Neda Shahabi Ghahfarokhi Thesis (PDF 1MB)
Minimising Capacitive Couplings and Distributing Copper Losses in Planar
Magnetic Elements
This thesis is submitted in partial fulfilment of requirements for the degree of
Master of Engineering
Neda Shahabi Ghafarokhi (B.Eg)
Engineering systems/Built Environment and Engineering
DECEMBER 2010
STATEMENT OF ORIGINAL AUTHOUSHIP
The work submitted in this thesis, has not been previously published for a degree or diploma, at any other education institution. To the best of my knowledge and belief the materials contained in this thesis are belongs to the author except from the referenced subjects.
Neda Shahabi Ghahfarokhi Date
ACKNOWLDGMENTS
I express my gratitude to my supervisor Associated Professor Firuz Zare for his continuous guidance and financial support over this work. I express my sincere thanks to my beloved husband, Arash, for his great assistance, encouragement and advices during this research. Finally I dedicate this trivial work to my dear parents for their infinite love and support.
ABSTRACT
Planar magnetic elements are becoming a replacement for their conventional rivals. Among the reasons supporting their application, is their smaller size. Taking less bulk in the electronic package is a critical advantage from the manufacturing point of view. The planar structure consists of the PCB copper tracks to generate the desired windings .The windings on each PCB layer could be connected in various ways to other winding layers to produce a series or parallel connection. These windings could be applied coreless or with a core depending on the application in Switched Mode Power Supplies (SMPS). Planar shapes of the tracks increase the effective conduction area in the windings, brings about more inductance compared to the conventional windings with the similar copper loss case. The problem arising from the planar structure of magnetic inductors is the leakage current between the layers generated by a pulse width modulated voltage across the inductor. This current value relies on the capacitive coupling between the layers, which in its turn depends on the physical parameters of the planar scheme. In order to reduce this electrical power dissipation due to the leakage current and Electromagnetic Interference (EMI), reconsideration in the planar structure might be effective. The aim of this research is to address problem of these capacitive coupling in planar layers and to find out a better structure for the planar inductance which offers less total capacitive coupling and thus less thermal dissipation from the leakage currents. Through Finite Element methods (FEM) several simulations have been carried out for various planar structures. The labs prototypes of these structures are built with the similar specification of the simulation cases. The capacitive couplings of the samples are determined with Spectrum Analyser whereby the test analysis verified the simulation results.
Keywords: Planar magnetic element, Equivalent capacitive coupling, High frequency modelling, Electromagnetic interferences, Power electronics.
CONTRIBIUTIONS
Planar magnetic elements have less bulk and are a better substitute for the conventional winding types of inductors. The main problem with these planar elements is the relatively high capacitive couplings between their layers. In this thesis different structures of planar elements are analysed and the main contributions are as followed:
1) In the third chapter with applying the 3D Finite Element analysis in two layer planar elements, different structures are compared. The main focus is on shifting effect of the layer positions with respect to the other, which is verified through the FE simulation and tests. Thus shifting would be effective in reduction of the total capacitive coupling in a planar element with two layers.
2) In chapter four, the idea of shifting the layers has been extended to multi- layer planar elements to find out the effectiveness of the layer shifting in the equivalent capacitive coupling reduction. The simulation and test results show the failure of this idea for multilayer structure.
3) The fifth chapter introduces of a novel structure for multi-layer planar elements which is effective in reduction of the total capacitive couplings compared to the simple structures. These results are verified with simulation and experimental tests.
The results of this research are prepared as two accepted international conference papers and two submitted journal papers: Neda Shahabi,F. Zare, G.ledwich, “New configuration winding method for reduction of capacitive coupling in planar magnetic elements,” EPE-PEMC ,power electronic and drives automation, OHRID,SEP 2010 published.
Neda Shahabi,F. Zare, G.ledwich, “ A novel structure to decrease of capacitive coupling in planar magnetic elements”, AUPEC ,Power Electronic and Drives Automation, New Zealand,DEC2010 accepted
Neda Shahabi,F. Zare, G.ledwich , “ Improving quality of planar inductors and transformers by minimizing capacitive couplings and distributing copper losses” under review for IET, Power Electronic journal.
