Flyback Micro-Converter Design with an Integrated Octagonal Micro-Transformer for DC-DC Conversion

.co.in Flyback Micro-Converter Design with an Integrated ░ ABSTRACT - The work presented in this paper concerns the design of an integrated flyback DC-DC micro-converter operating at high frequencies. The flyback converter consists of only one transformer. The integrated micro-transformer in the flyback micro-converter is composed of two planar stacked coils with spiral octagonal geometry. Basing on Mohan’s method, the geometrical parameters are evaluated. The different parasitic effects created in the stacked layers are grouped perfectly in the equivalent electrical circuit that summarizes all parasitic effects. The integrated micro-transformer is characterized by scattering parameters extraction. The thermal and electromagnetic effects generated in the micro-transformer are illustrated, using finite elements method on COMSOL Multiphysics 5.3 software. To validate the electrical model, the simulation of the flyback micro-converter containing the equivalent electrical circuit of the micro-transformer is established, using PSIM 9.0 software. The gap between the coils is considered as an integrated MIM capacitor created at high frequencies leads to create a low pass micro-filter with the secondary coil.

The objective of the integration of passive components is to make the converter fully integrated and stand-alone.The majority of surface is occupied by discrete passive components.To overcome this problem, the integrated components were introduced [1][2].Planar micro-transformers are currently extensively used in integrated circuits in many systems for several RF applications [3][4].The integration allows to compact the small size components with better efficiency and low fabrication costs [5][6].The easier technique for reducing sizes is to increase the operating frequency.Increasing the frequency has an impact for inductive components as the inductance, the size and the current.At high frequencies, inductive components can have a smaller size and hence smaller inductance [7][8].Many researchers presented various studies that aim to integrate the micro-transformer in the micro-converter.[9][10] presented the design and modeling of an octagonal planar inductor and transformer for integration into a converter.They performed an electromagnetic and thermal simulation.[11][12] presented a numerical simulation study of the magneto-thermal behavior allowing for an improved design of a square planar coil sandwiched between two magnetic materials.[13][14] presented a method of dimensioning a square spiral planar coil integrated in high voltage converter application a photovoltaic.They visualized the density of the magnetic flux and the electric potential.[15][16] developed a numerical model to determine the inductances of an elliptical planar transformer and its parasitic components.They demonstrated that the overall average error between the measured and proposed numerical model results was less than 5%.[17] presented a dimensioning and thermal modelling of a multilayer capacitor at low temperature cofired ceramic intended to be inserted in a low voltage converter.[18] performed a detailed study for designing an integrated structure with a dual-layer microtransformer model associated with two layers of magnetic cores.Their research focused the impact of thickness of a planar coil on the inductance value.[19] numerically visualized by the finite element method the thermal behavior of an integrated transformer operating in a DC-DC micro converter.They determined the operating temperature in the different layers of the component in the transient and stationary state.The aim of our work is the design of a DC-DC microconverter containing an octagonal planar spiral microtransformer.The micro-converter is operating for low powers and high frequencies.The micro-transformer is composed of two stacked coils of three and two turns of primary and secondary respectively.The dimensioning of different geometric and electric parameters is required to integrate the micro-transformer in the micro-converter.The geometric parameters describe the sizes of the coils and the different layer added in the micro-transformer and the electric parameters describe the different parasitic effects generated in the different layers due to the high frequency.Using the finite elements method allows to show the thermal and

░ 2. FLYBACK MICRO-CONVERTER PRESENTATION
The converter is the main step of the design and dimensioning of passive components.We have opted for a flyback DC-DC converter figure 1 for it contains just one transformer.The Flyback operation is based on the energy transfer from primary to secondary through a transformer [16].Operating frequency f =1GHz), we calculate the primary and secondary inductances (Lp, Ls) of the micro-transformer and their turn ratio m (Equations 1-3) [16].

░ 3. DIMESONING OF MICRO-TRANSFORMER
In this work, the integrated micro-transformer is composed of two stacked planar coils and their topologies are spiral octagonal figure 2.

Figure 2: Octagonal spiral planar micro-transformer
The octagonal micro-transformer is defined by geometrical parameters.The outer diameter is equal to 500 µm, the angles are equivalent to multiples of 45 degrees.

