3.2.1.4. Magnetic nanofluids used for planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid

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


Table 2. Normalized values of elements obtained from spectral analysis of ferrite 3F3, corresponding to Spectrum 1–7, 2000 magnification.

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

• The presence of oxygen in percent more than 20% indicates that the sample contains oxides with various chemical combinations. The compositional distribution of the highlighted elements is relatively uniform, variations being probably due to the surface geometry of the sample (roughness of hundreds of nm) or to a non-uniform distribution of

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

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

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

Std. deviation 4.49 2.28 0.83 2.80 0.77 Max. 25.46 28.91 10.93 42.17 9.13 Min. 12.80 22.63 8.73 34.95 7.00

Spectrum In stats. C O Mn Fe Zn Total % Spectrum 1 Yes 25.46 22.63 9.14 35.20 7.57 100.00 Spectrum 2 Yes 21.64 27.47 8.73 35.16 7.00 100.00 Spectrum 3 Yes 12.80 24.98 10.93 42.17 9.13 100.00 Spectrum 4 Yes 19.72 28.91 8.77 34.95 7.65 100.00 Spectrum 5 Yes 16.97 26.78 9.80 37.90 8.55 100.00 Spectrum 6 Yes 15.95 27.84 9.71 38.17 8.33 100.00 Mean 18.76 26.44 9.51 37.26 8.04 100.00

Processing option: all elements analysed (normalised); all results in weight%

• SEM micrographs have revealed a relatively uniform surface in terms of morphology, but which has a roughness due to the technological methods of obtaining the samples (of the

the carbon matrix (Figure 29);

5000 magnification.

the synthesis procedure for obtaining magnetic nanofluids based on non-polar organic liquids are indicated in [28–30, 35]. To be used as a transformer fluid core, magnetic nanofluid requires good colloidal stability and features adapted to the operating conditions and materials it is in contact with. The magnetic feature is the most important for this application that requires a high saturation magnetization, Figure 31.

The maximum volume fraction was set around 23% and the recommended saturation magnetization values ranging between 500 Gs and 1000 Gs. The quality of magnetic nanofluids (NFM) is related to many details of the synthesis process and their stabilization/dispersion in the base fluid (in our case the UTR40 transformer oil). Among these we mention the coprecipitation temperature, Fe2+ molar ratio to Fe3+, agitation rate, chemisorption temperature, reaction time, and so on. An essential aspect is the complete coverage of NFM with stabilizer and the elimination of the primary non-adsorbed primary surfactant. Repeated flocculation/redispersing NFM's remain coated with the optimal amount of surfactant [34, 35].

#### 3.2.2. Making a miniature planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid: V3

Planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid is used in electronic circuits as a separator transformer in the DC/DC converter in harvesting energy applications. The use of a specific colloidal magnetic nanofluid with high saturation magnetization between 500 Gs and 1000 Gs, as a liquid core as part of the magnetic circuit eliminates all air gaps and also the magnetic field of dispersion. Achieving an improved magnetic coupling is obtained by constructive form of planar coils. Use of symmetrically overlayed ferrite cores, Figure 32, in conjunction with the magnetic nanofluid to the magnetic circuit assembly, determines the extension of the frequency range up to 1000 Mhz, Figure 38. This planar microtransformer, Figures 32 and 36, is made up of a planar coils assembly, a magnetic circuit assembly and a housing assembly. Regarding the planar coils, these respect the same manufacturing technology (Figure 33 and 34).

A. The planar coils assembly

Figure 33. The section through a casing assembly.

ferrite 4a and 4b and colloidal magnetic nanofluid 5.

The planar coils assembly consists of four planar coils, Figures 32 and 34a and Figure 34c, respectively two identical planar coils, 1a and two identical planar coils 1b, each disposed on a glass-textolite plate of 1 mm thickness and diameter in the range 35–45 mm, covered on both sides with a copper layer thickness 35 μm and made by milling with a gap between 0.2–0.5 mm, dimensioned according to the current flow through the planar coils. Each primary planar coil, 1a, is formed of two semi-windings connected in series, double-sided disposed on the same glass-textolite plate. The two semi-windings each have 20 turns made by milling on the glass-textolite plate. Then the two semi-windings are inserted between them resulting in a primary coil 1a. Each secundary planar coil, Figures 34a and 34c, 1b, is formed of two semiwindings connected in series, double-sided disposed on the same glass-textolite plate. Also,

Figure 32. The section through a planar microtransformer with circular spiral windings 1a and 1b, with hybrid core—

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Figure 31. The first magnetization curve for analyzed NMF-UTR40-1000G and NMF-UTR40-500G samples (NMF-UTR40-1000G with Ms. = 78.61 kA/m and NMF-UTR40-500G with Ms. = 40.51 kA/m) [34].

