Sleeve ferrite cores are manufactured from a magnetic material that allows them to control RF noise in cables and reduce it at a certain frequency range. This range mainly depends on their intrinsic composition and internal structure. Ferrite cores belong to the ferromagnetic materials field and can be categorized into three groups: ceramics, composite materials and metals. Conventionally, the most used sleeve ferrite cores are based on ceramic materials such as MnZn and NiZn, whereas the NC core characterized in this research is included in metals. Ceramics are also known as polycrystalline materials because they can contain metal oxides, such as manganese or zinc oxide. The features that have made ceramics the most popular filtering solution are their strong adhesion forces, heat-resistance, hardness and high resistance to pressure. One of the main advantages of the ceramics is the possibility of manufacturing filtering components with many different shapes. In contrast to ceramics, currently, the manufacture of NC cores with different shapes is complicated due to the fact it is not a simple solid core. NC cores are formed by metal film layers that are rolled up to reach the desired size. This shape cannot be cut safely without undermining its EMI suppression ability because when the core is cut, small shortcuts are caused between the layers, lowering the magnetic properties of the core. Therefore, it is difficult to create snap ferrite cores that can be clamped on a cable because they are not a solid core. Nevertheless, the structure of the novel NC material presents the advantage of designing smaller components with greater magnetic properties for low-frequency applications due to its intrinsic properties which are obtained by means of its complex manufacturing procedure [
19]. This process consists of melting the material by heating it at 1300 °C. Next, the liquid is deposited on a wheel in order to cool it through spinning around at 100 km/h with the aim of reducing its temperature at a cooling rate of 106 K/s. Thereby, the amorphous structure is generated and the thickness of the film is defined. Thereafter, the film is rolled up to form the sleeve core and it is exposed to an annealing process where it is warmed up to 600 °C to achieve the nanocrystalline structure. Finally, strong magnetic fields are applied to the material in order to get greater magnetic properties. Hence, from comparing its magnetic properties to those provided by ceramic cores, it is possible to consider that NC can not only provide a high attenuation ratio in the ultra-low frequency range (9 kHz to 150 kHz) but also, it could be more effective than ceramic cores throughout an upper frequency range.
2.1. Magnetic Properties
One of the most important parameters that defines the ability of a material to absorb electromagnetic interferences is the relative permeability (
) [
13]. The permeability relates the magnetic flux density of a certain magnetic field in a defined medium, so that when a sleeve ferrite core is placed around a certain cable, the magnetic flux is concentrated in it. This ability to concentrate the magnetic flux is described by the material’s internal properties and it is represented through the permeability complex parameter. The losses of the magnetic flux can be determined by dividing it into its complex form; in this way, the real component (
) quantifies the real or inductive part and the imaginary or resistive component (
) is related to the material ability to absorb the electromagnetic interferences [
30,
31]. Thereby, the complex relative permeability is expressed by:
One governing rule of EMI suppression that relates the permeability to the frequency in powder ferrite cores is Snoek’s Law [
4] given by (2):
where
corresponds to the ferromagnetic resonance frequency,
is the magnetic saturation and
the initial permeability. This last parameter is measured at low frequency (usually at 10 kHz with a temperature of 25 °C) and it is used for manufacturers to organize the filtering ability of cable ferrites. Equation (2) shows that the higher the frequency of operation, the lower the permeability, and vice versa. Thus, if the material provides high initial permeability, the frequency fall off will be low and vice versa. For this reason, MnZn ferrite cores are normally focused on the high kHz or at most, the very low MHz region since this material yields an initial permeability value between 3000–10,000 [
32,
33]. With regard to NiZn materials, they usually provide an initial permeability that varies between 500–1200, so they are able to more effectively filter electromagnetic noise within a high-frequency range [
34,
35]. Otherwise, the NC material shows a much higher initial permeability than ceramics due to its internal structure and manufacturing process that improve its magnetic properties. This results in an important increase in the initial permeability, reaching values of nearly 100,000 [
22].
