- Email: [email protected]
Examining flux distributions in ferrite magnetic structures
Journal of Magnetism and Magnetic Materials 160 (1996) 318-322
ELSEVIER
Invited paper
,4pH journalof magnetism ~ H and magnetic ~ H materials
Examining flux distributions in ferrite magnetic structures Glenn Skutt *, Fred C. Lee Virginia Power Electronics Center, Virgillia Polytechnic h~stitute and State Unit ersity, Blacksburg, VA 24061-011 I, USA Abstract
The increased availability and power of scientific visualization tools in recent years has made it possible to construct useful tools for examining complex physical phenomena. This paper illustrates how such visualization tools can be used to examine the influence that geometrical shape and material characteristics can have on the distribution of magnetic flux in s o m e example ferrite cores. Keywords: Ferrites; Power electronics; Visualization; Flux density; Dimensional resonance: Finite elements
1. I n t r o d u c t i o n
The flux distribution in magnetic cores under various excitation conditions is strongly dependent on the geometry and material characteristics of the core. For example, a toroidal core has a uniform cross-sectional area throughout its magnetic path, and therefore the distribution of flux is primarily a function of the radius of the core. In other geometries - such as RM cores or any of a number of custom core shapes - the cross-sectional area varies for different portions of the core. These changes in core cross-sectional area mean that the flux density is not uniform throughout the core structure. In particular, sharp corners or transition regions where the core cross section changes from one shape to another can be regions of exceptionally high flux density. The non-uniform flux distribution in such cores can cause hot spots of core loss and the possibility of local saturation. These localized effects may or may not impact the overall performance of the core, but it is important to have a means of modeling and examining the flux distribution when it is shown to be problematic. The use of finite element aids in the visualization of flux-crowding and other loss 'hot-spot' phenomena. Such FEA tools generally contain post-processing routines [1,2] that can produce images of the field solution from a number of perspectives. These post-processors allow the user to isolate regions of particular interest and to explore in detail the field solutions through both visual and numerical representations of the data. The visual simulation results - quite independent of the quantitative calculation
of flux density, leakage inductance or core losses - provide intuitive insights to the experimenter that are not available from laboratory measurements alone. The usefulness of the information provided by standard FEA solvers can be enhanced through the use of improved visualization techniques. The visualization of flux in three-dimensional structures, for example, is well suited to examination using any of a variety of available data visualization software packages. While custom visualization tools aimed specifically at electromagnetic FEA such as presented in Ref. [3] are extremely useful, it is possible to use more general tools just as effectively. These visualization tools provide solution animations and even stereographic viewing capabilities that make the display of 3D field distributions comprehensible to both experienced researchers and general audiences alike. The continuing improvement of personal computer technologies and the widespread use computer graphics and multimedia tools mean that scientific visualization tools are now accessible to a much wider user community than ever before [4]. This change in available technology has been accompanied by the continued development in computer graphics engines and data manipulation routines, many of which are in the public domain. This paper focuses on the distribution of flux and losses in a set of ferrite core geometries typical of devices used in power electronics applications. We consider examples where the shape of the core, the existence of an air gap, the material characteristics of the core and the excitation frequency effect the distribution of flux density and core loss within the structure. 2. C o r e g e o m e t r i e s a n d e x c i t a t i o n s
Corresponding author. Email: [email protected]; fax: +1 703 231-6390.
