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In our ideal world, safety, quality and performance are paramount.In many cases, however, the cost of the final component, including the ferrite, has become the determining factor.This article is intended to help design engineers find alternative ferrite materials to reduce cost.
The desired intrinsic material properties and core geometry are determined by each specific application.Inherent properties that govern performance in low signal level applications are permeability (especially temperature), low core losses, and good magnetic stability over time and temperature.Applications include high-Q inductors, common mode inductors, broadband, matched and pulse transformers, radio antenna elements, and active and passive repeaters.For power applications, high flux density and low losses at operating frequency and temperature are desirable characteristics.Applications include switch-mode power supplies for electric vehicle battery charging, magnetic amplifiers, DC-DC converters, power filters, ignition coils, and transformers.
The intrinsic property that has the greatest impact on soft ferrite performance in suppression applications is the complex permeability [1], which is proportional to the impedance of the core.There are three ways to use ferrite as a suppressor of unwanted signals (conducted or radiated).The first, and least common, is as a practical shield, where ferrites are used to isolate conductors, components or circuits from the radiating stray electromagnetic field environment.In the second application, ferrites are used with capacitive elements to create a low pass filter, i.e. inductance – capacitive at low frequencies and dissipation at high frequencies.The third and most common use is when ferrite cores are used alone for component leads or board-level circuits.In this application, the ferrite core prevents any parasitic oscillations and/or attenuates unwanted signal pickup or transmission that may propagate along component leads or interconnects, traces or cables.In the second and third applications, ferrite cores suppress conducted EMI by eliminating or greatly reducing high frequency currents drawn by EMI sources.The introduction of ferrite provides high enough frequency impedance to suppress high frequency currents.In theory, an ideal ferrite would provide high impedance at EMI frequencies and zero impedance at all other frequencies.In effect, ferrite suppressor cores provide frequency-dependent impedance.At frequencies below 1 MHz, the maximum impedance can be obtained between 10 MHz and 500 MHz depending on the ferrite material.
Since it is consistent with the principles of electrical engineering, where AC voltage and current are represented by complex parameters, the permeability of a material can be expressed as a complex parameter consisting of real and imaginary parts.This is demonstrated at high frequencies, where the permeability splits into two components.The real part (μ’) represents the reactive part, which is in phase with the alternating magnetic field [2], while the imaginary part (μ”) represents the losses, which are out of phase with the alternating magnetic field. These can be expressed as series components (μs’μs”) or in parallel component (µp’µp”). The graphs in Figures 1, 2, and 3 show the series components of the complex initial permeability as a function of frequency for three ferrite materials. Material type 73 is a manganese-zinc ferrite, the initial magnetic The conductivity is 2500. Material type 43 is a nickel zinc ferrite with an initial permeability of 850. Material type 61 is a nickel zinc ferrite with an initial permeability of 125.
Focusing on the series component of the Type 61 material in Figure 3, we see that the real part of the permeability, μs’, remains constant with increasing frequency until a critical frequency is reached, and then decreases rapidly.The loss or μs” rises and then peaks as μs’ falls. This decrease in μs’ is due to the onset of ferrimagnetic resonance. [3] It should be noted that the higher the permeability, the more The lower the frequency. This inverse relationship was first observed by Snoek and gave the following formula:
where: ƒres = μs” frequency at maximum γ = gyromagnetic ratio = 0.22 x 106 A-1 m μi = initial permeability Msat = 250-350 Am-1
Since ferrite cores used in low signal level and power applications focus on magnetic parameters below this frequency, ferrite manufacturers rarely publish permeability and/or loss data at higher frequencies.However, higher frequency data is essential when specifying ferrite cores for EMI suppression.
The characteristic that most ferrite manufacturers specify for components used for EMI suppression is impedance.Impedance is easily measured on a commercially available analyzer with direct digital readout.Unfortunately, impedance is usually specified at a specific frequency and is a scalar representing the magnitude of the complex impedance vector.While this information is valuable, it is often insufficient, especially when modeling the circuit performance of ferrites.To achieve this, the impedance value and phase angle of the component, or the complex permeability of the specific material, must be available.