Neda Shahabi,F. Zare, G.ledwich, “ New configuration winding method for reduction of capacitive coupling in planar magnetic elements. selected by the editor of journal of Energy and Power ENG to be considered for publishing
TABLE OF CONTENTS
Statement of Original Authorship...... i Acknowledgment...... ii Abstract...... iii Keywords...... iv Contribution...... v Table of Contents...... vii List of Figures...... ix List of Tables...... xiii Abbreviations...... xiv
1.0 Introduction...... 1 1.1 Prologue to Investigation...... 1 1.2 Literature review...... 5 1.2.1 Capacitive Coupling in Planar Magnetic Elements...... 5 1.2.2 Methods for reduction f capacitive coupling...... 1.2.3 Electromagnetic Interference (EMI)...... 7 1.2.4 Skin Effect and Proximity Effect in Planar Elements...... 9 1.2.5 Inductance and Leakage Inductance in Planar Elements...... 10 1.2.6 Winding Arrangement in Planar Capacitive Coupling...... 13 1.3 Finite Element Method Introduction...... 15 1.3.1 Finite Element Introduction in Electrostatic Problem...... 17 1.3.2 Magnetostatic and Finite Element Equations...... 20 1.4 Instruction to ANSYS (Mechanical ADPL)...... 21
2.0 Planar Inductor Impedance Characteristics...... 24 2.1 Introduction...... 24 2.2 Capacitive Coupling in Planar Elements...... 26 2.2.1 Calculation of Capacitive Coupling between Planar Tracks...... 27 2.2.2 2D FE Analysis of Capacitive Coupling in Planar Elements...... 29 2.2.3 Shifting Effect on the capacitive coupling between Planar Tracks...... 29 2.2.4 Relation between Insulation Thickness and Capacitive Coupling of the Planar Tracks...... 29
2.3 Electrical Resistance in Planar Elements...... 38 2.3.1 Relation between Current Direction and Electrical Resistance...... 41 2.3.2 Effect of Shifting on the Electrical Resistance of Planar Tracks...... 50 2.3.3 Relation between Insulation Thickness and Resistance...... 53
3.0 Shifting Effect of Planar Layers on Total Capacitive Coupling of Two Planar Element...... 58 3.1 2D and 3D FE Analysis of Shifting in Two Layers Planar Element...... 58 3.2 2D and 3D FE Analysis of Distance between Tracks Two Layers Planar Element...... 63 3.3 Introduction to Spectrum Analyser...... 63 3.4 Experiment Results for Capacitive Coupling of Two Layers Planar Element...... 65
4.0 Total Capacitive Coupling in Multi Layer Planar Structure...... 70 4.1 Shifting Effect on ECC of Multi Layer Planar Elements...... 73 4.2 Insulation Thickness Effect on ECC of Multi Layer Planar Elements...... 76 4.3 Experiment Results for Comparison between different Structure of Planar Elements...... 78
5.0 A New Winding Structure to Decrease Capacitive Coupling for N- Layer...... 79 5.1 New Winding Structure...... 80 5.2 Modelling of Multi Layer Planar Structure...... 82 5.3 Experiment Results...... 90
6.0 Conclusion...... 93 7.0 Future Works and Further Research...... 94 References...... 95
LIST OF FIGURES
Figure 1.1- (a) a manufactured planar transformer (b) Scheme of a planar inductor with PCB layers and a magnetic core Figure 1.2- Capacitive coupling model of a planar transformer Figure 1.3- Leakage inductance in a planar inductor over the range of layers separation (mm) Figure 1.4-Illustaration of the geometrical parameters associated with field representation (a) near zero setup (b) far zone setup
Figure 2.1- A boost convertor circuit with a planar element and the circuit current Figure 2.2-Voltage and current is the boost convertor which includes a planar inductor Figure 2.3- (a) Effective common surface area between two none-shifted planar tracks (b) Effective common surface area between two shifted planar tracks Figure 2.4- A planar structure with two layer and two tracks in each layer Figure 2.5-Capacitive coupling between the two planar horizontal adjacent tracks Figure 2.6- Capacitive coupling between two crossing surface from two deferent layers Figure 2.7- Three layer planar structure with three tracks in each layer Figure 2.8- Capacitive coupling between two adjacent tracks in one layer over the shifting range for various distances between tracks. Figure 2.9- Capacitive coupling between two tracks with whole common surfaces, which is decreased within the shafting range in various cases of distance between the tracks. Figure 2.10-Capacitive coupling between two tracks in two immediate layers with no common surface area in none shifted mode but this area would increase within shifting range.
