3.2.1. Making a miniature planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid: V2

A key component of the devices used for energy harvesting from the environment is the electric transformer. In this case, we proposed a miniature planar transformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid, [27]. The proposed model has two circular spiral-wound, made from copper: 20 turns in primary and 40 turns in secondary. Windings, Figures 21 and 22, can be "grown" using LIGA technology on a ceramic substrate (Al2O3) as has been shown previously or can be obtained by machining, starting from a textolit board double plated with copper. Housing and central column are made of 3F3 ferrite. The cavity formed in the housing is filled with superparamagnetic colloidal nanofluid, NMF-UTR40-500G, Figure 21, having saturation magnetization of 500 Gs, [27]. The applications presented in [28, 29], uses a dilution of magnetic nanofluid acting also as a cooling agent, type NMF-UTR40-50G that having saturation magnetization of 50 Gs.

Figure 21. The planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid—V2 and the equivalent simplified 2D axial model [30].

Figure 22. Planar coils corresponding to primary and secondary coils of the microtransformer, INCDIE ICPE-CA concept.

We purpose now that the magnetic nanofluid be used both as a coolant and as part of the hybrid magnetic core, by using of the magnetic nanofluid type NMF-UTR40-500G.

#### 3.2.1.1. The mathematical model

The magnetic field inside the planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid—V2 for steady state conditions is described by the (10), (11), (12) and (13) equations as follows: inside the coils (J 6¼ 0), the ferrite part of the magnetic core (J = 0), and within the ceramic holders (J = 0).

$$\nabla \times \left(\mu\_0^{-1} \mu\_r^{-1} \nabla \times \mathbf{A}\right) = \mathbf{J},\tag{10}$$

where, u [m/s<sup>2</sup>

3.2.1.2. The practical achievements

are represented in Figure 26.

Figure 23. The 3F3 ferrite parts of magnetic circuit.

Figure 24. The ferrite magnetic circuit and microtransformer housing.

] is the velocity, p [N/m<sup>2</sup>

is the dynamic viscosity, and [N/m<sup>3</sup>

the outer boundaries of the MNF core close the flow problem.

] is the pressure, r [kg/m3

forces of thermal nature are not significant here [30–32]. No slip (zero velocity) conditions on

In Figure 23, the 3F3 ferrite parts of magnetic circuit can be seen and in Figure 24 the ferrite magnetic circuit and microtransformer housing. Parts of the housing, the ferrite magnetic circuit and the four planar coils which form the primary and the secondary circuit of the microtransformer it can be seen in Figure 25. Finally, two assembled planar microtransformers

ð13Þ

]

39

] is the mass density, <sup>η</sup> [N�s/m2

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] is the magnetization body force. Body

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inside the magnetic nanofluid (MNF) core.

$$\nabla \times \left( \mu\_0^{-1} \nabla \times \mathbf{A} - \mathbf{M} \right) = \mathbf{0},\tag{11}$$

where <sup>A</sup> [T�m] is the magnetic vector potential, <sup>J</sup> [A/m<sup>2</sup> ] is the electric current density, <sup>μ</sup><sup>0</sup> = 4π�10�<sup>7</sup> H/m is the magnetic permeability of the free space, <sup>μ</sup><sup>r</sup> is the relative magnetic permeability, and M [A/m] is the magnetization of the MNF, approximated here through, where H [A/m] is the magnetic field strength, and α, β are empiric constants selected to accurately fit the magnetization curve. The problem is closed by magnetic insulation boundary conditions, n � A = 0, where n is the outward pointing normal, [30–32].