But even before starting to model the performance of ferrite components in a circuit, designers should know the following:
where μ’= real part of complex permeability μ”= imaginary part of complex permeability j = imaginary vector of unit Lo= air core inductance
The impedance of the iron core is also considered to be the series combination of the inductive reactance (XL) and the loss resistance (Rs), both of which are frequency dependent.A lossless core will have an impedance given by the reactance:
where: Rs = total series resistance = Rm + Re Rm = equivalent series resistance due to magnetic losses Re = equivalent series resistance for copper losses
At low frequencies, the impedance of the component is primarily inductive.As the frequency increases, the inductance decreases while the losses increase and the total impedance increases.Figure 4 is a typical plot of XL, Rs and Z versus frequency for our medium permeability materials.
Then the inductive reactance is proportional to the real part of the complex permeability, by Lo, the air-core inductance:
The loss resistance is also proportional to the imaginary part of the complex permeability by the same constant:
In Equation 9, the core material is given by µs’ and µs”, and the core geometry is given by Lo.Therefore, after knowing the complex permeability of different ferrites, a comparison can be made to obtain the most suitable material at the desired frequency or frequency range.After choosing the best material, it’s time to choose the best size components.The vector representation of complex permeability and impedance is shown in Figure 5.
Comparison of core shapes and core materials for impedance optimization is straightforward if the manufacturer provides a graph of complex permeability versus frequency for ferrite materials recommended for suppression applications.Unfortunately, this information is rarely available.However, most manufacturers provide initial permeability and loss versus frequency curves.From this data a comparison of materials used to optimize core impedance can be derived.
Referring to Figure 6, the initial permeability and dissipation factor [4] of Fair-Rite 73 material versus frequency, assuming the designer wants to guarantee a maximum impedance between 100 and 900 kHz.73 materials were selected.For modeling purposes, the designer also needs to understand the reactive and resistive parts of the impedance vector at 100 kHz (105 Hz) and 900 kHz.This information can be derived from the following chart:
At 100kHz μs ‘ = μi = 2500 and (Tan δ / μi) = 7 x 10-6 because Tan δ = μs ”/ μs’ then μs” = (Tan δ / μi) x (μi) 2 = 43.8
It should be noted that, as expected, the μ” adds very little to the total permeability vector at this low frequency. The impedance of the core is mostly inductive.
Designers know that the core must accept #22 wire and fit into a 10 mm x 5 mm space.The inner diameter will be specified as 0.8 mm.To solve for the estimated impedance and its components, first select a bead with an outer diameter of 10 mm and a height of 5 mm:
Z= ωLo (2500.38) = (6.28 x 105) x .0461 x log10 (5/.8) x 10 x (2500.38) x 10-8= 5.76 ohms at 100 kHz
In this case, as in most cases, maximum impedance is achieved by using a smaller OD with a longer length.If the ID is bigger, eg 4mm, and vice versa.
The same approach can be used if plots of impedance per unit Lo and phase angle versus frequency are provided.Figures 9, 10 and 11 represent such curves for the same three materials used herein.
Designers want to guarantee maximum impedance over the 25 MHz to 100 MHz frequency range.The available board space is again 10mm x 5mm and the core must accept #22 awg wire.Referring to Figure 7 for the unit impedance Lo of the three ferrite materials, or Figure 8 for the complex permeability of the same three materials, select the 850 μi material.[5] Using the graph in Figure 9, the Z/Lo of the medium permeability material is 350 x 108 ohm/H at 25 MHz.Solve for the estimated impedance:
The preceding discussion assumes that the core of choice is cylindrical.If ferrite cores are used for flat ribbon cables, bundled cables, or perforated plates, the calculation of Lo becomes more difficult, and fairly accurate core path length and effective area figures must be obtained to calculate the air core inductance .This can be done by mathematically slicing the core and adding the calculated path length and magnetic area for each slice.In all cases, however, the increase or decrease in impedance will be proportional to the increase or decrease in the height/length of the ferrite core.[6]
As mentioned, most manufacturers specify cores for EMI applications in terms of impedance, but the end user usually needs to know the attenuation.The relationship that exists between these two parameters is:
This relationship depends on the impedance of the source generating the noise and the impedance of the load receiving the noise.These values ​​are usually complex numbers, whose range can be infinite, and are not readily available to the designer.Choosing a value of 1 ohm for the load and source impedances, which can occur when the source is a switch mode power supply and loads many low impedance circuits, simplifies the equations and allows comparison of the attenuation of ferrite cores.
The graph in Figure 12 is a set of curves showing the relationship between shield bead impedance and attenuation for many common values ​​of load plus generator impedance.