Figure 32. The section through a planar microtransformer with circular spiral windings 1a and 1b, with hybrid core ferrite 4a and 4b and colloidal magnetic nanofluid 5.

Figure 33. The section through a casing assembly.

#### A. The planar coils assembly

the synthesis procedure for obtaining magnetic nanofluids based on non-polar organic liquids are indicated in [28–30, 35]. To be used as a transformer fluid core, magnetic nanofluid requires good colloidal stability and features adapted to the operating conditions and materials it is in contact with. The magnetic feature is the most important for this application that requires a

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

The maximum volume fraction was set around 23% and the recommended saturation magnetization values ranging between 500 Gs and 1000 Gs. The quality of magnetic nanofluids (NFM) is related to many details of the synthesis process and their stabilization/dispersion in the base fluid (in our case the UTR40 transformer oil). Among these we mention the coprecipitation temperature, Fe2+ molar ratio to Fe3+, agitation rate, chemisorption temperature, reaction time, and so on. An essential aspect is the complete coverage of NFM with stabilizer and the elimination of the primary non-adsorbed primary surfactant. Repeated flocculation/redispersing NFM's remain coated with the optimal amount of surfactant [34, 35].

3.2.2. Making a miniature planar microtransformers with circular spiral windings with hybrid

these respect the same manufacturing technology (Figure 33 and 34).

UTR40-1000G with Ms. = 78.61 kA/m and NMF-UTR40-500G with Ms. = 40.51 kA/m) [34].

Planar microtransformers with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid is used in electronic circuits as a separator transformer in the DC/DC converter in harvesting energy applications. The use of a specific colloidal magnetic nanofluid with high saturation magnetization between 500 Gs and 1000 Gs, as a liquid core as part of the magnetic circuit eliminates all air gaps and also the magnetic field of dispersion. Achieving an improved magnetic coupling is obtained by constructive form of planar coils. Use of symmetrically overlayed ferrite cores, Figure 32, in conjunction with the magnetic nanofluid to the magnetic circuit assembly, determines the extension of the frequency range up to 1000 Mhz, Figure 38. This planar microtransformer, Figures 32 and 36, is made up of a planar coils assembly, a magnetic circuit assembly and a housing assembly. Regarding the planar coils,

Figure 31. The first magnetization curve for analyzed NMF-UTR40-1000G and NMF-UTR40-500G samples (NMF-

high saturation magnetization, Figure 31.

core—ferrite and colloidal magnetic nanofluid: V3

The planar coils assembly consists of four planar coils, Figures 32 and 34a and Figure 34c, respectively two identical planar coils, 1a and two identical planar coils 1b, each disposed on a glass-textolite plate of 1 mm thickness and diameter in the range 35–45 mm, covered on both sides with a copper layer thickness 35 μm and made by milling with a gap between 0.2–0.5 mm, dimensioned according to the current flow through the planar coils. Each primary planar coil, 1a, is formed of two semi-windings connected in series, double-sided disposed on the same glass-textolite plate. The two semi-windings each have 20 turns made by milling on the glass-textolite plate. Then the two semi-windings are inserted between them resulting in a primary coil 1a. Each secundary planar coil, Figures 34a and 34c, 1b, is formed of two semiwindings connected in series, double-sided disposed on the same glass-textolite plate. Also,

Figure 34. (a) Planar coil, (b) magnetic ferrite cores and (c) arrangement of planar coils in ferrite cores, practical achievements.

the two semi-windings each have 20 turns made by milling on the glass-textolite plate. Then the two semi-windings are inserted between them resulting in a secundary coil 1b. All coils are isolated from each other by three insulation, 2, of 0.1 mm thick made of "hostaphan" (polyethylene terephthalate), Figure 12. The planar coils assembly are fixed relative to the two upper 4a and lower 4b magnetic cores by means of two spacers 3a and 3b made of glass-textolite, Figure 32.

#### B. The magnetic circuit assembly

The magnetic circuit assembly consists of: two magnetic cores, top 4a and bottom 4b, 3F3 of the "pot" type, identical from ferrite, symmetrically overlapping according to Figures 32 and 34b; a liquid core consisting of a magnetic nanofluid, 5, Figure 32 in which are immersed the planar coil assembly and the two magnetic cores 4a and 4b Figure 34 C, placed in the casing assembly. The role of a liquid core made of a magnetic nanofluid as part of the magnetic circuit, eliminates all air gaps and also the magnetic field of dispersion. The most important magnetic feature for this usage is high saturation magnetization, between 500 Gs and 1000 Gs, Figure 31. Volume fraction (the ratio between the volume of magnetite nanoparticles and the volume of the entire magnetic nanofluid) corresponding to this saturation magnetization is in the range of 22–24%.