Primary and secondary turn's number np, ns
We find in literature several expressions that allow us to calculate the turn's number of micro-coils according to the inductance, we opted for Mohan's method [14] (equations [4][5].
Primary and secondary total length ltp, lts N is the number of sides which is 8 in our case.The magnetic core volume (Equation 12) is related to the total magnetic stored energy Wt (Equation 13) and the maximum energy volume density Wvmax (Equation 14).Therefore, 0.050 mm3 of ferrite NiFe is necessary to store 1.2 nJ of energy.(17) tgap is the spacing between primary and secondary coils, relative permittivity of Si3N4 equals to 6.

Primary and secondary substrate capacitance Csubp, Csubs
Relative permittivity of silicon is 11.8

Primary and secondary spacing capacitance Csp, Css
Cs p = ε Si3N4 ⋅ ⌊ Copper resistivity ρCu = 1.7 10−8 Ω⋅m and teff is the effective thickness (Equation 22) [19], δ is the skin thickness (Equation 23), it depends on the frequency figure 4 [19].We observe that the Q factor is smaller when the traces are thinner.For lower frequencies the 60μm wide microtransformer has a better Q-factor and the resonance frequency is close to the operating frequency, however the quality factor of the 40μm wide micro-transformer presents an important resonance frequency.The increase of the Q-factor for thin width traces is compensated by a reduction on the equivalent capacitance, which is related to the surface occupied by the micro-transformer.

░ 6. THERMAL EFFECT IN THE INTEGRATED MICRO-TRANSFORMER
In this section, we show 3D simulations of thermal effects on the integrated micro-transformer.

Mathematical Model
To resolve equation ( 26), we determine the analytical solution for homogeneous problem Th(y,t) and steady-state problem Ts(y), as equation ( 27).
T(y,t) = Th(y,t) + Ts(y) (27) The continuity conditions at the interfaces are given by (28); By resolving the heat equation ( 29) and taking into account certain boundary conditions, we determine the different thermal effects.In figure 12a, we observe the distributed temperature in the micro-transformer alone in the air without the other layers.We observe that the temperature value achieves 110°C in the conductor coils in copper.Figure 12b shows the distributed temperature in the micro-transformer composed of all different layers.We observe that the temperature values decrease to 75°C.Thus, adding the NiFe ferrite, which has a high permeability, for magnetic layer allows to reduce the temperature caused by Joule effect created by the current circulation in the conductor coils.We have compared our results with those from the literature [18][24] and we notice that they are the same.In figure 13, the enthalpy decreases to 4.5 10 4 J/Kg in the coils and it remains confined in the stacked micro-transformer.In figure 14, we observe that the temperature gradient increases and achieves 4 10 6 K/m in the coils.In figure 15, we observe that the total heat flow achieves 0.5 10 6 W/m² in the coils and it increases to 0.2 10 8 W/m² for the entire micro-transformer.
In figure 16, we observe that the heat flow by conduction achieves 0.25 10 6 W/m² in the coils and it increases to 0.3 10 8 W/m² for the entire micro-transformer.

░ 7. ELECTROMAGNETIC EFFECT IN THE INTEGRATED MICRO-TRANSFORMER
In this section, we show 3D simulations of electromagnetic effect on the integrated micro-transformer.

Mathematical Model
The electromagnetic effects are obtained by resolving Maxwell's electromagnetism equations [22][23][24][25] which link the electrical effect to the magnetic effect.The electrical effect is characterized by the displacement field D, the electric field E, the current density J and the density of free electric charges .The magnetic effect is characterized by both the magnetic induction B and the magnetic field H (Equations 30 to 33).

Visualization of the Electromagnetic Behavior
Using Comsol Multiphysics 5.3 software and basing on finite elements method, we present the electromagnetic effects in the micro-transformer.For a good precision, we choose the extremely fine mesh.Figure 19a shows the distribution of the magnetic field lines in the micro-transformer.We observe that there is an overflow of the magnetic field lines in all directions in the microtransformer in the air and the lines occupy all the space limited by the simulator boundaries.Therefore, this distribution can make trouble of the nearby components in the circuit.In figure 19b, we observe that the overflow of the magnetic field lines is limited by the magnetic layer in NiFe ferrite thanks to its high permeability.Therefore, it restricts to disturb the nearby components in the same circuit.
In figure 20, we observe that the stack of the spiral planar coils on the ferrite layers allows to confine the power flow in the micro-transformer and avoids to lose the storage energy.The values are close to the main parameters (Vout = 5 V and Iout = 1A) of the DC-DC flyback micro-converter.This deline is due to the magnetic core losses in ferrite layers, the Joule losses in conductor coils, the capacitive losses between coils and also to the voltage drop across the transistor and diode.The primary coil V1 acheives 12 V and the secondary V2 is about 5 V.When the transistor is closed, the primary is directly connected to the input voltage source and the primary current increases storing energy in the magnetic layer of micro-transformer.When the transistor is opened, the diode become forward and the secondary allows the current to flow from the micro-transformer.The results confirm that microconverter operates correctly and the dimensioning of the micro-transformer is well done.