The devices considered in this paper include three
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 2 15-6
G. Skutt, F.C. Lee / Journal of Magnetism and Magnetic Materials 160 (1996) 318-322
different core structures meant to illustrate different physical processes that lead to uneven flux distribution in cores. In all cases, the focus is on the flux distribution in the core, and therefore the device windings are modeled by ideal copper foils. The mechanical details for each of the devices are included in the figures that present the geometries of the respective cores. The first study shows the distribution of flux hysteresis loss for an EE core inductor with an air gap. This simulation illustrates the variations that exists even in a relatively uniform core under routine excitation conditions. The second study examines the uneven distribution of flux density in an RM-10 core. The flux distribution in this core is shown to be concentrated at the sharp corners in the core. This flux crowding results in higher loss densities in the corner regions that are not predicted by standard design equations. The final study presented examines the establishment of magnetic standing waves that can occur with the onset of dimensional resonance in large ferrite cores. This simulation illustrates the use of time and parameter animation techniques in presenting a series of FEA field distribution results. These results are presented in the paper as still images; the animations themselves add considerably to the usefulness of the FEA results and help provide an intuitive understanding of the underlying physics of the dimensional resonance problem. For each of the example case studies, the intension of the simulation is to provide visual insights into flux distributions in generic types of structures. As such, the charac-
319
teristics of the ferrite materials simulated are taken as representative of the characteristics of MnZn ferrites in general; the specific core material values for permeability, permittivity, and conductivity are given in each case, but they should be considered as representative values and not as characteristics of any particular core manufacture's material. 3. Flux distribution in a gapped EE core
One of the most widely used magnetic cores is the EE core pair. This core has a simple magnetic path that is nearly uniform in-cross section and that provides for a relatively uniform distribution of flux. The main variation in flux density in such a core occurs at the sharp-edged corners where the legs of the core meet the upper and lower bars. In many cases the flux crowding at these corners is of little concern, but at high flux density levels, the core will saturate first in these regions and localized losses can be high. This crowding of the flux to the inner edge of the core cannot be measured in the lab, but it is relatively simple to examine from a field simulation or in some simple cases from analytic solutions. The EE structure lends itself to use in inductor and transformer applications since the windings can be wound separately and then mounted on the core halves. This construction results in a gapped core structure, and this gap can be adjusted in energy storage devices to control the inductance. The amount of fringing flux that exists around the gap is often of concern for the noise and eddy current
EE-55 core geometry with foil winding
(a)
\
Fig. 1. Flux and hysteresis loss in a gapped EE core. (a) Core geometry, (b) plot of the flux on the outer surface of the core, (c) nested isosurface plots of flux at values of l, 5 and 7 mT. (d) nested isosurface plots of hysteresis loss at 1, 300 and 1000 W / m 3.
320
G. Skutt, F.C. Lee / Jourmtl of Magnetism and Magnetic Materials 160 (1996) 318-322
induction effects it can cause. Fig. 1 shows the FEA simulation results fo, the gapped EE core excited with ten amps of magnetizing current at 100 kHz. The core is modeled with a complex relative permeability of 3 0 0 0 - j 3 0 0 and a conductivity of 0.22 S / r e . The plots in Fig. I represent: (a) the geometry of the device including the single-layer foil winding, (b) an image that shows the flux on the outer surface of the core, (c) nested surfaces of constant flux density within the core plotted at 1, 5, and 7 roT, (d) nested isosurfaces of hysteresis loss at values of 1300 and 1000 W / m 3. The average flux density for this model is 6 roT, and the total hysteresis loss is 6.35 roW.
(
a
)
~
4. R M 1 0 core m o d e l i n g The RM10 core geometry shown in Fig. 2a is a popular core for use in power conversion circuits and in particular in low-profile, high-density d c - d c converters. It has the advantage of a relatively wide window region and when used in an E - I type of configuration can provide reasonable power densities. This core is particularly interesting from a flux distribution perspective because the relatively large center post intersects with relatively thin and narrow. The flux, therefore, tends to crowd in these regions resulting in a high flux density. The flux crowding at the inner corners is similar to that present in the EE core, but it is more pronounced in the RM core; in the RM core the total core area in the intersecting region is somewhat smaller than that in the rest of the core. In order to examine this phenomenon we model the core with its winding by taking advantage of the three-fold symmetry of the device. This symmetry allows the entire core to be modeled by simulating only one-eight of the core. The core material characteristics for the model are: /.t,. = 2 9 0 0 - j 3 5 0 , e,. = 1, and ~r - 7.5 S / m .