with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid, practical achievements. The casing assembly, Figures 32 and 33 consists of the box 6 and the lid 7, both made by duralumin, the gasket 8 and the central screw 9, which is fixing the magnetic circuit and the planar coils with the box 6. The lid 7 contains the plate with terminals 10, the system of the magnetic nanofluid supply 11 (made by a supply nozzle 12, by a nozzle

Figure 36. The planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic

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As I have shown, by using a specific magnetic nanofluid with high saturation magnetization, ranging between 500 Gs and 1000 Gs, as a liquid core of a magnetic circuit, the air gaps and the dispersive magnetic field lines are removed. Thus, magnetic nanofluid is used both as a coolant and as part of the hybrid magnetic core. Also, an improved magnetic coupling by up to 10% is noticed, together with an increase of the overall efficiency by up to 5%. As we will see below, experimental measurements in dinamic mode proves extension of the frequency range up to 1000 MHz, by symmetrical superposition of the ferrite magnetic cores in conjunction

lid 13 and a nozzle gasket 14), fixing screws 15 and four location screws 16.

with the specific magnetic nanofluid.

nanofluid, practical achievements.

Figure 35. Parts of the casing assembly.

#### C. The casing assembly

The casing assembly, Figure 35, in which are immersed in magnetic nanofluid both the planar coils assembly and the magnetic circuit assembly. Figure 36 shows a planar microtransformer

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Figure 35. Parts of the casing assembly.

the two semi-windings each have 20 turns made by milling on the glass-textolite plate. Then the two semi-windings are inserted between them resulting in a secundary coil 1b. All coils are isolated from each other by three insulation, 2, of 0.1 mm thick made of "hostaphan" (polyethylene terephthalate), Figure 12. The planar coils assembly are fixed relative to the two upper 4a and lower 4b magnetic cores by means of two spacers 3a and 3b made of glass-textolite,

Figure 34. (a) Planar coil, (b) magnetic ferrite cores and (c) arrangement of planar coils in ferrite cores, practical achieve-

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

The magnetic circuit assembly consists of: two magnetic cores, top 4a and bottom 4b, 3F3 of the "pot" type, identical from ferrite, symmetrically overlapping according to Figures 32 and 34b; a liquid core consisting of a magnetic nanofluid, 5, Figure 32 in which are immersed the planar coil assembly and the two magnetic cores 4a and 4b Figure 34 C, placed in the casing assembly. The role of a liquid core made of a magnetic nanofluid as part of the magnetic circuit, eliminates all air gaps and also the magnetic field of dispersion. The most important magnetic feature for this usage is high saturation magnetization, between 500 Gs and 1000 Gs, Figure 31. Volume fraction (the ratio between the volume of magnetite nanoparticles and the volume of the entire magnetic nanofluid) corresponding to this saturation magnetization is in the range

The casing assembly, Figure 35, in which are immersed in magnetic nanofluid both the planar coils assembly and the magnetic circuit assembly. Figure 36 shows a planar microtransformer

Figure 32.

ments.

of 22–24%.

C. The casing assembly

B. The magnetic circuit assembly

Figure 36. The planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid, practical achievements.

with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid, practical achievements. The casing assembly, Figures 32 and 33 consists of the box 6 and the lid 7, both made by duralumin, the gasket 8 and the central screw 9, which is fixing the magnetic circuit and the planar coils with the box 6. The lid 7 contains the plate with terminals 10, the system of the magnetic nanofluid supply 11 (made by a supply nozzle 12, by a nozzle lid 13 and a nozzle gasket 14), fixing screws 15 and four location screws 16.

As I have shown, by using a specific magnetic nanofluid with high saturation magnetization, ranging between 500 Gs and 1000 Gs, as a liquid core of a magnetic circuit, the air gaps and the dispersive magnetic field lines are removed. Thus, magnetic nanofluid is used both as a coolant and as part of the hybrid magnetic core. Also, an improved magnetic coupling by up to 10% is noticed, together with an increase of the overall efficiency by up to 5%. As we will see below, experimental measurements in dinamic mode proves extension of the frequency range up to 1000 MHz, by symmetrical superposition of the ferrite magnetic cores in conjunction with the specific magnetic nanofluid.

3.2.2.1. Experimental measurements on the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid

#### A. Experimental measurements performed in static mode

Static mode measurements have been made with the bridge "Precision LCR Agilent E 4980A" for the microtransformer without magnetic nanofluid as well as for the microtransformer with hybrid core—ferrite and colloidal magnetic nanofluid with 500 Gs saturation magnetization, for a frequency variation in the range of 100–300 kHz (Figure 36).

Number of turns of the primary coil are N1 = 80 turns and number of turns of the secondary coil are N2 = 80 turns, (separator transformer). The bridge "Precision LCR Agilent E 4980A" it is used with option LEVEL = 2 V.