Figure 2.11-Capacitive coupling of C12, within the shifting range for various distances between tracks in h=.2mm and h=2mm
Figure2.12- Comparison of the electrical fringing fluxes between two planar tracks for different distance between the tracks
Figure 2.13-Simulation results for C24, over the shifting range for various distances between the tracks in insulation thickness of 2mm and .2mm Figure 2.14- Current density in three frequencies (a) 100Hz (b) 1KHz (c) 1 MHz Figure 2.15- (a) Current density in two planar conductive at 1MHz with opposite Current direction (b) Current density in two planar conductive at 1MHz with similar Current direction (c) Current density in two planar conductive at 10MHz with opposite Current direction (d) Current density in two planar conductive at 1MHz with similar Current direction. Figure 2.16- (a) Current density in two shifted planar tracks at the frequency of 1MHz (b) Current density in two shifted planar tracks at the frequency of 10MHz
Figure 2.17- Electrical resistance of the tracks in a planar structure for Different current direction over the shifting range at the frequency of 1MHz Figure 2.18- (a, b) Current density distribution in the vertical direction of the planar track edge(c, d) current density in the vertical direction of the middle part in a planar track Figure 2.19- (a, b) Current density distribution along the specified array when all the tracks have similar current direction(c, d) current density distribution along the specified array when the middle track has opposite current direction Figure 2.20- (a, b) Current density distribution along the specified array when all the tracks have similar current direction(c, d) current density distribution along the specified array when the middle track has opposite current direction Figure 2.21-Electrical resistance of the tracks in three layer structures over the shifting range for various cases of distance between the tracks Figure 2.22-Electrical resistance of tracks in a three layer planar element over the shifting range for insulation thickness of 2mm and .2 mm Figure 3.1- (a) Physical parameters of a planar layer (b) capacitive coupling between a two layer planar element and its physical parameter Figure 3.2-Two infinite plate with commo surface area of A and vertical distance of h Figure 3.3-2D and 3D, FE simulation results over the shifting range and comparison with calculation result Figure 3.4-(a, b) Electrical field(E) In two layer planar shifted and none shifted structure with insulation thickness .18mm(c, d) In two layers planar shifted and none shifted Structure with insulation thickness’ of 1mm (e) Colour code for E magnitude Figure 3.5- Spectrum analyser used in this research for measuring the planar elements impedance Figure 3.6-Caliber kit used in this research for measurement calibration of spectrum analyser Figure 3.7-A prototype sample planar structure measured with spectrum analyser Figure 3.8-Magnetitude and phase of a planar structure measured with Spectrum Analyser Figure 3.9- (a) A prototype capacitive impedance over the frequency range (b) Test results for capacitive coupling of over the shifting range the two layers planar structure and comparison with simulation result Figure 3.10- Test measurements for capacitive coupling of the two layer shifted planar structure for various distance between the tracks (d) And comparison with simulation result
Figure 4.1- (a) Capacitance-inductance model for two layer planar elements (b) A four layer shifted structure model and the relevant parameters. Figure 4.2- (a) Series connection of the four layers planar in shifted structure (b) Series connection of the none-shifted four layer planar structures. Figure 4.3- Comparison between the ECC in none shifted and shifted planar structure with the formulas calculated values. Figure 4.4- (a) Four layer planar structure (b) Capacitive coupling between the layers(c) Electrical field between the layers and shielding effect of the layers on its distribution and magnitude Figure 4.5- (a) changing the capacitive couplings of X, Y and ECC within the distance range and comparison between the shifted and none-shifted structure (b)
Changing the capacitive couplings of X, Y and ECC within the shifting range Figure 4.6-(a) Comparison between the ECC for different distance (d) In Simple and shifted structure with the insulation thickness of .2mm (b) Comparison between the ECC for different distance (d) in simple and shifted structure with the insulation thickness of 1mm Figure 4.7- (a) Ten layer planar inductor with shifted structure (b) Ten layer planar inductor none-shifted structure
Figure 5.1- (a) two layer planar magnetic elements with 8 turn windings in simple structure.(b, c) Two layer planar magnetic with two windings in each layer with the turn number of eight. Figure 5.2-(a) Four layer with eight turn windings in the simple structure (b) split structure with four layers which is consisted of two, eight turn windings in each layer. Figure 5.3-Connections of multi layer planar magnetic elements a) Simple structure b) Split Structure Figure 5.4- The simplified model of two adjacent layers Figure 5.5- Capacitances between two tracks Figure 5.6-Capacitive inductive model of simple (a) split structures (c). Simplified circuits for simple (b) and split (d) structures Figure 5.7-(a) Comparison between the equal capacitance for simple and split winding structures for different Cv (b) Comparison between the equal capacitance for simple and split winding structures for different Ch,(c)Comparison between the equal capacitance for simple and split winding structures for different Chm Figure 5.8- Changing the outer layers width to reduce the equivalent capacitive coupling Figure 5.9- The effect of outer track width on equivalent capacitance Figure 5.10- (a) Split structure of a four planar layers inductor (b) a simple structure of a four a planar layer inductor Figure 5.11- Test and simulation results of ECC for different winding layers for both
LIST OF TABLES
Table 2.I- Electrical resistance of a planar track in the three cases
Table 2.2- Conductive resistance of a planar structure for different current direction in some frequencies
Table 3.I- Physical parameters of the two layer planar structure Table 3.II-Capacitive coupling values over the shifting range in two layer structure from 2d & 3d, FE analysis Table 3.III- 2D & 3D FE simulation results of a two planar layer for different distances between the tracks Table 4.I-Capacitive couplings in multi layer shifted and none-shifted structure Table 5.I-Capacitive couplings in simple structure Table 5.II- Capacitive coupling in simple structure Table 5.III-Capacitive couplings in split structure Table 5.IV- Physical characteristic of the planar magnetic
ABBRIVIETIONS
SMPS Switched Mode Power Supplies
ECC Equivalent Capacitive Coupling
CC Capacitive Coupling
ADPL ANSYS Parametrical Design Language
LCC A Resonance circuit with two Capacitors and one Inductor
MMF Magneto Motive Force
EMI Electromagnetic Interference
DoE Design of Experiment
CCD Central Composite Design
1. INTRODUCTION
1.1. Prologue to investigation Miniaturisation of inductive devices for signal transformation, sensitive magnetic field detection or switched mode power supply applications is an increasingly important subject today. Often these devices determine, to an important extent, the size of the complete application in which they are employed. Fig.1.1 illustrates a manufactured planar transformer and a general scheme of the planar inductor.
