Design and Modeling of an Integrated Micro-Transformer in a Flyback Converter

This paper presents the design and modeling of a square micro-transformer for its integration in a flyback converter. From the specifications of the switching power supply, we determined the geometric parameters of this micro-transformer. The π-electrical model of this micro-transformer highlights all parasitic effects generated by stacking of different material layers and permits to calculate the technological parameters by using the S-parameters. A good dimensioning of the geometrical parameters reduces efficiently the energy losses in the micro-transformer and permits to reach the desirable value of the converter output voltage. We have also simulated the electromagnetic effects with the help of the software FEMLAB3.1 in two cases. The first case, without ferromagnetic core, the second case with ferromagnetic core, in order to choose the micro-transformer that has better electromagnetic compatibility with the vicinity components. To validate dimensioning of the geometrical and technological parameters, we have simulated with the help of the software PSIM6.0, the equivalent electrical circuit of the converter containing the electrical circuit of the dimensioned planar micro-transformer.


Introduction
Since its appearance, power electronics has never ceased to evolve.Currently, this discipline is present in the majority of electrical systems, ensuring control of energy supply and the integrity of the components.Planar micro-transformers are widely used in monolithic integrated circuits; so, new techniques must be developed to reduce the size of elements and reach better efficiency.The monolithic and hybrid integration of power electronic devices pose new research challenges in the coming years.The micro-transformer constitutes an important component of the switching power supply such as the flyback that is the most commonly used for low output power applications where the output voltage needs to be isolated from the input main supply.The output power of flyback circuits may vary from few watts to less than 100 watts.

Presentation Of Flyback Converter
The converter is the starting point of the design of the micro-transformer.We have chosen a flyback converter (figure 1) because it is composed of a transformer and few passive components.The principle of operation of the flyback is based on the energy transfer from primary to secondary through a transformer [1]- [3].The specifications shown as Table 1 and  Table 2 Table 2. Material Specifications

Dimensioning of the Micro-Transformer
By taking into account selected electrical and magnetic characteristics, we evaluate the volume of the magnetic core.This enables us to define the section on which we will put the electrical circuit of the micro-transformer; then we will evaluate the dimensions of this circuit in order to meet the specifications of the converter in terms of magnetic storage of energy and losses in materials.

Dimensioning of the magnetic circuit
Turn ratio The primary inductance L p is calculated for a maximum current undulation α = 0.5: The secondary inductance L s is derived from the relation (2): * The total magnetic energy stored is therefore: Maximum volume density of energy: So, 0.122mm 3 of NiZn is necessary to store 3.125nJ.We have chosen the square form (figure 2) for the windings with outer diameter equal to 1500 µm and inner diameter equal to 750 µm.
Core thickness:

Calculation of the geometrical parameters
The planar square windings are geometrically described by five parameters to each winding (Figure 2) which are: turn's number n, width w, the thickness t, spacing between windings s and total length l t .To calculate the number of turns, we have opted to the Wheeler method which is represented by relation 8 [5]: The coefficients k 1 and k 2 depend on the geometrical form used.For the square geometry: k 1 =2,34 and k 2 =2,75.
So, primary and secondary turns' numbers are: The calculation of these two parameters (Primary thickness and width) depends on skin thickness (equation 11) which determines the width of the zone where the current concentrates in a conductor [6] [7] [8].
To circumvent the problem of the skin effect and make the current flowing in the entire conductor, it is necessary to fulfill one of the following conditions: The current density for x ranging from 0 to t/2 is given by; The average value of the current density is: One of the two values t or w set in order to find the other.The width of the primary conductor w p is is derived from the equations ( 14) and ( 15) for a value of t = 2.δ (t: thickness of the conductors of primary and secondary).
Where Sc p : primary conductor's section.
We have taken the same spacing for both the primary and secondary windings: Secondary total length: The magnetic circuit design must also take into account the existence of losses and the appearance of the skin effect in relation to the high-frequency operation.These side effects, which degrade the performance of the component, can be reduced by flipping the magnetic cores.This may, however, increase the total volume of the core.