Analyzing the results obtained, synthesized in Tables 3 and 4, following conclusions are resulted:


In order to perform experimental measurements in dynamic mode, the transformer is connected in an electronic circuit diagram as shown in Figure 37. The Arbitrary Waveform Generator FLUKE PM 5138A was set to provide an excitation signal with a rectangular


waveform, with features: the amplitude 10 V peak-to-peak, duty cycle k = 50% and frequency in the range of f = 100 to 1000 kHz. In Blue, at the bottom, Figure 18, the waveform capture of the arbitrary function generator is highlighted. Also, the output (secondary winding) waveforms capture in yellow, at the top is highlighted, Figure 38. Both waveforms captures are

Figure 37. Electronic circuit diagram for testing the planar microtransformer with circular spiral windings with hybrid

The waveforms capture results for the frequency in the range of f = 100 to 1000 kHz can be concluded as shown in Figure 38a–h. These shows a good behavior of the planar microtransformer

achieved with a digital oscilloscope Tektronix TDS 2014B.

core—ferrite and colloidal magnetic nanofluid, on dynamic mode.

Measured parameters for primary coil in the case with presence of magnetic nanofluid

Measured parameters for secondary coil in the case with presence of magnetic nanofluid

UTR40-500G type.

Frequency 100 kHz 150 kHz 200 kHz 250 kHz 300 kHz Lp<sup>1</sup> [mH] 3.23 1.725 1.1 0.79 0.614 D<sup>1</sup> [] 4.34 3.30 2.64 2.21 1.92 Q<sup>1</sup> [] 0.23 0.3 0.38 0.45 0.52 G<sup>1</sup> [mS] 2.13 2.03 1.91 1.78 1.65 Rp<sup>1</sup> [Ω] 470 492 522 560 602 Rdc<sup>1</sup> [Ω] 10.62 10.62 10.62 10.62 10.62

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Lp<sup>2</sup> [mH] 1.9 1.09 0.782 0.635 0.555 D<sup>2</sup> [] 2.143 1.54 1.22 1.024 0.89 Q<sup>2</sup> [] 0.46 0.64 0.81 0.97 1.11 G<sup>2</sup> [mS] 1.788 1.5 1.246 1.029 0.859 Rp<sup>2</sup> [Ω] 559 664 802.54 971 1160 Rdc<sup>2</sup> [Ω] 10.8 10.8 10.8 10.8 10.8

Table 4. Measured parameters for primary and secondary coil in the case with presence of the magnetic nanofluid, NMF-

Table 3. Measured parameters for primary and secondary coil in the case if not magnetic nanofluid.


3.2.2.1. Experimental measurements on the planar microtransformer with circular spiral windings

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

Static mode measurements have been made with the bridge "Precision LCR Agilent E 4980A" for the microtransformer without magnetic nanofluid as well as for the microtransformer with hybrid core—ferrite and colloidal magnetic nanofluid with 500 Gs saturation magnetization,

Number of turns of the primary coil are N1 = 80 turns and number of turns of the secondary coil are N2 = 80 turns, (separator transformer). The bridge "Precision LCR Agilent E 4980A" it

Analyzing the results obtained, synthesized in Tables 3 and 4, following conclusions are

• in the presence of magnetic nanofluid, the quality factor for the primary planar coil as well

In order to perform experimental measurements in dynamic mode, the transformer is connected in an electronic circuit diagram as shown in Figure 37. The Arbitrary Waveform Generator FLUKE PM 5138A was set to provide an excitation signal with a rectangular

Frequency 100 kHz 150 kHz 200 kHz 250 kHz 300 kHz Lp<sup>1</sup> [mH] 3.672 2.129 1.378 0.981 0.75 D<sup>1</sup> [] 4.45 3.743 3.117 2.647 2.3 Q<sup>1</sup> [] 0.23 0.27 0.32 0.38 0.44 G<sup>1</sup> [mS] 1.92 1.865 1.793 1.712 1.624 Rp<sup>1</sup> [Ω] 520 536.32 557.58 584.25 615.78 Rdc<sup>1</sup> [Ω] 10.64 10.64 10.64 10.64 10.64

Lp<sup>2</sup> [mH] 2.89 1.615 1.051 0.764 0.600 D<sup>2</sup> [] 3.292 2.6 2.091 1.739 1.488 Q<sup>2</sup> [] 0.3 0.38 0.48 0.57 0.67 G<sup>2</sup> [mS] 1.8 1.705 1.581 1.448 1.314 Rp<sup>2</sup> [Ω] 553.5 586.64 632.47 690.75 761 Rdc<sup>2</sup> [Ω] 10.8 10.8 10.8 10.8 10.8

Table 3. Measured parameters for primary and secondary coil in the case if not magnetic nanofluid.

as the quality factor for the secondary planar coil increases significantly;

• there is a better frequency behavior in the presence of magnetic nanofluid.

with hybrid core—ferrite and colloidal magnetic nanofluid

is used with option LEVEL = 2 V.

resulted:

A. Experimental measurements performed in static mode

for a frequency variation in the range of 100–300 kHz (Figure 36).