The flux density distribution in this core at 500 kHz for the core material values used and listed in Fig. 2 - can be viewed by plotting density contours on planes cut through the device. One such plot showing a variety if internal planar sections of the core is shown in Fig. 2b. This image shows the flux density magnitude inside the RM10 core using the following cross sections of the core: (1), (2) the center line of the core, (3) the cross section where the top and bottom half of two RM10 core halves come together, (4) the point just above where the center post joins with the bottom plate of the core. The flux crowding near the top of the center post appears as the bright areas of the plot in Fig. 2b. However, this crowding is earlier to see as surface plots similar to those used in the gapped EE core considered above. Fig. 2c shows one such isosurface representation of the flux density in the R M I 0 core simulation. This image is created (using AVS visualization software running on an SGI workstation) from the same data set used in Fig. 2b, but now the three-dimensional nature of the flux density
Fig. 2. RMI0 core flux density. (a) Core geometry showing the lines of symmetry, (b) flux density on several 2D planes within the modeled one-eighth section of the core, (c) isosurface visualization of the flux density in the modeled region. The highest flux density region, A. is the white ring along the top of the core center post. The lower flux density regions B, C. and D surround the A region. The D region shows the outer periphery of the core.
distribution is shown more explicitly. The printed image in Fig. 2c suffers greatly in comparison with the animated representation from which it is extracted. However we can still see several interesting features in the image that expand our understanding of the distribution of flux in this core. In particular, the peak flux density in the core is shown by the surface indicated as surface A in the figure. The outer isosurface of the field, D, has a low flux density value and so it acts to essentially distinguish the outer surface of the core volume. Surfaces B and C represent intermediate values of flux density. 5. D i m e n s i o n a l r e s o n a n c e
The type of flux density variations we have examined to this point are functions of the core geometry alone. That
G. Skutt, F. C. Lee / Journal ()['Magnetism and Magnetic MateriaL~ 160 (1996) 318-322
The frequency at which a dimensional resonance can exist depends on the permeability and permittivity of the ferrite core. Since MnZn ferrites have a large dielectric constant at lower frequencies and since in this frequency range the relative permeability is also high, the electromagnetic wavelength within the material can be quite short. The actual value of the wavelength in a given material is given in terms of the permeability, /x, permittivity, E, conductivity, o-, and angular frequency, to, by
7b mm
DI
II (a)
11
A= 2w//3= 2~r/Im{~/jtolXO--W21xe ),
240
(l)
where /3 is the phase constant within the material. This equation can often be approximated by the simpler relation for a lossless medium, 60
P ~
120
321
90
A=
H1t/1 180
150
270
(b)
300
210
330
Fig. 3. Dimensional resonance in an EE core. (a) Gapped EE-core geometry including two-layer foil winding, (b) time sequence of flux lines for a core with dielectric constant of 100000~ r, /x,. = 3000-j200, (r = 0.5, f = 1 MHz. The discrete circular patterns represent closed flux paths which indicate the standing wave nature of the flux distribution.
is the flux variations are not necessarily functions of the excitation frequency. If the ferrite cores are sufficiently large or the excitation frequency is high enough, however, there exists the possibility of a dimensional resonance arising in the core. In the final study conducted for this paper, the establishment of such a resonance is examined in a large EE core structure (Fig. 3a) using a 2D FEA analysis. The dimensional resonance phenomenon derives its name from the fact that the physical dimension of the core is a significant percentage of the electromagnetic wavelength in the ferrite material. This means that a standing wave of magnetic flux can be established in the core and this standing wave gives rise to high losses and ineffective coupling of electrical energy through the transformer. It may be critical, therefore, to avoid dimensional resonance in order to maintain efficient power processing capability [5-7].