The magnetic field, produced by the electric currents, generates magnetic body forces within the MNF, which are responsible for the flow of the fluid part of the core described, in steady state conditions, through.

momentum conservation (Navier–Stokes)

$$\varphi(\mathbf{u}\cdot\nabla)\mathbf{u} = -\nabla \times \left[p\mathbf{I} + \eta\nabla\mathbf{u} + \left(\nabla\mathbf{u}\right)^{T}\right] + \mathbf{f}\_{\text{mag}},\tag{12}$$

mass conservation law

$$\nabla \cdot \mathbf{u} = \mathbf{0},\tag{13}$$

where, u [m/s<sup>2</sup> ] is the velocity, p [N/m<sup>2</sup> ] is the pressure, r [kg/m3 ] is the mass density, <sup>η</sup> [N�s/m2 ] is the dynamic viscosity, and [N/m<sup>3</sup> ] is the magnetization body force. Body forces of thermal nature are not significant here [30–32]. No slip (zero velocity) conditions on the outer boundaries of the MNF core close the flow problem.

#### 3.2.1.2. The practical achievements

We purpose now that the magnetic nanofluid be used both as a coolant and as part of the

Figure 22. Planar coils corresponding to primary and secondary coils of the microtransformer, INCDIE ICPE-CA concept.

The magnetic field inside the planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid—V2 for steady state conditions is described by the (10), (11), (12) and (13) equations as follows: inside the coils (J 6¼ 0), the ferrite

<sup>μ</sup><sup>0</sup> = 4π�10�<sup>7</sup> H/m is the magnetic permeability of the free space, <sup>μ</sup><sup>r</sup> is the relative magnetic permeability, and M [A/m] is the magnetization of the MNF, approximated here through,

selected to accurately fit the magnetization curve. The problem is closed by magnetic insula-

The magnetic field, produced by the electric currents, generates magnetic body forces within the MNF, which are responsible for the flow of the fluid part of the core described, in steady

tion boundary conditions, n � A = 0, where n is the outward pointing normal, [30–32].

where H [A/m] is the magnetic field strength, and α, β are empiric constants

ð10Þ

ð11Þ

ð12Þ

] is the electric current density,

hybrid magnetic core, by using of the magnetic nanofluid type NMF-UTR40-500G.

38 Advanced Electronic Circuits - Principles, Architectures and Applications on Emerging Technologies

part of the magnetic core (J = 0), and within the ceramic holders (J = 0).

where <sup>A</sup> [T�m] is the magnetic vector potential, <sup>J</sup> [A/m<sup>2</sup>

3.2.1.1. The mathematical model

state conditions, through.

mass conservation law

momentum conservation (Navier–Stokes)

inside the magnetic nanofluid (MNF) core.

In Figure 23, the 3F3 ferrite parts of magnetic circuit can be seen and in Figure 24 the ferrite magnetic circuit and microtransformer housing. Parts of the housing, the ferrite magnetic circuit and the four planar coils which form the primary and the secondary circuit of the microtransformer it can be seen in Figure 25. Finally, two assembled planar microtransformers are represented in Figure 26.

Figure 23. The 3F3 ferrite parts of magnetic circuit.

Figure 24. The ferrite magnetic circuit and microtransformer housing.

• Spectral analysis is multipoint type because the spectra were superimposed to see the

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41

• All the spectra were normalized to 100%. The unit was expressed in the concentration of

• Elements that were highlighted were C, O, Mn, Fe and Zn, Tables 1 and 2 and Figure 28

intensity and variation of the elements in the selected points/areas;

Figure 28. The 3F3 spectra analyze, corresponding to Spectrum 1 and 5000 magnification.

Figure 27. Scanning electron microscopy image (SEM) of the 3F3 ferrite, 5000 magnification.

After analysis, the following features were noted:

for Spectrum 1;

the elements of interest was the percentage by mass (weight percent%).

Figure 25. Parts of the housing, the ferrite magnetic circuit and the four planar coils which form the primary and the secondary circuit of the microtransformer, INCDIE ICPE-CA concept [33].

Figure 26. Two assembled planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid—V2, after the magnetic nanofluid loading process.

#### 3.2.1.3. Analysis of 3F3 ferrite as part of magnetic circuit

Analysis of 3F3 ferrite done by scanning electron microscopy (SEM) coupled with energy dispersive micro-probe X-ray under the following conditions:

The two areas of interest were at an increase of 5000 and 2000, Figures 27 and 29;


After analysis, the following features were noted:

• Elements that were highlighted were C, O, Mn, Fe and Zn, Tables 1 and 2 and Figure 28 for Spectrum 1;

Figure 27. Scanning electron microscopy image (SEM) of the 3F3 ferrite, 5000 magnification.