• Experimental measurements performed on dynamic mode

Measured parameters for primary coil in the case if not magnetic nanofluid

Measured parameters for secondary coil in the case if not magnetic nanofluid

Table 4. Measured parameters for primary and secondary coil in the case with presence of the magnetic nanofluid, NMF-UTR40-500G type.

Figure 37. Electronic circuit diagram for testing the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid, on dynamic mode.

waveform, with features: the amplitude 10 V peak-to-peak, duty cycle k = 50% and frequency in the range of f = 100 to 1000 kHz. In Blue, at the bottom, Figure 18, the waveform capture of the arbitrary function generator is highlighted. Also, the output (secondary winding) waveforms capture in yellow, at the top is highlighted, Figure 38. Both waveforms captures are achieved with a digital oscilloscope Tektronix TDS 2014B.

The waveforms capture results for the frequency in the range of f = 100 to 1000 kHz can be concluded as shown in Figure 38a–h. These shows a good behavior of the planar microtransformer

with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid. Thereby, it results in the possibility of using this type of transformer in DC/DC converters, for applications

Figure 40. DC/DC converters, practical achievements for applications such as energy harvesting made with the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V3.

Figure 39. DC/DC converters, practical achievements for applications such as energy harvesting, made with the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V2.

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As shown in Figures 39 and 40, the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V2 and V3 is used in applications of energy harvesting. Figure 41, the electronic circuit diagram of DC/DC converter, designed

3.2.3. Numerical simulation of the planar transformer with circular spiral windings with hybrid

Variant V4 of the planar transformer corresponds to the DC/DC converters of high active power, that exceeding 100 watts. Choosing a particular type of magnetic nanofluid for a given application is an essential stage in design and can be facilitated by numerical modeling that

such as energy harvesting.

3.2.3.1. CAD design

for energy harvesting applications is shown.

core-Ferrite and colloidal magnetic nanofluid-V4

Figure 38. The waveform capture of the arbitrary function generator at the bottom and the output (secondary winding) waveforms capture at the top is highlighted, for the frequency in the range of f = 100–1000 kHz, from a. to h.

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Figure 39. DC/DC converters, practical achievements for applications such as energy harvesting, made with the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V2.

Figure 40. DC/DC converters, practical achievements for applications such as energy harvesting made with the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V3.

with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid. Thereby, it results in the possibility of using this type of transformer in DC/DC converters, for applications such as energy harvesting.

As shown in Figures 39 and 40, the planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid –V2 and V3 is used in applications of energy harvesting. Figure 41, the electronic circuit diagram of DC/DC converter, designed for energy harvesting applications is shown.

3.2.3. Numerical simulation of the planar transformer with circular spiral windings with hybrid core-Ferrite and colloidal magnetic nanofluid-V4

#### 3.2.3.1. CAD design

Figure 38. The waveform capture of the arbitrary function generator at the bottom and the output (secondary winding)

waveforms capture at the top is highlighted, for the frequency in the range of f = 100–1000 kHz, from a. to h.

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

Variant V4 of the planar transformer corresponds to the DC/DC converters of high active power, that exceeding 100 watts. Choosing a particular type of magnetic nanofluid for a given application is an essential stage in design and can be facilitated by numerical modeling that uses quantitative estimates of material properties (magnetoreological, thermal, magnetic, electrical, etc.) for the validation of numerical models used in designing and evaluating the behavior of the planar transformer. The evaluation of the magnetic flux inside the planar transformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid is done for two propose magnetic nanofluid, NMF-UTR40-50G and NMF-UTR40- 500G, whose magnetization at saturation is of 50 Gs and 500 Gs respectively. Mathematical models and numerical simulation are defined, under stationary hypothesis, by the finite element (FEM) technique [38, 39]. The computational domain was constructed by CAD

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Also, the details of the primary and secondary windings profiles are shows in Figures 43 and 44. To reduce the complexity of the model and the computational efforts, some elements (e.g. between layers, supports, etc.) have been excluded from the computational domain.

methods, based on the design dimensions of the transformer, Figure 42.

Figure 43. Details of the primary windings profiles.

Figure 44. Details of the secondary winding profiles.

Figure 45. The discretization network (mesh) of the transformer, numerical model.

Figure 41. Electronic circuit diagram of DC/DC converter, designed for energy harvesting applications, made of LM22517 Texas Instruments and planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid [33, 36, 37].