= l/(/,/;7)
= Ao/
,
(2)
where Ao is the fi'ee-space wavelength at the given frequency. Clearly then the wavelength is dependent on the values of permeability, /z r, and permittivity, e r, in the material. For ferrites, these material characteristics are functions of many factors including operating temperature, frequency, excitation amplitude and dc bias. Since the magnetic permeability of ferrite provides the magnetic function of the circuit element, there is much more information available for it than there is for permittivity. In the simulations that follow, the value of permeability and conductivity are taken as 3000 and 0.5, respectively, which are values typical of M n - Z n ferrites at lower frequencies (below 1 MHz) and room temperature. The permittivity is varied from that of free space (which is the usual assumption for many approximate solutions) to 100000E o which is typical for M n - Z n ferrites below 1 MHz at room temperature [4]. Given the above values for e r, tt£r, and cr, the dimensional resonance phenomenon is examined using the core shown in Fig. l a. This simple EE core structure is representative of the type of core that could be used in highpower, high-frequency applications. For an excitation frequency of 1 MHz, relative permeability of 3000, and relative permittivity of 100 000, the wavelength is approximately 20 mm. Therefore this core - with cross-sectional dimension of 10 mm or half a wavelength - should exhibit some dimensional effects. The use of visual tools to represent the wave propagation characteristics of the flux distribution under such conditions aids in the analysis of the problem by providing insight - literally - into the way that flux is distributed throughout core during the entire the sinusoidal excitation cycle.
5.1. Simulation results For the presentation accompanying this report, the outputs of the finite element solver are saved for various conditions of material characteristics and frequency. In the
322
G. Skutt, F.C. Lee / Jourmd Of MagHelism and Ma~,,netic Materials 160 (1996) 318-322
first animation, the frequency is held constant at I M H z and the dielectric constant of the core is varied flom in ten steps from one to 100000e o. In the second animation, the dielectric constant is set to 100000e o and the phase angle of the exciting current is varied at 15 ° increments through one cycle. For both animations, plots of flux distribution and power loss distribution are displayed along with plots indicating the excitation conditions and calculated results. 5.1.1. Printed results jbr flux cersus time The propagating nature of the wave solution is quite evident in the time-based animation of the flux density for the core under resonant conditions. Fig. 3b shows a printed representation of the individual frames of this time sequence. In this representation we plot the solution for each phase angle in a separate small figure and then place the figures together in storyboard fashion. While this is a widely used method of showing a time sequence, it is difficult to see from such plots the actual wave nature of the flux in the core.
6. Conclusions The simulation results presented in this paper are mtended as an introduction to the study of non-unilk)rm flux distribution within fenite cores. By examining how various geometric or material changes affect the distribution of flux it should be possible to improve designs liar commer-
cial and custom core. The three-dimensional nature of the flux distribution makes visualization tools particularly usefnl: the effective exploitation of such tools provides new insights into the propagation aspects of the flux distributitms in tile cores. In the case of the dimensional resonance in ferrites, the sensitivity of the value of the wavelength o f electromagnetic fields in tile ferrite to variations in material characteristics gives a new rationale for nlore thorough characterization of these materials under a wider range of excitation conditions. Once the required basic data is correctly included in the device models, the use of numerical simulation can provide a powerful way to investigate the effects of minor changes in geometry or excitation conditions.
References [ 1] Maxwell Users Manual, Ansoft Corporation (1993). [2] G. Meunier, J.C. Sabonnadiere and J.L. Coulomb. IEEE Trans. Magn. 27 {1991) 3786. [3] H. Yamashita. T. Johkoh and E. Nakamae, IEEE Trans. Magn. 28 (1992) 1778. [4] K. Kornbluh, IEEE Spectrum 31 (1994) 57. [5] E.C. Snelling, Soft Ferrites: Properties and Applications (Butterworths, London, 1988) pp. 126-129. [6] J. Smit and H.P,J. Wijn, Ferrites (Wiley, New York, 1959) chap. 12, pp. 229-242. [7] R.L. Sanford and l.L. tooter, Basic Magnetic Quantities and the Measurement of the Magnetic Properties of Materials, National Bureau of Standards Monograph 47 (1962).