The magnitude of the relative permeability of the NC material is represented together with MnZn and NiZn permeability traces in
Figure 2 to study the frequency region covered by each material [
10]. This graph shows that from the point of view of the magnetic properties, the NC core, despite being the material with higher initial permeability provides higher permeability than the ceramic materials throughout almost the entire frequency range studied. MnZn is able to provide a permeability around 3000 up to the 2 MHz point, providing a similar value to NC at this frequency point. In the high-frequency region, NC demonstrates a better performance than NiZn although it is possible to observe how the slope of NC is greater and, thus, NiZn may be more effective. In this way, the NC core, despite being the material with a higher initial permeability, provides higher permeability than the ceramic materials throughout the frequency range studied.
More information about the sleeve ferrite cores analyzed can be obtained by splitting into real and imaginary components the complex relative permeability of the three materials. These traces allow one to determine the magnetic resonance frequency (
) of each material, as shown in
Figure 3. This corresponds to the frequency value at which the real part of the relative permeability begins to fall and the imaginary part reaches the maximum peak [
36]. Generally, the inductance component is steady below the
and decreases significantly from this frequency value [
24]. The NC minigraph shows the lower frequency value at which the
takes place; however, the absorption loss represented by the imaginary part shows the weakest slope, if it is compared with MnZn and NiZn imaginary traces. From this information, together with the fact that NC provides a higher initial permeability, results in this sleeve ferrite solution could yield a greater attenuation ratio in a wider frequency range than ceramic cores. The equipment used to carry out these relative permeability measurements is based on the E4991A Material Analyzer (Keysight, Santa Rosa, CA, USA) that is interconnected with the 16454A Magnetic Material Text Fixture. This fixture measures accurately the permeability parameter of round-shaped magnetic materials because its features emulate one turn winding the core without magnetic flux leakage. Consequently, direct readouts of the complex permeability are obtained.
There is also a capacitance component that represents the dielectric effects of the ferrite magnetic material. This appears in the bandwidth above the
, where the inductive component of the permeability becomes negative [
13,
37]. As can be observed in
Figure 3, this stray capacitance due to the magnetic material is noted beyond 1.8 MHz and 85.1 MHz and 282.7 MHz in case of MnZn, NC and NiZn cores, respectively.
2.2. Impedance and Phase Description
Although the permeability parameter is used to describe the behavior of the core material, the performance of a certain sleeve ferrite core takes into account, besides the material features, other variables such as the self-inductance defined by the dimensions and the shape. Thereby, sleeve ferrite cores are usually defined and classified through specifying the magnitude of the impedance (Z
F), which is obtained from the equivalent component parameters such resistance (R) and inductance (L) [
4,
27]. The magnitude of the impedance is given by:
where R corresponds to the equivalent resistance and X
L is the impedance of the inductive part of the sleeve ferrite core. The vector relationship between impedance and permeability components is shown in
Figure 4.
There is a proportional relation between the attenuation ratio or insertion loss provided by a certain sleeve ferrite core and the impedance of the system where it is set. Thus, it is essential to select a sleeve ferrite core that provides an impedance value that is higher than the system impedance at the frequency to be filtered. This is due to the fact they are more effective when they are used on cables connected to circuits with low impedance [
5]. Sometimes it is difficult to accurately determine the impedance of the system with EMI problems; however, depending on the kind of lead, it is possible to estimate this value: for instance, ground leads usually present between 1 and 2 Ω, supply voltage lines have impedances from 10 to 20 Ω and video, clock and data lines from 90 Ω to 150 Ω [
27].