Figure 42. The CAD design and computational domain of the transformer submerged in magnetic nanofluid NMF-UTR40-50G or NMF-UTR40-500G.

models and numerical simulation are defined, under stationary hypothesis, by the finite element (FEM) technique [38, 39]. The computational domain was constructed by CAD methods, based on the design dimensions of the transformer, Figure 42.

Also, the details of the primary and secondary windings profiles are shows in Figures 43 and 44. To reduce the complexity of the model and the computational efforts, some elements (e.g. between layers, supports, etc.) have been excluded from the computational domain.

Figure 43. Details of the primary windings profiles.

uses quantitative estimates of material properties (magnetoreological, thermal, magnetic, electrical, etc.) for the validation of numerical models used in designing and evaluating the behavior of the planar transformer. The evaluation of the magnetic flux inside the planar transformer with circular spiral windings with hybrid core—ferrite and colloidal magnetic nanofluid is done for two propose magnetic nanofluid, NMF-UTR40-50G and NMF-UTR40- 500G, whose magnetization at saturation is of 50 Gs and 500 Gs respectively. Mathematical

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

Figure 41. Electronic circuit diagram of DC/DC converter, designed for energy harvesting applications, made of LM22517 Texas Instruments and planar microtransformer with circular spiral windings with hybrid core—ferrite and colloidal

Figure 42. The CAD design and computational domain of the transformer submerged in magnetic nanofluid NMF-

magnetic nanofluid [33, 36, 37].

UTR40-50G or NMF-UTR40-500G.

Figure 44. Details of the secondary winding profiles.

Figure 45. The discretization network (mesh) of the transformer, numerical model.

Figure 46. The spectra of electric field in the primary planar copper winding by colored boundary map in volts.

The problem is solved by the Galerkin finite element (FEM) technique. A discretization network consisting of 850,000, tetrahedral, quadratic Lagrange elements was generated automatically to model the field, Figure 45.

#### 3.2.3.2. Mathematical model

The magnetic field source, the electrical currents in the windings, must be known. Therefore, an electrokinetic field analysis is defined by the partial differential equation (PDE). Firstly, the magnetic field source as well as the electrical currents in the windings must be known. Therefore, an electrokinetic field analysis is defined by the partial differential equation, (14), (15), (16) and (17),

$$\nabla\_{\mathbf{t}} \cdot d(\sigma \nabla\_{\mathbf{t}} V) = dQ\_{\mathbf{j}} \tag{14}$$

<sup>∇</sup> � <sup>μ</sup>�<sup>1</sup>

where A [T�m] is the magnetic vector potential, Js

m/A for NMF-UTR40-500G).

working conditions of the transformer are considered.

density of the shell (Js

<sup>β</sup> = 1.5�10�<sup>5</sup>

<sup>β</sup> = 2.5 � <sup>10</sup>�<sup>5</sup>

3.2.3.3. Numerical simulation results

<sup>0</sup> <sup>μ</sup>�<sup>1</sup>

magnetization in the magnetic nanofluid, approximated by the analytic formula [40],

permeability of free space, and μ<sup>r</sup> is the relative permeability. For the 3CP90 ferrite core μ<sup>r</sup> = 1720 and for the copper windings and the free space μ<sup>r</sup> = 1. Also, M [A/m] is the

here H [A/m] is the magnetic field strength, and α, β are empiric constants selected to fit the experimental magnetization characteristic of the magnetic nanofluid (α = 3050 A/m and

An iterative flexible generalized minimum residual solver (FGREMS) was used to solve the mathematical model (5), (6), (7) and (8). Figures 46 and 47 present the electric field in the windings by voltage boundary color map, boundary conditions were chosen for nominal

Figure 47. The spectra of electric field in the secondary planar copper winding by colored boundary map in volts.

m/A for the NMF-UTR40-50G, respectively, <sup>α</sup> = 4.85 � 104

<sup>r</sup> <sup>∇</sup> � <sup>A</sup> � <sup>M</sup> <sup>¼</sup> <sup>0</sup>, (16)

New Energy Harvesting Systems Based on New Materials

<sup>M</sup> <sup>¼</sup> <sup>α</sup> arctan <sup>β</sup><sup>H</sup> , (17)