Figure 13 is an equivalent circuit of an interference source with an internal resistance of Zs. The interference signal is generated by the series impedance Zsc of the suppressor core and the load impedance ZL.
Figures 14 and 15 are graphs of impedance versus temperature for the same three ferrite materials.The most stable of these materials is the 61 material with an 8% reduction in impedance at 100º C and 100 MHz.In contrast, the 43 material showed a 25% drop in impedance at the same frequency and temperature.These curves, when provided, can be used to adjust the specified room temperature impedance if attenuation at elevated temperatures is required.
As with temperature, DC and 50 or 60 Hz supply currents also affect the same inherent ferrite properties, which in turn result in lower core impedance.Figures 16, 17 and 18 are typical curves illustrating the effect of bias on the impedance of a ferrite material.This curve describes the impedance degradation as a function of field strength for a particular material as a function of frequency.It should be noted that the effect of the bias diminishes as the frequency increases.
Since this data was compiled, Fair-Rite Products has introduced two new materials.Our 44 is a nickel-zinc medium permeability material and our 31 is a manganese-zinc high permeability material.
Figure 19 is a plot of impedance versus frequency for beads of the same size in 31, 73, 44 and 43 materials.The 44 material is an improved 43 material with higher DC resistivity, 109 ohm cm, better thermal shock properties, temperature stability and higher Curie temperature (Tc).The 44 material has slightly higher impedance versus frequency characteristics compared to our 43 material.The stationary material 31 exhibits a higher impedance than either 43 or 44 over the entire measurement frequency range.The 31 is designed to alleviate the dimensional resonance problem that affects the low frequency suppression performance of larger manganese-zinc cores and has been successfully applied to cable connector suppression cores and large toroidal cores.Figure 20 is a plot of impedance versus frequency for 43, 31, and 73 materials for Fair-Rite cores with 0.562″ OD, 0.250 ID, and 1.125 HT. When comparing Figure 19 and Figure 20, it should be noted that for For smaller cores, for frequencies up to 25 MHz, 73 material is the best suppressor material. However, as the core cross section increases, the maximum frequency decreases. As shown in the data in Figure 20, 73 is the best The highest frequency is 8 MHz. It is also worth noting that the 31 material performs well in the frequency range from 8 MHz to 300 MHz. However, as a manganese zinc ferrite, the 31 material has a much lower volume resistivity of 102 ohms -cm, and more impedance changes with extreme temperature changes.
Glossary Air Core Inductance – Lo (H) The inductance that would be measured if the core had uniform permeability and the flux distribution remained constant.General formula Lo= 4π N2 10-9 (H) C1 Ring Lo = .0461 N2 log10 (OD/ID) Ht 10-8 (H) Dimensions are in mm
Attenuation – A (dB) The reduction in signal amplitude in transmission from one point to another.It is a scalar ratio of input amplitude to output amplitude, in decibels.
Core Constant – C1 (cm-1) The sum of the magnetic path lengths of each section of the magnetic circuit divided by the corresponding magnetic region of the same section.
Core Constant – C2 (cm-3) The sum of the magnetic circuit lengths of each section of the magnetic circuit divided by the square of the corresponding magnetic domain of the same section.
The effective dimensions of the magnetic path area Ae (cm2), the path length le (cm) and the volume Ve (cm3) For a given core geometry, it is assumed that the magnetic path length, cross-sectional area, and volume of the toroidal core have the same material properties as The material should have magnetic properties equivalent to the given core.
Field Strength – H (Oersted) A parameter characterizing the magnitude of the field strength.H = .4 π NI/le (Oersted)
Flux Density – B (Gaussian) The corresponding parameter of the induced magnetic field in the region normal to the flux path.
Impedance – Z (ohm) The impedance of a ferrite can be expressed in terms of its complex permeability.Z = jωLs + Rs = jωLo(μs’- jμs”) (ohm)
Loss Tangent – ​​tan δ The loss tangent of a ferrite is equal to the reciprocal of the circuit Q.
Loss Factor – tan δ/μi Phase removal between fundamental components of magnetic flux density and field strength with initial permeability.
Magnetic Permeability – μ The magnetic permeability derived from the ratio of the magnetic flux density and the applied alternating field strength is…
Amplitude permeability, μa – when the specified value of flux density is greater than the value used for initial permeability.
Effective Permeability, μe – When the magnetic route is constructed with one or more air gaps, the permeability is the permeability of a hypothetical homogeneous material that would provide the same reluctance.
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