ELSEVIER
Invited paper
,4pH journalof magnetism ~ H and magnetic ~ H materials
Examining flux distributions in ferrite magnetic structures Glenn Skutt *, Fred C. Lee Virginia Power Electronics Center, Virgillia Polytechnic h~stitute and State Unit ersity, Blacksburg, VA 24061-011 I, USA Abstract
The increased availability and power of scientific visualization tools in recent years has made it possible to construct useful tools for examining complex physical phenomena. This paper illustrates how such visualization tools can be used to examine the influence that geometrical shape and material characteristics can have on the distribution of magnetic flux in s o m e example ferrite cores. Keywords: Ferrites; Power electronics; Visualization; Flux density; Dimensional resonance: Finite elements
1. I n t r o d u c t i o n
The flux distribution in magnetic cores under various excitation conditions is strongly dependent on the geometry and material characteristics of the core. For example, a toroidal core has a uniform cross-sectional area throughout its magnetic path, and therefore the distribution of flux is primarily a function of the radius of the core. In other geometries - such as RM cores or any of a number of custom core shapes - the cross-sectional area varies for different portions of the core. These changes in core cross-sectional area mean that the flux density is not uniform throughout the core structure. In particular, sharp corners or transition regions where the core cross section changes from one shape to another can be regions of exceptionally high flux density. The non-uniform flux distribution in such cores can cause hot spots of core loss and the possibility of local saturation. These localized effects may or may not impact the overall performance of the core, but it is important to have a means of modeling and examining the flux distribution when it is shown to be problematic. The use of finite element aids in the visualization of flux-crowding and other loss 'hot-spot' phenomena. Such FEA tools generally contain post-processing routines [1,2] that can produce images of the field solution from a number of perspectives. These post-processors allow the user to isolate regions of particular interest and to explore in detail the field solutions through both visual and numerical representations of the data. The visual simulation results - quite independent of the quantitative calculation
of flux density, leakage inductance or core losses - provide intuitive insights to the experimenter that are not available from laboratory measurements alone. The usefulness of the information provided by standard FEA solvers can be enhanced through the use of improved visualization techniques. The visualization of flux in three-dimensional structures, for example, is well suited to examination using any of a variety of available data visualization software packages. While custom visualization tools aimed specifically at electromagnetic FEA such as presented in Ref. [3] are extremely useful, it is possible to use more general tools just as effectively. These visualization tools provide solution animations and even stereographic viewing capabilities that make the display of 3D field distributions comprehensible to both experienced researchers and general audiences alike. The continuing improvement of personal computer technologies and the widespread use computer graphics and multimedia tools mean that scientific visualization tools are now accessible to a much wider user community than ever before [4]. This change in available technology has been accompanied by the continued development in computer graphics engines and data manipulation routines, many of which are in the public domain. This paper focuses on the distribution of flux and losses in a set of ferrite core geometries typical of devices used in power electronics applications. We consider examples where the shape of the core, the existence of an air gap, the material characteristics of the core and the excitation frequency effect the distribution of flux density and core loss within the structure. 2. C o r e g e o m e t r i e s a n d e x c i t a t i o n s
Corresponding author. Email: [email protected]; fax: +1 703 231-6390.