] is the external electric current

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A/m and

55

<sup>e</sup> [A/m<sup>2</sup>

<sup>e</sup> 6¼ 0 inside the planar coils), <sup>μ</sup><sup>0</sup> = 4<sup>π</sup> � <sup>10</sup>�<sup>7</sup> [H/m] is the magnetic

where <sup>σ</sup> [S/m] is the electrical conductivity, Qj [W/m<sup>3</sup> ] is an external current source and d [m] is the thickness of the shell. The operator ∇<sup>t</sup> represents the tangential derivative along the shell [40]. The stationary magnetic field is computed by solving [38–40], for the copper windings and free space

$$\nabla \times \left(\mu\_0^{-1} \mu\_r^{-1} \nabla \times \mathbf{A}\right) = \mathbf{J}\_\mathbf{s}^{\varepsilon} \tag{15}$$

for the magnetic fluid

New Energy Harvesting Systems Based on New Materials http://dx.doi.org/10.5772/intechopen.72613 55

$$\nabla \times \left( \mu\_0^{-1} \mu\_r^{-1} \nabla \times \mathbf{A} - \mathbf{M} \right) = 0,\tag{16}$$

where A [T�m] is the magnetic vector potential, Js <sup>e</sup> [A/m<sup>2</sup> ] is the external electric current density of the shell (Js <sup>e</sup> 6¼ 0 inside the planar coils), <sup>μ</sup><sup>0</sup> = 4<sup>π</sup> � <sup>10</sup>�<sup>7</sup> [H/m] is the magnetic permeability of free space, and μ<sup>r</sup> is the relative permeability. For the 3CP90 ferrite core μ<sup>r</sup> = 1720 and for the copper windings and the free space μ<sup>r</sup> = 1. Also, M [A/m] is the magnetization in the magnetic nanofluid, approximated by the analytic formula [40],

$$M = \alpha \arctan(\beta H),\tag{17}$$

here H [A/m] is the magnetic field strength, and α, β are empiric constants selected to fit the experimental magnetization characteristic of the magnetic nanofluid (α = 3050 A/m and <sup>β</sup> = 1.5�10�<sup>5</sup> m/A for the NMF-UTR40-50G, respectively, <sup>α</sup> = 4.85 � 104 A/m and <sup>β</sup> = 2.5 � <sup>10</sup>�<sup>5</sup> m/A for NMF-UTR40-500G).

#### 3.2.3.3. Numerical simulation results

The problem is solved by the Galerkin finite element (FEM) technique. A discretization network consisting of 850,000, tetrahedral, quadratic Lagrange elements was generated automat-

Figure 46. The spectra of electric field in the primary planar copper winding by colored boundary map in volts.

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

The magnetic field source, the electrical currents in the windings, must be known. Therefore, an electrokinetic field analysis is defined by the partial differential equation (PDE). Firstly, the magnetic field source as well as the electrical currents in the windings must be known. Therefore, an electrokinetic field analysis is defined by the partial differential equation, (14), (15), (16) and (17),

the thickness of the shell. The operator ∇<sup>t</sup> represents the tangential derivative along the shell

∇<sup>t</sup> � dð Þ¼ σ∇tV dQj (14)

e

] is an external current source and d [m] is

, (15)

ically to model the field, Figure 45.

for the copper windings and free space

for the magnetic fluid

where <sup>σ</sup> [S/m] is the electrical conductivity, Qj [W/m<sup>3</sup>

[40]. The stationary magnetic field is computed by solving [38–40],

<sup>∇</sup> � <sup>μ</sup>�<sup>1</sup>

<sup>0</sup> <sup>μ</sup>�<sup>1</sup> <sup>r</sup> <sup>∇</sup> � <sup>A</sup> <sup>¼</sup> Js

3.2.3.2. Mathematical model

An iterative flexible generalized minimum residual solver (FGREMS) was used to solve the mathematical model (5), (6), (7) and (8). Figures 46 and 47 present the electric field in the windings by voltage boundary color map, boundary conditions were chosen for nominal working conditions of the transformer are considered.

Figure 47. The spectra of electric field in the secondary planar copper winding by colored boundary map in volts.

The current shell density resulting from the electric field problem is used to solve the magnetic field problem in the transformer. Figure 48 shows the magnetic field in the transformer submerged in the magnetic nanofluid NMF-UTR40-50G through field lines for different

powering alternatives: (a) both windings are "ON", the currents are in opposite directions – differential magnetic fluxes, (b) primary winding is "ON" and secondary winding is "OFF"

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57

The magnetic field simulation result indicates that the fascicular magnetic field lines close mainly through the ferrite core, which offers a lower reluctance path than the magnetic nanofluid. In Figure 49 the flux inside the solid ferrite core is presented by color map of

The magnetic field problem was solved also for the NMF-UTR40-500G magnetic nanofluid which has higher saturation limit, Figure 50 shows the magnetic flux density (tubes) for

Figure 50. Magnetic flux density (tubes) for different powering schemes (NMF-UTR40-500G magnetic nanofluid).

and (c) primary winding is "OFF" and secondary winding is "ON".

different powering schemes.

normalized magnetic induction, B, as well as the lines of magnetic field density.

Figure 48. Magnetic flux density (tubes) for different powering schemes (NMF-UTR40-50G magnetic nanofluid).