(a)
(b) Fig.1: (a) A manufactured planar transformer 1 (b) Scheme of a planar inductor with PCB layers and a magnetic core
Planar magnetic are distinguished from typical magnetic designs mainly by their physical ratio of low profile of height relative to the width and length of the component. High frequency transformers which have been used in high frequency converters provide low profile structure and less winding turns. Planar transformers can be constructed as standalone components with a stacked layer design or a small multilayer PCB or integrated in a multilayer board of power supply. Important advantages of planar magnetic elements are 2: Structures with low profile allow, for certain applications, better volumetric efficiency and high power density; The increase in the area of the core central leg permits a reduction in the number of turns; The possibility of obtaining low leakage inductance due to simplicity in the interleaving of layers and reduced amount of turns this reduces the voltage spikes and oscillations that can destroy some semiconductor devices; The decrease in the high frequency winding losses, since the skin effect is minimized due to conductor thickness reduction; Higher conversion efficiency due to the better magnetic coupling; Better thermal control, because planar elements present a larger relation area/volume; increasing the available surface for the heat transfer mechanism, thus reducing the thermal resistance. Although planar magnetic elements offer these advantages, there are serious drawbacks in the planar magnetic structures. In short, planar magnetic structures have a relatively high leakage current in the high operation frequencies which could result in more resistance dissipation and decreases the efficiency of the power electronic circuits. Since the capacitive couplings between the different layers windings is responsible of these unwanted currents, any changes in physical parameters in the direction of these capacitors decrease would be efficient. The other problem related to planar elements is their need to have larger surfaces of insulation as the winding turn numbers increases with the planar element size. The planar magnetic structures are based on the PCB scheme of the desired windings on the substrate which are connected in different orders to generate various series and parallel windings with a desired turn number. This research seeks to change the physical parameters in the structure of this planar inductor, which might be effective on reduction of the total capacitive coupling observed from the terminals. These changes should be in the direction of decreasing the common surface area between the conductive surfaces. In this research, the key focus is on minimising the total capacitance coupling between the planar conductive terminals which can decrease the peak of the leakage current.
In the spite of being an inevitable trade off between leakage inductance and coupling capacitances, it could be possible to take advantage of this relatively high leakage inductance. It could be used as the inductance part in a LCC resonant convertor. So optimization design of the parasitic resonant elements in planar transformer can be achieved to meet requirement of the circuit. Reduction of the AC resistance in conductor is also desirable, in order to lower the copper losses in the whole planar transformer. These improvements are achieved by changing the physical dimension and elements of the configuration. Meanwhile, it has been considered that shifting the conductor tracks together on a PCB, could play the partial shielding role. In some cases, this would reduce the coupling capacitance size and eventually lower the total size of the planar transformer. Within the scope of this research the following questions arise: Which physical parameters affect the impedance of the planar elements? Do these physical parameters have a similar effect on capacitive coupling reduction? What are the optimum structures which have less total capacitive coupling?
Based on the above questions, this thesis contains seven chapters:
Chapter 1- Introduction: This chapter introduces the planar magnetic structures and provides an overview of other chapters of this thesis. Meanwhile the previous works in this area is described briefly as a literature review section. An introduction to the Finite Element methods as a mathematical solution to solve the electromagnetic problem in the case of complexity is addressed; meanwhile it provides a description on the ANSYS softwares which is applied in this research as a solver of Finite Element problems.