The devices considered in this paper include three
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. PH S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 2 15-6
G. Skutt, F.C. Lee / Journal of Magnetism and Magnetic Materials 160 (1996) 318-322
different core structures meant to illustrate different physical processes that lead to uneven flux distribution in cores. In all cases, the focus is on the flux distribution in the core, and therefore the device windings are modeled by ideal copper foils. The mechanical details for each of the devices are included in the figures that present the geometries of the respective cores. The first study shows the distribution of flux hysteresis loss for an EE core inductor with an air gap. This simulation illustrates the variations that exists even in a relatively uniform core under routine excitation conditions. The second study examines the uneven distribution of flux density in an RM-10 core. The flux distribution in this core is shown to be concentrated at the sharp corners in the core. This flux crowding results in higher loss densities in the corner regions that are not predicted by standard design equations. The final study presented examines the establishment of magnetic standing waves that can occur with the onset of dimensional resonance in large ferrite cores. This simulation illustrates the use of time and parameter animation techniques in presenting a series of FEA field distribution results. These results are presented in the paper as still images; the animations themselves add considerably to the usefulness of the FEA results and help provide an intuitive understanding of the underlying physics of the dimensional resonance problem. For each of the example case studies, the intension of the simulation is to provide visual insights into flux distributions in generic types of structures. As such, the charac-
319
teristics of the ferrite materials simulated are taken as representative of the characteristics of MnZn ferrites in general; the specific core material values for permeability, permittivity, and conductivity are given in each case, but they should be considered as representative values and not as characteristics of any particular core manufacture's material. 3. Flux distribution in a gapped EE core
One of the most widely used magnetic cores is the EE core pair. This core has a simple magnetic path that is nearly uniform in-cross section and that provides for a relatively uniform distribution of flux. The main variation in flux density in such a core occurs at the sharp-edged corners where the legs of the core meet the upper and lower bars. In many cases the flux crowding at these corners is of little concern, but at high flux density levels, the core will saturate first in these regions and localized losses can be high. This crowding of the flux to the inner edge of the core cannot be measured in the lab, but it is relatively simple to examine from a field simulation or in some simple cases from analytic solutions. The EE structure lends itself to use in inductor and transformer applications since the windings can be wound separately and then mounted on the core halves. This construction results in a gapped core structure, and this gap can be adjusted in energy storage devices to control the inductance. The amount of fringing flux that exists around the gap is often of concern for the noise and eddy current
EE-55 core geometry with foil winding
(a)
\
Fig. 1. Flux and hysteresis loss in a gapped EE core. (a) Core geometry, (b) plot of the flux on the outer surface of the core, (c) nested isosurface plots of flux at values of l, 5 and 7 mT. (d) nested isosurface plots of hysteresis loss at 1, 300 and 1000 W / m 3.
320
G. Skutt, F.C. Lee / Jourmtl of Magnetism and Magnetic Materials 160 (1996) 318-322
induction effects it can cause. Fig. 1 shows the FEA simulation results fo, the gapped EE core excited with ten amps of magnetizing current at 100 kHz. The core is modeled with a complex relative permeability of 3 0 0 0 - j 3 0 0 and a conductivity of 0.22 S / r e . The plots in Fig. I represent: (a) the geometry of the device including the single-layer foil winding, (b) an image that shows the flux on the outer surface of the core, (c) nested surfaces of constant flux density within the core plotted at 1, 5, and 7 roT, (d) nested isosurfaces of hysteresis loss at values of 1300 and 1000 W / m 3. The average flux density for this model is 6 roT, and the total hysteresis loss is 6.35 roW.
(
a
)
~
4. R M 1 0 core m o d e l i n g The RM10 core geometry shown in Fig. 2a is a popular core for use in power conversion circuits and in particular in low-profile, high-density d c - d c converters. It has the advantage of a relatively wide window region and when used in an E - I type of configuration can provide reasonable power densities. This core is particularly interesting from a flux distribution perspective because the relatively large center post intersects with relatively thin and narrow. The flux, therefore, tends to crowd in these regions resulting in a high flux density. The flux crowding at the inner corners is similar to that present in the EE core, but it is more pronounced in the RM core; in the RM core the total core area in the intersecting region is somewhat smaller than that in the rest of the core. In order to examine this phenomenon we model the core with its winding by taking advantage of the three-fold symmetry of the device. This symmetry allows the entire core to be modeled by simulating only one-eight of the core. The core material characteristics for the model are: /.t,. = 2 9 0 0 - j 3 5 0 , e,. = 1, and ~r - 7.5 S / m .