A sleeve ferrite core can be represented by a simplified equivalent circuit consisting of an inductance, a resistance and a capacitance, as shown in
Figure 5. This circuit represents a sleeve ferrite core within the frequency range analyzed in this contribution without taking into consideration the system where it could be placed, since the surrounding elements may introduce additional parasitic effects. The behavior of the sleeve ferrite core at a low-frequency range is usually mostly inductive, blocking CM currents due to its inductive reactance (L
F). The impedance becomes more resistive (R
F) as the frequency is increased, absorbing and dissipating CM currents as heat. Hence, L
F and R
F are the predominant components below the ferromagnetic resonance frequency; however, from this frequency value, the stray capacitance of the ferromagnetic material becomes predominant, defining the fall slope of the impedance. Regarding C
F, it represents a parasitic capacitance because of the winding effect [
24]. When a sleeve ferrite is set around a cable, it is equivalent to one turn or one winding coil. An interesting feature of sleeve ferrite cores is the possibility of winding the wire around them multiple times, considering each pass of the cable through the sleeve core as one turn. This technique results in an increase of the ferrite impedance proportionally to the number of turns squared. Nevertheless, increasing the number of turns also increases the winding capacitance C
F, shifting the point of maximum impedance to a lower frequency value [
25]. Therefore, there is a balance between the number of turns and winding capacitance, because a higher number of turns implies a worse performance at high frequencies. Nevertheless, increasing the number of turns N, it is possible to increase to obtain a higher inductance L
F value, but at the same time, the stray capacitance C
F increases [
13]. This last fact could generate a self-resonance (SRF) at a certain frequency. Above the value of the SRF, the impedance becomes predominantly capacitive and the effectiveness of the sleeve ferrite core to filter EMI is degraded [
38,
39]. Therefore, SFR due to C
F could superpose the ferromagnetic resonance due to the intrinsic material parameters described above. This is one of the main reasons why more than two or three turns are not usually used. In this contribution, the characterization is carried out by winding one and two turns in the sleeve ferrite cores.
The measurement setup currently in use by manufacturers for characterizing a sleeve ferrite core is based on the measurement of its impedance by means of introducing along the core a wire with a defined length and cross-section, which is connected to an Impedance Analyzer. The wire selected should be as short as possible, but long enough to achieve one and two turns around the sleeve ferrite core. With this conventional method, the influence of the wire in the total impedance measured can only be neglected if its length is short compared to the wavelength and this limit is usually a least 1/10 of the wavelength (λ). Some investigations have evaluated this measurement method and agree that it is not sufficiently accurate for very high frequency characterizations, because if an AWG26 (American Wire Gauge) cable is used, the minimum length required to wind two turns around the NC sleeve ferrite core is 150 mm. As a result, the maximum frequency that can be measured is 200 MHz (following the restriction of λ/10). If this procedure is used to characterize sleeve ferrite cores from 200 MHz, the wire represents a series inductance whose value becomes higher as the wire length increases. At the same time, this length increase causes the SRF to shift to a lower region, considering not only the impedance of the core but also the impedance introduced by the cable [
25,
26]. In the case of winding only one turn around the sleeve ferrite core, it is possible to use an AWG26 cable with a length of 70 mm with the aim of reducing the influence of the cable in the total impedance measurement.
Figure 6 shows the impedance of both AWG cables used to determine the impedance of the sleeve ferrite cores. From these traces, the magnitude of the impedance provided by the two cables employed to measuring the impedance of the sleeve ferrite cores can be observed. It is important to take this fact into account, especially in those sleeve cores whose impedance can be similar to the impedance provided by the cable.
Subsequently, considering these conditions, a calibration procedure has been performed with the aim of reducing the influence of the AWG cable, especially in the frequencies closer to the (λ/10) limit, when the 150 mm cable is employed. Taking this fact into consideration, it is possible to determine the direct impedance measurement through the E5061B Vector Network Analyzer (Keysight, Santa Rosa, CA, USA) connected to the Terminal Adapter 16201A (Keysight, Santa Rosa, CA, USA) and the Spring Clip Fixture 16092A (Keysight, Santa Rosa, CA, USA) [
40]. These fixtures are internally compensated by impedance standard calibration in order to take into account the electrical length path and the impedance variations caused by parasitic elements. The measurements of R and X
L obtained from the three sleeve ferrite cores with this setup are shown in
Figure 7.
Figure 7a shows the magnitude of the impedance measurement in which the most effective range of EMI suppression in the NC sleeve ferrite core compared to the ceramic cores analyzed can be observed. This minigraph shows that MnZn provides the higher impedance from 0.88 MHz to 2.73 MHz and NiZn offers a more effective behavior from 91.61 MHz, whereas in the rest of the frequencies, NC sleeve ferrite yields the best performance. If this data is compared to the permeability traces, it is possible to observe a correlation between both characterization methods, since MnZn provides a greater response than NC within a similar frequency region, which is shown in the permeability graph. With regard to the comparison between the NC and NiZn sleeve ferrite core, NC shows a higher impedance value of up to 91.61 MHz. At this frequency value, the inductance component of the analyzed NC sleeve ferrite core reaches negative values that match the SRF point. Consequently, the capacitive component of the core generates a degradation in the impedance performance, reducing it sharply with respect to NiZn sleeve ferrite core. In
Figure 7b–d, the resistive (R) and inductance (X
L) components can be observed in order to know the contribution of each of them related to the total impedance. As described above, the studied sleeve ferrites show higher values of X
L within the low-frequency region; however, these become less important as the frequency increases if compared to the R component. The resonance frequency of MnZn and NC cores is located at 2.02 MHz whereas the resonance frequency of NiZn is located above 200 MHz.