Chapter 2- Planar Inductors Impedance Characteristic: In this chapter, the main problem of the capacitive coupling between the planar layers is addressed, with 2D simulation results and analysis of the capacitive coupling and electrical resistance in various planar structures. It also introduces the proximity and skin effect in planar layers.
Chapter 3- Shifting Effect of Planar Tracks on Total Capacitive Coupling of Two Layer Planar Element: this chapter describes two layer planar elements structures and compares the capacitive coupling of shifted and none-shifted structures using 3D- FE simulations. Finally it proves the simulation results with testing the laboratory prototypes.
Chapter 4- Total Capacitive Coupling in Multi-layer Structures: This chapter analyses the multi-layer structures of planar elements and compares these multi-layer structures capacitive couplings through the 3D, FE simulations. Finally experimental tests have been carried out to verify the simulation results.
Chapter 5- A New Winding Structure to Decrease Capacitive Coupling for n- layer Planar Magnetic Element: This chapter introduces a novel structure for planar elements and analyses different cases of potential structure for this proposed method and compares it with simple conventional planar structures to prove that, this novel case would provide less equal capacitive coupling. Meanwhile the simulation results are verified through experiment results based on laboratory prototypes.
Chapter 6- Conclusions: The results which are achieved in this thesis are summarised and the solutions for a better planar structure are concluded from its context.
Chapter 7 –Future Works and Further Research: Potential extensions of this research for further development of the planar structure are discussed in this section.
1.2. Literature Review
Lower levels of the parasitic characteristics of the planar elements, increases the efficiency and boosts its performance. However, this is often a complex trade-off process since the conditions which often minimize one parasitic effect will maximize another. In this literature review, five main areas related to planar transformers parasitic characteristic and planar structures are investigated. This literature review includes these issues: capacitive coupling, Electromagnetic Interference (EMI), skin effect and proximity effect in planar elements, planar element inductance and winding arrangement.
1.2.1. Capacitive Coupling in Planar Elements
Stray capacitances in high frequency transformers arise from distributed or parasitic electrical coupling between any two conducting objects in or around the transformer. They can be classified as a turn to turn capacitance between two turns in the same winding or two different windings, capacitances between the windings and the magnetic cores, and the capacitances between the windings and the ground. They are heavily geometry-dependent and distributed in nature. It has become widely known that stray capacitances in high frequency magnetic components, such as inductors and transformers, have significant effects on the performance of the components, as well as the entire power electronic systems that contain these magnetic components. The stray capacitances significantly affect the magnetic components performance in such a way that the current waveform on the excitation side would be distorted and the overall efficiency of the system would be decreased. Furthermore, the stray capacitance seen from the excitation side is responsible for the resonant frequencies of the system whereas the stray capacitance between windings contributes to EMI. These effects are very important in high voltage converters, and in topologies that intend to integrate the parasitic effects in the converter topologies. For determination of the stray capacitance in high frequency transformers, there are some techniques that fall into two categories: 1) The two port network approach 2) The step response approach The first approach applies high frequency transformer circuit models with the effect of stray capacitances, modelled as a π-shape network of three lumped stray capacitances, while the second method is suitable for the transformer circuit with the overall effects of stray capacitance, modelled as a lumped stray capacitance connected a cross the primary side as shown in Fig.1.2.
C6
C + 4 Vhigh V Magnetic high V1 C1 Coupling C2 V2 And loeses Vlow Vlow
C3
C5
V3 Fig.1.2: Capacitive coupling model of a planar transformer
The stray capacitance generates unwanted high frequency leakage current due to voltage stress created by a power converter 3. Meanwhile a dynamic circuit model of high frequency transformers with stray capacitances is introduced, where a ladder network is used to account for the magnetic hysteresis and eddy currents in the magnetic core 4. Afterwards it concludes that the stray capacitance of high frequency can be incorporated into the equivalent dynamic circuit by a π shaped network of three capacitors. Because of the small leakage of inductances of transformers, the overall effects of three capacitances can be taken into account by a single equivalent capacitor on the primary side. The experimental method proved this hypothesis 5-9. In 10,11 , the three capacitors of the two windings are determined by short circuit tests within the range of normal operation frequencies and fitting the π-shaped capacitor model to the voltage and current reading. For experimental determination of capacitors in high frequency magnetic component, two approaches are presented based on forced resonance, but these references proposed three new methods:
1) Identifying inductance and capacitance by low and high frequency test. 2) Identifying circuit parameters for a single frequency. 3) Identifying average circuit parameters over a range of frequencies.