Flyback Micro-Converter Efficiency
Efficiency ƞ calculated by equation 42 represents the ratio of the output and input power of the micro-converter [14][15][16][17][18].In figure 37, we notice that the output power 5 W of the DC-DC flyback micro-converter, containing the integrated microtransformer, corresponds to an efficiency of 76.5%.Therefore, the micro-transformer dimensioning results are compatible with the integration in electronics and they are in accordance with the literature [19][26].

Integration of the load capacitance
To fully integrate the flyback micro-converter, we can consider the micro-transformer coupling capacitance as the load capacitance of the micro-converter figure 38.The capacitor is located between metal spiral layers.It is considered as an integrated MIM (Metal-Insulator-Metal) capacitor.We compared between putting the dielectric material or the air between the coils of the micro-transformer.The capacitance is given by equation 43.
The integration of the micro-transformer with the load capacitance of the micro-converter leads to create an integrated component called LCT (Inductor-Capacitance-Transformer).The inductor in this case is created from the leakage inductance [25][26].Figure 39 shows the influence of the gap thickness t gap on the capacitance between the coils of the micro-transformer.We notice that adding the dielectric material allows to increase the capacitance, whereas the air permits to decrease it whatever the gap thickness.Besides, we notice from figure 40 that the increase of the frequency permits to decrease the capacitance.

Low Pass Micro-Filter
The load capacitance C feeds the loads resistance R. these two passive components represent a micro-filter [27][28].Figure 41 shows the frequency response of the integrated micro-filter.We observe that the attenuation achieves 64 dB at the operating frequency 1 GHz.The phase mentions that the cut frequency is also at the operating frequency 1 GHz.Therefore, with the integration of the micro-capacitance, we have obtained a low pass micro-filter.It allows to pass the maximum low frequencies under 1 GHz.

░ 9. CONCLUSION
This paper presents the design of a Flyback DC-DC microconverter containing an integrated spiral planar octagonal micro-transformer.The first considered parameter was the shape of the coils.Octagonal spiral planar is the geometry of the stacked micro-transformer with three and two turns for primary and secondary coils respectively.This work is planned for the application requiring a conversion of energy of low power (5 W) and high frequency (1 GHz).We have fulfilled the geometric dimensioning using the Mohan's method, which is used for planar polygonal shapes and reduced number of turns.We have extracted the different electric parameters of the equivalent electrical circuit, which determines the parasitic effects created in stacked layers and generated at high frequency such as Joule effects losses in the coils, coupling capacitances and induced current in the magnetic substrate layers.The Q factor is an important characteristic for the coil's behavior, it presents the energy dissipation.Thinner coils and larger outer diameter allow to decrease the Q factor.Using finite element method, we have displayed the thermal and electromagnetic effects generated in the micro-transformer to confirm the advantage to use the magnetic core in ferrite.Hence, the insertion of ferrite with high permeability allows to confine the magnetic field lines, to limit the spread of the heat and decease the temperature value in order to avoid to disturb the close components in the integrated circuits.To validate our study, we have integrated the electrical circuit of the micro-transformer into a flyback micro-converter to test the good operation of the component.
The results confirm that micro-converter operates correctly and the efficiency achieves 76.5%.Then, we have integrated the micro-capacitance to obtain a low pass micro-filter and we have concluded that the air is more comfortable than the dielectric materials.We conclude that the simulation results are in accordance with the literature and compatible with the integration in electronics.

Flyback
Micro-Converter Design with an Integrated Octagonal Micro-Transformer for DC-DC Conversion Website: www.ijeer.forexjournal.co.inFlyback Micro-Converter Design with an Integrated electromagnetic effects created in the micro-transformer operating at high frequencies.The addition of a ferrite magnetic material layer shows its importance in the microtransformer.The simulations of the global integrated structure of DC-DC flyback micro-converter with the integrated microtransformer validate the studies and the MIM capacitor allows to create an integrated low pass micro-filter.