3.2.1.3. Analysis of 3F3 ferrite as part of magnetic circuit

magnetic nanofluid—V2, after the magnetic nanofluid loading process.

secondary circuit of the microtransformer, INCDIE ICPE-CA concept [33].

40 Advanced Electronic Circuits - Principles, Architectures and Applications on Emerging Technologies

quantitatively;

dispersive micro-probe X-ray under the following conditions:

dispersive microprobe produced by Oxford Instruments;

Analysis of 3F3 ferrite done by scanning electron microscopy (SEM) coupled with energy

Figure 26. Two assembled planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal

Figure 25. Parts of the housing, the ferrite magnetic circuit and the four planar coils which form the primary and the

• Acquisitions have been made with the help of the secondary electron detector in the sample chamber, type "Everhart – Thornley", coupled with "INCA Energy 250" energy

• Two categories of spectra were achieved, namely: punctual, with the elemental distribution of the electron beam spot on the surface of the sample and another as micro-area, integrated where the composition of the elements of the microarray was determined

The two areas of interest were at an increase of 5000 and 2000, Figures 27 and 29;

Figure 28. The 3F3 spectra analyze, corresponding to Spectrum 1 and 5000 magnification.

intrinsic material) or the mechanical processing methods used to obtain the investigated

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43

• It is also observed the presence of some impurities on the surface of investigated samples such as Al, Si and Ca elements, Table 2 and Figure 30 for Spectrum 1, but in very small

3.2.1.4. Magnetic nanofluids used for planar microtransformers with circular spiral windings with

Magnetic nanofluids used as the core liquid in the micro-electric transformer obtained by coprecipitation method [27, 35], is a colloidal suspension of nanoparticles of magnetite (Fe3O4), covered with a layer of surfactant oleic acid and dispersed in transformer oil. The main steps in

Spectrum In stats. C O Al Si Ca Mn Fe Zn Total % Spectrum 1 Yes 32.45 27.82 – 0.17 6.99 26.69 5.88 100.00 Spectrum 2 Yes 55.59 21.24 1.18 3.78 2.13 2.92 11.22 1.95 100.00 Spectrum 3 Yes 31.73 28.83 – 0.39 – 6.50 26.67 5.87 100.00 Spectrum 4 Yes 36.77 25.41 – 0.60 – 6.53 25.41 5.28 100.00 Spectrum 5 Yes 33.90 29.16 – 0.60 – 6.19 24.83 5.32 100.00 Spectrum 6 Yes 54.25 10.65 0.16 0.63 0.53 6.15 23.36 4.27 100.00 Spectrum 7 Yes 20.86 28.69 – 0.28 – 8.87 34.09 7.21 100.00

Max. 55.59 29.16 1.18 3.78 2.13 8.87 34.09 7.21 Min. 20.86 10.65 0.16 0.17 0.53 2.92 11.22 1.95

Figure 30. The 3F3 spectra analyze, corresponding to Spectrum 1 and 2000 magnification.

Table 2. Normalized values of elements obtained from spectral analysis of ferrite 3F3, corresponding to Spectrum 1–7,

percentages and they are not likely to jeopardize their functional role.

hybrid core—ferrite and colloidal magnetic nanofluid

Processing option: all elements analyzed (normalized); all results in weight%

piece;

2000 magnification.

Figure 29. Scanning electron microscopy image (SEM) of the 3F3 ferrite, 2000 magnification.


Table 1. Normalized values of elements obtained from spectral analysis of ferrite 3F3, corresponding to Spectrum 1–6, 5000 magnification.


intrinsic material) or the mechanical processing methods used to obtain the investigated piece;

• It is also observed the presence of some impurities on the surface of investigated samples such as Al, Si and Ca elements, Table 2 and Figure 30 for Spectrum 1, but in very small percentages and they are not likely to jeopardize their functional role.