The stray capacitance per unit length of the copper track can be obtained by simple calculations neglecting fringing effect of the electric field between plates. However the fringing effect can be significant when the tracks are thin and widely spaced. An analytic model has been developed for the winding capacitance and dielectric losses of planar transformers. It can be seen that the eddy current winding losses decrease significantly when the thickness of the insulation layers is decreased from the largest relevant values in practice (several 100 µm) .So there is an optimum thickness of the insulation layers about 100µm, that the total losses increase significantly, if the thickness of insulation layers is either increased to several 100µm or decreased to several 10 µm 12-16. Based on the electro statistical analysis in planar elements and calculation formulas 17-20 for the stray capacitance the optimal solutions can be conducted as follows: 1) Reducing static layer capacitance by enhancing the distance or lowering the overlapping surface area between two conductor plates 2) Reducing the number of turns in each layer and increasing the number of layers 3) Reducing the number of intersections between the primary and secondary 4) Arranging winding configuration to obtain the minimal energy associated with the electrical field.
1.2.3. Methods for Reduction of Capacitive Coupling in Planar Elements A major disadvantage is the high parasitic capacitance that the planar windings exhibit. The capacitance manifests itself in two main areas: the capacitance between the windings of a multiple winding component and the self-capacitance of the windings and conductors to the surroundings. It is this self-capacitance that is a major contributing factor to the common mode electromagnetic interference (EMI) of the circuit. The common mode EM1 of a system with planar magnetic components is significantly larger than a similar system with conventional magnetic components. This necessitates the use of large common mode filters to reduce the EM1 to within the relevant allowable standards. These common mode filters contribute significantly to the size and cost of the overall system, especially at moderate to low powers .this method is based on marinating the charge balance within the transformer during the current rising in the inductors in power supplies 21. In order to reduce the parasitic capacitance, alternating winding method has been introduced in high frequency planar magnetic design to partially cancel the electric field strength between alternating turns 22, 23. However, alternating all the windings through the PCB substrate requires special treatment on the PCB such as many via holes for linking individual turns in series. Such winding structure increases both winding resistance and the manufacturing cost 24.
1.2.2. Electromagnetic Interference (EMI)
Electromagnetic Interference (EMI) could be appeared with the radiated electromagnetic fields or conducted currents. The electromagnetic interference could be detected by a susceptible element in the circuit through the coupling path .These coupling paths include:
Conduction-electric current Radiation -electromagnetic field Capacitive coupling-electric field Inductive coupling -magnetic field Conducted noise is coupled between components through interconnecting wires such as through power supply and ground wires. Common impedance coupling is caused when currents from two or more circuits flow through the same impedance such as in power supply and ground wires. Radiated electromagnetic field coupling may be treated as two cases. In the near field, E and H field coupling are treated separately. In the far field, coupling is treated as a plane wave coupling. Electric field coupling is caused by a voltage difference between conductors. The coupling mechanism may be modelled by a capacitor. Magnetic field coupling is caused by current flow in conductors. The coupling mechanism may be modelled by a transformer. Electromagnetic radiation involves electric (E) and magnetic (H) fields. Any change in the flux density of a magnetic field will produce an electric field change in time and space (Faraday's Law). This change in an electric field causes another change in the magnetic field due to the displacement current (Maxwell). A time- varying magnetic field produces an electric field and a time-varying electric field results in a magnetic field. This forms the basis of electromagnetic waves and time- varying electromagnetic (Maxwell's Equations). Wave propagation occurs when there are two forms of energy and the presence of a change in one leads to a change in the other. Energy interchanges between electric and magnetic fields as the wave progresses. Electromagnetic waves exist in nature as a result of the radiation from atoms or molecules when they change from one energy state to another and by natural fluctuations such as lightning. The EMI related to Switching Mode Power Supplies (SMPS) circuits could arise from the third categories of the EMI source, capacitive coupling between the layers in planar magnetic structure applied in the circuits. These capacitive couplings in high frequencies result in the current spikes between the layers which interfere with the source current of the circuit as an EMI source. Thus the main idea behind this research could be reducing these capacitive couplings as the EMI path in power electronic circuits. The most common methods of noise reduction include a proper equipment circuit design, shielding, grounding, filtering, isolation, separation and orientation, circuit impedance level control, cable design, and noise cancellation techniques25.