Figure 49. Normalized magnetic induction, by boundary color map, and tubes of magnetic flux density.

powering alternatives: (a) both windings are "ON", the currents are in opposite directions – differential magnetic fluxes, (b) primary winding is "ON" and secondary winding is "OFF" and (c) primary winding is "OFF" and secondary winding is "ON".

The current shell density resulting from the electric field problem is used to solve the magnetic field problem in the transformer. Figure 48 shows the magnetic field in the transformer submerged in the magnetic nanofluid NMF-UTR40-50G through field lines for different

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

Figure 48. Magnetic flux density (tubes) for different powering schemes (NMF-UTR40-50G magnetic nanofluid).

Figure 49. Normalized magnetic induction, by boundary color map, and tubes of magnetic flux density.

The magnetic field simulation result indicates that the fascicular magnetic field lines close mainly through the ferrite core, which offers a lower reluctance path than the magnetic nanofluid. In Figure 49 the flux inside the solid ferrite core is presented by color map of normalized magnetic induction, B, as well as the lines of magnetic field density.

The magnetic field problem was solved also for the NMF-UTR40-500G magnetic nanofluid which has higher saturation limit, Figure 50 shows the magnetic flux density (tubes) for different powering schemes.

Figure 50. Magnetic flux density (tubes) for different powering schemes (NMF-UTR40-500G magnetic nanofluid).

and also to Dr. Elena Chitanu, researcher at National Institute for Electrical Engineering ICPE-CA, Bucharest, Romania, for valuable results concerning the development of technologies to obtain ZnO nanostructured materials. The research was performed with the support of UEFISCDI, PNCDI II Programme – Joint Applied Research Projects, Romania, Contract 63/ 2014, "Environment energy harvesting hybrid system by photovoltaic and piezoelectric con-

New Energy Harvesting Systems Based on New Materials

http://dx.doi.org/10.5772/intechopen.72613

59

Lp1 inductance of the primary coil, corresponding to an equivalent Lp1 – Rp1 pattern

Lp2 inductance of the secondary coil, corresponding to an equivalent Lp2 – Rp2 pattern

G1 conductivity (1/Rp1) of the primary coil, corresponding to an equivalent Lp1 – Rp1

G2 conductivity (1/Rp2) of the secondary coil, corresponding to an equivalent Lp2 – Rp2

Rp1 the resistance of the primary coil, corresponding to an equivalent Lp1 – Rp1 pattern

Rp2 the resistance of the secondary coil, corresponding to an equivalent Lp2 – Rp2 pattern

\* and Lipan Laurențiu Constantin<sup>2</sup>

1 National Institute for Electrical Engineering ICPE-CA, Bucharest, Romania

version, DC/DC transformation with MEMS integration and adaptive storage".

Nomenclature

disposed in parallel;

disposed in parallel;

Q1 Quality factor for the primary coil; Q2 Quality factor for the secondary coil;

pattern disposed in parallel;

pattern disposed in parallel;

Rdc1 the resistance of the primary coil measured in DC; Rdc2 the resistance of the secondary coil measured in DC.

\*Address all correspondence to: lucian.pislaru@icpe-ca.ro

2 University Politehnica of Bucharest, Bucharest, Romania

disposed in parallel;

disposed in parallel;

Author details

Lucian Pîslaru-Dănescu1

D1 tangent of the loss angle for the primary coil; D2 tangent of the loss angle for the secondary coil;

Figure 51. Planar coil corresponding to primary and secondary coils, practical achievements.

Figure 52. Planar transformer with planar windings with hybrid core—ferrite and colloidal magnetic nanofluid—V4, practical achievements.

The result indicates insignificant differences between the two types of magnetic nonfluids in terms of the magnetic flux distribution inside the fluid part of the magnetic core. However, because of the higher saturation limit, the NMF-UTR40-500G it is expected to perform better in higher power applications. For different models, the numerical investigations was performed under steady state conditions, to estimate the lumped parameters of the transformer and to evaluate the thermal behavior [41].

Figure 51 shows the planar coil corresponding to primary and secondary coils, practical achievements, for V4 variant of planar transformer. Also, Figure 52 shows the practical achievement of the planar transformer with planar windings with hybrid core—ferrite and colloidal magnetic nanofluid—V4 variant.

## Acknowledgements

The authors express special thanks to Dr. Jean Bogdan Dumitru, researcher at University Politehnica of Bucharest, Romania, for valuable results concerning the numerical simulations and also to Dr. Elena Chitanu, researcher at National Institute for Electrical Engineering ICPE-CA, Bucharest, Romania, for valuable results concerning the development of technologies to obtain ZnO nanostructured materials. The research was performed with the support of UEFISCDI, PNCDI II Programme – Joint Applied Research Projects, Romania, Contract 63/ 2014, "Environment energy harvesting hybrid system by photovoltaic and piezoelectric conversion, DC/DC transformation with MEMS integration and adaptive storage".