Figure 1 :
Figure 1: Electrical circuit of DC-DC flyback converter Our target is to integrate completely the converter and to reduce its sizes.From the main parameters of the DC-DC flyback micro-converter (Input voltage Vin=12V, Output voltage Vout =5V, Duty cycle α=0.5,Output power Pout=5W, Operating frequency f =1GHz), we calculate the primary and secondary inductances (Lp, Ls) of the micro-transformer and their turn ratio m (Equations 1-3) [16].

Figure 5 :Figure 6 :Figure 7 :
Figure 5: Scattering parameters S11, S22 and S21 of on-chip microtransformer As shown in figure 5, the S-parameters are represented in Smith chart.The curves of S11 and S22 display an inductance characterization.S11 shows a nearly short circuit at low frequencies (100 MHz).Therefore, S22 shows a very low impedance over the whole frequency range.The microtransformer has a self-resonance frequency of about 2.3 GHz.The coupling factor k, given by Equation (24)[21], is shown on figure 6 versus frequency.A k-factor of the microtransformer is equal to 0.9 at the operating frequency 1 GHz.

Figure 8 :Figure 8
Figure 8: Quality factor over frequency with different width tracesFigure8illustrates the measurement results with different width.We observe that the Q factor is smaller when the traces are thinner.For lower frequencies the 60μm wide microtransformer has a better Q-factor and the resonance frequency is close to the operating frequency, however the quality factor of the 40μm wide micro-transformer presents an important resonance frequency.The increase of the Q-factor for thin width traces is compensated by a reduction on the equivalent capacitance, which is related to the surface occupied by the micro-transformer.

Figure 9 :Figure 10 :Figure 11 :Figure 12 :
Figure10shows the 3D extremely fine mesh of the integrated micro-transformer in the air and with all different layers.

Figure 13 :Figure 14 :Figure 15 :Figure 16 :
Enthalpy in the micro-transformer: (a) In air, (b) With all layers Temperature gradient in the micro-transformer: (a) In air, (b) With all layers Total heat flow in the micro-transformer: (a) In air, (b) With all layers (a) (b) Heat flow by conduction in the micro-transformer: (a) In air, (b) With all layers

Figure 17 :
: Electric field [V/m], J : Electric current density [A/m²], D ⃗⃗ : Displacement field [c/m²], B ⃗ ⃗ : Magnetic flux density [T], H ⃗⃗ : Magnetic field [A/m], they are then defined by (Equations 34 to 36). ⃗ ⃗ =  ⋅  ⃗ of study area are demonstrated by the normal vectors (Equations 37-38)n x ⋅ J x + n y ⋅ J y + n z ⋅ J z = 0 (37) n x ⋅ A x + n y ⋅ A y + n z ⋅ A z = 0 (38)The reference impedance equals to 50 Ω, the Lorentz force contribution equals to 10 9 N/m², the electrical conductivity in the coils is 3 10 7 S/m figure 17a, the surface current density in the coils is equal to 0.1 10 5 A/m figure 17b, the current density in the coils is equal to 1.5 10 10 A/m² figure 17c and the electromagnetic volume loss density equals to 1.5 10 13 W/m 3 figure 17d.Flyback Micro-Converter Design with an Integrated (a) Electrical conductivity, (b) Surface current density, (c) Current density, (d) Electromagnetic volume loss density, in the spiral coils

Figure 18 :Figure 18 Figure 19 :Figure 20 :
Figure18shows the 3D extremely fine mesh of the integrated micro-transformer in the air and with all different layers

Figure 32 :
Figure 32: Flyback DC-DC micro-converter with the integrated micro-transformer

Figure 34 :Figure 35 :Figure 36 :
Figure 34: Output voltage and current of flyback micro-converter with the integrated micro-transformer

Figure 37 :
Figure 37: Flyback DC-DC micro-converter efficiency versus output power

Figure 39 :
Figure 39: Capacitance between the coils of the micro-transformer versus gap thickness

Figure 40 :
Figure 40: Capacitance between the coils of the micro-transformer versus frequency

Figure 41 :
Figure 41: Attenuation and phase for low pass micro-filter Figure 41 shows the Bode diagram of the attenuation (|S21|) and the phase (/_S21) for the micro-filter versus frequency.We observe that the attenuation achieves 64 dB at the operating frequency 1 GHz.The phase mentions that the cut frequency is also at the operating frequency 1 GHz.Therefore, with the integration of the micro-capacitance, we have obtained a low pass micro-filter.It allows to pass the maximum low frequencies under 1 GHz.