1.2.3. Skin Effect and Proximity Effect in Planar Elements
The AC resistance is also lower in planar transformers. The reason is that the area/perimeter ratio in planar transformer conductors is very low. This makes possible a better usage of the copper because the current flows across the whole conductor section, reducing skin effect. At high frequencies, the eddy current in conductors results in the reduction of surface, carrying current. This reduction means increasing the total heat losses in transformer and eventually reduction in efficiency. In switched power supplies, operating in high frequencies, the effect of eddy current and proximity effect could impair the whole circuit as the circuit wiring and magnetic fields change in high frequencies. At low frequencies the current distributes uniformly to minimise the resistance loss. While, in high frequencies the flux within the wire changes rapidly and the current density increases in surfaces ;Meaning that the effective surface of the conductor carrying the current reduces so that AC resistance increases dramatically in high frequencies 26-29. Penetration depth indicates the effective area of the conductor and consequently the ratio of DC resistance to AC resistance. When two or more conductors are near each other, their electromagnetic fields effect the others current distribution. In the case of two wires carrying the same orientated current, the surface which is near to the other conductor shows more current distribution. This is due to the proximity effect which reinforces the field from the other conductors. In transformers windings, without any gap the fields tend to cancel their field effect not only outside the windings but also between them as well. At high frequency, current flow is on the outside of the inner windings and inside of the outer windings, adjacent to the field. The position of primary and secondary winding to each other and the position of the air gap have a great influence on the core losses and coupling between windings. If the winding is located symmetrically around the air gap, the fringing flux nearly vanishes. So the core losses can be reduced to 55% of the winding when located at the gap- centred position. When putting the windings close together, the losses would be minimum. Based on the Dowell’s assumption and the general field solutions for the distribution of current density in a single layer of an infinitely foil conductor the expression for AC resistance of the mth layer is derived 30-34:
R sinh sin sinh sin ac,m (2m 1)2. R 2 cosh cos cosh cos dc,m (1.1) h , and δ is skin depth at fundamental frequency is the insulation thickness and m is defined as a ratio in35,
F(h) m F(h) F(0) (1.2)
F (0) and F (h) are MMFs at the limits of a planar layer. The first term in (1) describes the skin effect and the second term represents the proximity effect factor. The proximity effect loss in a multi layer winding, may strongly dominate over the skin effect loss depending the value of m which is related to the winding arrangement.AC resistance is not only related to the MMF ratio m but also dependant on the ratio .With a given frequency, a minimal AC resistance can be determined by the layer-thickness of windings. For a large m, the proximity effect dominates over skin effect which leads to a higher winding resistance 36.
1.2.4. Inductance and Leakage Inductance in Planar Inductors
The leakage inductance is the inductance used to represent the leakage energy storage. The leakage energy is the part of the energy due to the leakage flux, which is the flux that is not in the common magnetic path. If two windings were placed exactly in the same physical position, no leakage flux would be generated, and then no leakage energy would exist. If the situation is different from that (all the real situations), some leakage energy appears. The higher the separation of the windings means the higher leakage energy. Besides of other geometry and material parameters, the low value in the leakage inductance in planar transformers is due to the proximity of the different layers of the windings. The gap between two adjacent layers is very small, so the magnetic energy stored in it is very low. The leakage inductance of planar magnetic structures designed for high frequency power electronics applications is a critical performance parameter that significantly affects circuit operation structures. The leakage inductance can be increased five times if the separation of the layers is increased up to 1mm. Therefore, the thinnest insulator which compiles the electrical insulation requirements should be used in order to obtain the lowest leakage inductance37. Fig.1.3 shows the relation of leakage inductance in a planar magnetic with the insulation separation as explained above.
Leakage Inducatnce (nH) 16 14 12 10 8 6 4 2 0 0.02 0.05 0.1 0.4 1
Leakage Inducatnce (nH)
Fig.1.3: Leakage inductance in a planar inductor over the range of layers separation (mm)
Obviously this parasitic inductance parameter could not be neglected especially at high frequency, so that many applications prone to use the leakage inductance parameters as a resonance element in converters. The effective inductance, which a transformer presents to the circuit, is many times greater than the calculated results. The termination inductance can easily cause apparent leakage inductance of the transformers which is several times of the device specification. The finite element method shows this as well. The secondary winding termination can greatly increase the leakage inductance .One of the methods to design a transformer with low leakage inductance is to consider the low leakage 38 terminators . Analysis of the transformer characteristics in high frequency with Finite Element has been done from the view points of joule losses, iron losses and temperatures, using the LITZ wiring method. The reason is that, this kind of wiring in the spite of their high expenses, technically eliminates the eddy current through mitigating the skin effect. In other words proximity effect dominates the skin effect. Also it is necessary to create a core gap in order to keep a constant inductance and stable output. It is possible to design transformers, considering both the impedance characteristics and heat generation by coupling both electromagnetic field analysis and the thermal 39 analysis . Quantifying the magnitude of the leakage parameters is especially important for optimizing the functionality, efficiency and modelling of power convertors. Two standard tests are known as the short circuit and the open circuit .However; they show deficiencies such as increasing the winding series resistance and the varying leakage of primary and secondary with respect to the geometry and configuration. This could be overcome through a third test based on the secondary open circuit inductance. In the case of the high power, high leakage planar transformers, the short circuit and differential coupling tests are suitable to investigate the special variation of the primary and secondary leakage inductance. However, in the case of a low power, high leakage and high resistance planar transformer, the differential coupling tests 40 are proved to be a more useful and accurate test than the short circuit test .
