, Curie temperature TC The initial permeability µi as a function of T is given for all materials (see chapter on SIFERRIT ma- terials). Important parameters for a µ(T) curve are the position of the secondary permeability max- imum (SPM) and the Curie temperature. Minimum losses occur at the SPM temperature. Above the Curie temperature TC ferrite materials lose their ferrimagnetic properties, i.e. µi drops to µi = 1. This means that the parallel alignment of the elementary magnets (spontaneous magnetiza- tion) is destroyed by increasing thermal activation. This phenomenon is reversible, i.e. when the temperature is reduced below TC again, the ferrimagnetic properties are restored. The Curie tempertature TC is defined as the cross of the straight line between 80% and 20% of Lmax with the temperature axes (figure 7). 6.2 Temperature coefficient of permeability α By definition the temperature coefficient α represents a straight line of average gradient between the reference temperatures T1 and T2. If the µ(T) curve is approximately linear in this temperature range, this is a good approximation; in the case of heavily pronounced maxima, as occur particularly with highly permeable broadband ferrites, however, this is less true. The following applies: µi1 = Initial permeability µi at T1 = 25 °C µi2 = The initial permeability µi associated with the temperature T2 6