The impedance traces obtained by winding two turns into the sleeve ferrite cores are shown in
Figure 8. The increase of the number of turns generates higher values of the impedance magnitude in the three traces and causes a shift in the cross points of different sleeve ferrite traces. Therefore, NC provides the best performance up to 0.76 MHz, as well as in the frequency region from 2.75 MHz to 68.10 MHz. If the 10 MHz frequency point is taken as a reference, the values of the three traces have been increased about four times (the number of turns squared). Specifically, in the case of NC from 159.9 Ω to 651.2 Ω, MnZn 55.3 Ω to 227.0 Ω and NiZn cable ferrite from 100.9 Ω to 415.9 Ω.
From this data, the phase angle, which is defined by the angle whose sine is X
L/R (ϕ) can be represented. In this way, it is possible to determine the behavior of a certain sleeve ferrite core by means of studying its phase: when it corresponds to 90°, the ferrite core works as a pure inductor, whereas for 0°, it works as a pure resistor. If the phase reaches negative values, the sleeve ferrite core reduces its EMI suppression ability due to the fact that it is starting to show a capacitive and undesired behavior.
Figure 9a shows the course of the phase angle of NC sleeve ferrite cores that can be used as a frequency response indication and it can be compared with the ceramic sleeve ferrite cores. Note that in the NC case, the phase angle goes from 68° to 0° in the frequency range 0.01–72.50 MHz for one turn and 0.01–33.13 MHz for two turns. NC becomes more resistive than the other sleeve ferrites at lower frequencies and the transition between inductive and resistive behavior is less abrupt, since the phase of MnZn goes from 90° to 0° in the frequency range 0.01–2.52 MHz, matching for one and two turns and, in the case of NiZn, it crosses 0° at 94.55 MHz for two turns and beyond this frequency point, for one turn. Thus, it is possible to observe the broadband effectiveness than can provide the NC sleeve ferrite core in relation to ceramic ones.
These graphs also allow one to determine from which frequency value the phase angle of each sleeve ferrite becomes negative and, therefore, the component shows a capacitive behavior. As it has been described, in the case of MnZn, this frequency value corresponds to the , whereas for NC and NiZn, it is possible to observe that the phase angle trace crosses 0° at a lower frequency value, which demonstrates their complex relative permeability traces. This effect is caused by the shift of the SFR due to two factors: (a) the stray capacitance added to the sleeve ferrite response when the cable is winding it and (b) due to the self-resonance produced by the sleeve ferrite core dimensions (with smaller cores of the same material, the SFR appears at a higher frequency value). Therefore, the impedance magnitude is increased by winding a higher number of turns around the sleeve ferrite core but, at the same time, the effective frequency range is reduced.
In order to validate the impedance used to characterize the novel NC and ceramic sleeve ferrite cores, in
Section 4, this data is compared with the impedance calculated from the relative permeability through the quasi-static model from the real and imaginary permeability components and the dimension of the sleeve ferrite core [
13]. Generally, this model can be used for evaluating cores up to the SFR, since beyond this frequency value, the static magnetic flux distribution can fluctuate. This deviation could be because the core dimensions, saturation, core losses, and frequency-dependent magnetic effects that are significant above the SFR are not being taken into account [
24]. Equations (4) and (5) show the link between the material permeability and dimensions of the sleeve ferrite core with the impedance (inductance and resistance components):
where µ
0 is the permeability of the air,
is the inductance permeability component,
is the loss permeability component of the sleeve ferrite, ℓ is the effective magnetic path length of a toroidal core (m), N is the number of turns of a cable to carry out the measurement, A corresponds to the toroidal core cross-sectional area (m
2) and ω is the angular frequency.