The flux density distribution in this core at 500 kHz for the core material values used and listed in Fig. 2 - can be viewed by plotting density contours on planes cut through the device. One such plot showing a variety if internal planar sections of the core is shown in Fig. 2b. This image shows the flux density magnitude inside the RM10 core using the following cross sections of the core: (1), (2) the center line of the core, (3) the cross section where the top and bottom half of two RM10 core halves come together, (4) the point just above where the center post joins with the bottom plate of the core. The flux crowding near the top of the center post appears as the bright areas of the plot in Fig. 2b. However, this crowding is earlier to see as surface plots similar to those used in the gapped EE core considered above. Fig. 2c shows one such isosurface representation of the flux density in the R M I 0 core simulation. This image is created (using AVS visualization software running on an SGI workstation) from the same data set used in Fig. 2b, but now the three-dimensional nature of the flux density
Fig. 2. RMI0 core flux density. (a) Core geometry showing the lines of symmetry, (b) flux density on several 2D planes within the modeled one-eighth section of the core, (c) isosurface visualization of the flux density in the modeled region. The highest flux density region, A. is the white ring along the top of the core center post. The lower flux density regions B, C. and D surround the A region. The D region shows the outer periphery of the core.
distribution is shown more explicitly. The printed image in Fig. 2c suffers greatly in comparison with the animated representation from which it is extracted. However we can still see several interesting features in the image that expand our understanding of the distribution of flux in this core. In particular, the peak flux density in the core is shown by the surface indicated as surface A in the figure. The outer isosurface of the field, D, has a low flux density value and so it acts to essentially distinguish the outer surface of the core volume. Surfaces B and C represent intermediate values of flux density. 5. D i m e n s i o n a l r e s o n a n c e
The type of flux density variations we have examined to this point are functions of the core geometry alone. That
G. Skutt, F. C. Lee / Journal ()['Magnetism and Magnetic MateriaL~ 160 (1996) 318-322
The frequency at which a dimensional resonance can exist depends on the permeability and permittivity of the ferrite core. Since MnZn ferrites have a large dielectric constant at lower frequencies and since in this frequency range the relative permeability is also high, the electromagnetic wavelength within the material can be quite short. The actual value of the wavelength in a given material is given in terms of the permeability, /x, permittivity, E, conductivity, o-, and angular frequency, to, by
7b mm
DI
II (a)
11
A= 2w//3= 2~r/Im{~/jtolXO--W21xe ),
240
(l)
where /3 is the phase constant within the material. This equation can often be approximated by the simpler relation for a lossless medium, 60
P ~
120
321
90
A=
H1t/1 180
150
270
(b)
300
210
330
Fig. 3. Dimensional resonance in an EE core. (a) Gapped EE-core geometry including two-layer foil winding, (b) time sequence of flux lines for a core with dielectric constant of 100000~ r, /x,. = 3000-j200, (r = 0.5, f = 1 MHz. The discrete circular patterns represent closed flux paths which indicate the standing wave nature of the flux distribution.
is the flux variations are not necessarily functions of the excitation frequency. If the ferrite cores are sufficiently large or the excitation frequency is high enough, however, there exists the possibility of a dimensional resonance arising in the core. In the final study conducted for this paper, the establishment of such a resonance is examined in a large EE core structure (Fig. 3a) using a 2D FEA analysis. The dimensional resonance phenomenon derives its name from the fact that the physical dimension of the core is a significant percentage of the electromagnetic wavelength in the ferrite material. This means that a standing wave of magnetic flux can be established in the core and this standing wave gives rise to high losses and ineffective coupling of electrical energy through the transformer. It may be critical, therefore, to avoid dimensional resonance in order to maintain efficient power processing capability [5-7].