Modelling of Integrated Planar Micro-Transformer
The electrical behavior of an integrated micro-transformer is shown in Figure 3.

Calculation of the technological parameters
The analytical expressions of different elements are:

Concept of S-parameters
The scattering parameters of the micro-transformer can be easily obtained from the localized model.The S-parameters of Figure 4 are calculated as follows [13]: First, we calculate the ABCD matrices for each block.

(x)
Then, we can combine the large intermediate block I with block φ in parallel.The final ABCD matrix of the entire transformer F is given below: Here, Z 0 is the characteristic impedance of the line.Also, note that due to reciprocity, we will have A .D B .C 1; therefore, S 12 =S 21 .

Geometric dimensioning results
The geometric parameters of micro-transformer are shown in the Table 3.We note that the values of the calculated geometric parameters are according with technical integration.

Results of electrical parameters
The Table 4 shows the electrical parameters calculated.

Influence of frequency on the primary and secondary inductances and serial resistances
The curves of Figure 5 show the influence of the frequency on inductors and series resistances (primary and secondary) Figure 5 shows the influence of the frequency on the inductance and series resistance of primary and secondary windings.We observe the characteristics of inductance behavior: The inductive behavior, a transition zone and finally the capacitive behavior [14].

Influence of frequency on the quality factor of primary and secondary windings
The quality factor expresses losses of power in the micro-transformer; it is defined as following [10] [12]: (31) The quality factors of inductors primary and secondary are given by the formulas (32) (32) Figure 6 shows the evolution of the quality factor as a function of frequency for the primary and secondary inductances.

Simulation Of The Operating Converter
We performed simulations in order to test the operation of our flyback converter in three cases: The converter contains an ideal transformer (lossless), a real transformer (with losses) and an integrated micro-transformer.The simulation was performed using PSIM software 6.0.Initially, we need to calculate the following three parameters:

Load resistance of the flyback converter
The load resistance of the flyback converter is given by Equation 33.
Capacitance of the flyback converter The capacity of the fly-back converter is given by the formula below.For a voltage undulation equal to 0.25V, the capacitor C is equal to:

Simulation of the operating converter with an ideal transformer
In this simulation, the circuit of Figure 7 contains an ideal transformer and the Figure 8 shows the waveform of the output voltage and current of the converter.We also note in Figure 7 the two modes of the converter: the transient and steady state.The output voltage is 4.9 V instead of 5V.This is due to voltage drops across the diode and transistor.In the steady state, the current is 0.98A, which corresponds to an output power of 4.8 W in place of 5 W. The Figure 9 shows the waveform of the voltage and current across of both transistor and diode of the flyback.

Simulation of the operating converter with a real transformer
In this simulation, the circuit of Figure 10 contains a real transformer and the Figure 11 shows the waveform of the output voltage and current of the converter.We also note here the existence of two modes of operation of the converter: the transient and steady state.The output voltage is 4.25 V instead of 5V.This is due to the voltage drop across the diode and the transistor, the resistive losses in the conductor and then the magnetic core losses.In the steady state, the current is 0.85A, which corresponds to an output power of 3.6Win place of 5 W. The Figure 12 shows the waveform of the voltage and current across of both transistor and diode of the flyback.

Simulation of the operating converter with an integrated micro-transformer
In this simulation, the circuit of Figure 13 contains an integrated micro-transformer and the Figure 14 shows the waveform of the output voltage and current of the converter.We note again, the existence of two regimes of operation of the converter: transient and steady state.The output voltage is 4.24V instead of 5V.This is the voltage drop across the diode and the transistor, the resistive losses in the conductors and then the magnetic core losses.In steady state, the current is 0.84 A, which corresponds to an output power of 3.6W instead of 5 W. The Figure 15 shows the waveform of the voltage and current across of both transistor and diode of the flyback.We note that the micro-transformer delivers the same power as a real transformer.