= l/(/,/;7)
= Ao/
,
(2)
where Ao is the fi'ee-space wavelength at the given frequency. Clearly then the wavelength is dependent on the values of permeability, /z r, and permittivity, e r, in the material. For ferrites, these material characteristics are functions of many factors including operating temperature, frequency, excitation amplitude and dc bias. Since the magnetic permeability of ferrite provides the magnetic function of the circuit element, there is much more information available for it than there is for permittivity. In the simulations that follow, the value of permeability and conductivity are taken as 3000 and 0.5, respectively, which are values typical of M n - Z n ferrites at lower frequencies (below 1 MHz) and room temperature. The permittivity is varied from that of free space (which is the usual assumption for many approximate solutions) to 100000E o which is typical for M n - Z n ferrites below 1 MHz at room temperature [4]. Given the above values for e r, tt£r, and cr, the dimensional resonance phenomenon is examined using the core shown in Fig. l a. This simple EE core structure is representative of the type of core that could be used in highpower, high-frequency applications. For an excitation frequency of 1 MHz, relative permeability of 3000, and relative permittivity of 100 000, the wavelength is approximately 20 mm. Therefore this core - with cross-sectional dimension of 10 mm or half a wavelength - should exhibit some dimensional effects. The use of visual tools to represent the wave propagation characteristics of the flux distribution under such conditions aids in the analysis of the problem by providing insight - literally - into the way that flux is distributed throughout core during the entire the sinusoidal excitation cycle.
5.1. Simulation results For the presentation accompanying this report, the outputs of the finite element solver are saved for various conditions of material characteristics and frequency. In the
322
G. Skutt, F.C. Lee / Jourmd Of MagHelism and Ma~,,netic Materials 160 (1996) 318-322
first animation, the frequency is held constant at I M H z and the dielectric constant of the core is varied flom in ten steps from one to 100000e o. In the second animation, the dielectric constant is set to 100000e o and the phase angle of the exciting current is varied at 15 ° increments through one cycle. For both animations, plots of flux distribution and power loss distribution are displayed along with plots indicating the excitation conditions and calculated results. 5.1.1. Printed results jbr flux cersus time The propagating nature of the wave solution is quite evident in the time-based animation of the flux density for the core under resonant conditions. Fig. 3b shows a printed representation of the individual frames of this time sequence. In this representation we plot the solution for each phase angle in a separate small figure and then place the figures together in storyboard fashion. While this is a widely used method of showing a time sequence, it is difficult to see from such plots the actual wave nature of the flux in the core.
6. Conclusions The simulation results presented in this paper are mtended as an introduction to the study of non-unilk)rm flux distribution within fenite cores. By examining how various geometric or material changes affect the distribution of flux it should be possible to improve designs liar commer-
cial and custom core. The three-dimensional nature of the flux distribution makes visualization tools particularly usefnl: the effective exploitation of such tools provides new insights into the propagation aspects of the flux distributitms in tile cores. In the case of the dimensional resonance in ferrites, the sensitivity of the value of the wavelength o f electromagnetic fields in tile ferrite to variations in material characteristics gives a new rationale for nlore thorough characterization of these materials under a wider range of excitation conditions. Once the required basic data is correctly included in the device models, the use of numerical simulation can provide a powerful way to investigate the effects of minor changes in geometry or excitation conditions.
References [ 1] Maxwell Users Manual, Ansoft Corporation (1993). [2] G. Meunier, J.C. Sabonnadiere and J.L. Coulomb. IEEE Trans. Magn. 27 {1991) 3786. [3] H. Yamashita. T. Johkoh and E. Nakamae, IEEE Trans. Magn. 28 (1992) 1778. [4] K. Kornbluh, IEEE Spectrum 31 (1994) 57. [5] E.C. Snelling, Soft Ferrites: Properties and Applications (Butterworths, London, 1988) pp. 126-129. [6] J. Smit and H.P,J. Wijn, Ferrites (Wiley, New York, 1959) chap. 12, pp. 229-242. [7] R.L. Sanford and l.L. tooter, Basic Magnetic Quantities and the Measurement of the Magnetic Properties of Materials, National Bureau of Standards Monograph 47 (1962).