The Flyback Converter Efficiency
The efficiency of converter (Formula 36) tells us about his performance.Pj is copper losses and Pf is Iron losses. . . (39) The efficiency found is around 82%, so near to the performance of an operating flyback converter which is 85%.We conclude that this reduction corresponds to the joules losses generated by conducting windings and the iron losses in the ferromagnetic core.

Simulation 3d Of The Electromagnetic Effects In A Planar Micro-Transformer
In this section, we present the distribution of the electromagnetic field in a microtransformer with and without core.This simulation was performed using the software FEMLAB 3.1.

Simulation without magnetic core
Figure 17 shows the planar micro-transformer without magnetic core.Figure 18 shows the distribution of magnetic field lines in the micro-transformer.

Simulation with magnetic core
Figure 19 shows the micro-planar transformer with magnetic core.Figure 20 shows the distribution of magnetic field lines in the micro-transformer.When we insert a ferromagnetic layer on the top and bottom of the insulating layer, the majority of the magnetic field lines are concentrated at the walls of the magnetic block (Figure 20).So, we conclude that the ferromagnetic layers are required to have a good electromagnetic compatibility in the case of the integration of a transformer.Next, by using a software simulation PSIM6.0,we have compared the waveforms of the converter output voltages for the three simulations.Finally, by using the software FEMLAB3.1, we have visualized the electromagnetic phenomenon in planar micro-transformers, with and without magnetic core.The aim of this simulation is to study the electromagnetic compatibility of the micro-transformer with the vicinity components in the converter.We conclude that the results of dimensioning in this paper are interesting indeed.

TELKOMNIKA ISSN: 1693- 6930 
Design and Modeling of an Integrated Micro-Transformer in a Flyback Converter (Derkaoui) 673 Figure 3. 3D cross section of an integrated planar micro-transformer.

Figure 4 .
Figure 4. Equivalent circuit of an integrated planar micro-transformer [10]-[12] Finally, we can convert the A, B, C, D parameters to S-parameters as follows: TELKOMNIKA ISSN: 1693-6930  Design and Modeling of an Integrated Micro-Transformer in a Flyback Converter (Derkaoui)

Figure 5 .
Figure 5.Primary and secondary inductances (a) and serial resistances (b) versus frequency

Fig. 6 :
Fig.6: Quality factor of the primary and secondary windings versus frequency.
Design and Modeling of an Integrated Micro-Transformer in a Flyback Converter (Derkaoui) 677

Figure 7 .Figure 9 .
Figure 7. Flyback with an ideal transformer Figure 8.Output voltage and current of flyback with an ideal transformer

Figure 10 .Figure 12 .
Figure 10.Flyback with a real transformer Figure 11.Output voltage and current of flyback with a real transformer

Figure 13 .
Figure 13.Flyback with an integrated microtransformer Figure 14.Output voltage and current of flyback with an integrated micro-transformer

Figure 16 .Figure 17 .
Figure 16.Evolution of the flyback converter efficiency versus frequency

Figure 18 .Figure 19 .Figure 20 .
Figure 18.Propagation of magnetic field lines in a planar micro-transformer without magnetic core

Table 3 .
Results of dimensioning of geometrical parameters

Table 4 .
Electrical parameters results Primary serial resistance: Rs p Secondary serial resistance : Rs s Primary magnetic resistance : R magp Secondary magnetic resistance :R mags Primary resistance of silicon substrate :R subp Secondary resistance of silicon substrate :R subs Primary oxide capacitance :C oxp Secondary oxide capacitance :C oxs Primary capacitance of silicon substrate :C subp Secondary capacitance of silicon substrate :C subs TELKOMNIKA Vol.11, No. 4, December 2013: 669 -682 676