The role of a designed planar bus bar has been described as minimising the EMI especially common mode conducted electromagnetic interference via reducing the high voltage spikes during switching as this planar bus bar has a very low 41 inductance compared to standard inventor designs . The planar transformers compared to low profile ones, proves that the planar transformer offers a better interleaving of primary and secondary. Therefore, the planar transformers lower the leakage inductance dramatically at the expense of high capacitance coupling between primary and secondary windings which leads to increasing the common mode noise current 42. It should also be noted that, moderate deviations from the optimum shape will have a minor effect on size, weight and loss. The planar windings are made of both thinner and wider tracks, reducing leakage inductance. The planar transformer has a number of advantages over conventional solenoid windings, printed circuit or flexible fan 43 fold windings, such as simple construction and more performance provision .
1.2.5. Wiring Arrangement in Planar Elements
The new model of planar transformers is presented in 44, where the elements of the models are calculated on the basis of a theoretical l-D field and network analysis. The coupling of the windings can be easily increased by using multiply stacked windings which are connected in Series or parallel. Increased losses due to the skin effect, inside the windings can be avoided by using a large winding width .This model is valid both, in time domain or in the frequency domain and the results are compared with Finite Element Analysis. Analysing this model gets the method to reduce the parasitic capacitance and leakage inductances. It could be deduced that for reducing the coupling capacitance, there are some ways such as, adding the copper thickness of PCB which increases the resistance, choosing a material with a lower permeability and minimising the surface area, which will again add to the resistor. A very good method is to change the relative position of the traces in which the effective area of the flat board formed by the trace is reduced; consequently parasitic capacitance is reduced while resistance does not increase 45, 46. Some planar element researchers study the cases of silicon based planar inductor for high frequency transformers and show the role of the coreless inductor design in increasing the performance of the planar transformer. From the results, it is clear that the higher turns of windings, the higher the inductances value. However, more windings increase the eddy current in high frequencies. The low cost and high performance of the silicon CMOS fabrication process offers a great opportunity and prefers silicon technology over other technologies 47-49. At high frequency operation, skin and proximity effects cause the AC currents in winding conductors to flow non-uniformly near the surface of the conductor. This non uniform distribution increases in the winding resistance. In 3D Finite Element Analysis, the interleaving windings shows lower AC resistance, and the ratio of the
Lm “leakage inductance” to the Lk “magnetizing inductance” which is called 50-52 coupling efficiency is better than non-interleaving windings . Paralleling of the secondary windings is essential for low voltage and high current planar transformers. This method is effective for increasing the current handling capacity of the windings. In 36 it has been shown that the winding arrangement of the primary and secondary would have great effects on the current distribution in parallel layers. As a result of circulating current between layers, due to the leakage fluxes, the current shares between the layers are not equal. In the symmetrical cases the AC losses are decreased compared to the asymmetrical cases, but there is a critical frequency in which the eddy current losses dominate the total winding losses. So that winding arrangement behaviour differs from the point of losses changing with frequency view. Another point is that the different implementation of secondary termination ways. In the case of using non-interleaved pins; it brings about more uniformly current distributions. Combination of all these analysis, winding loss, coreless leakage inductance and stray capacitances leads to finding an optimum design for planar elements. That’s because in most cases an improvement in one characteristic is, at the expense of worsening the other parasitic parameter. As an example ,the turn number N brings about less winding loss but more core loss lower leakage inductance and less stray capacitance. Thus, in design there should be a trade-off between these parameters to obtain the highest circuit efficiency. Winding arrangement also can in part bring an optimal behaviour in the tradeoffs without any sacrifices, which play an important role in optimizing planar elements. There are many limitations on the validity of (1) such as minimum distances between consecutive turns, between adjacent layers, and between the conductor edge and magnetic core as well as sinusoidal waveform however these factors are usually derived from complicated coefficient Tables. Outside these minimum boundaries it is advisable to determine winding losses with FEA simulations. An improved method in interleaving winding is suggested (.5P-S- P-S-P-S-.5P) in which the top layer is parallel with the bottom layer and then connected series with the other turns of primary. So that a lower magneto motive forces (MMF) ratio m can be obtained as well as minimized AC resistance, leakage inductance and even stray capacitance 36. Parasitic characteristic of planar elements determine the behaviour of power convertors in terms of switching stress, efficiency and associated EMI effects. Modelling the effects of every combination of these parameters using a mechanistic approach would require a significant time investment without any guarantee. The statistical Design of Experiments (DoF) combine with FE simulations provides a solution to model the planar transformer parasitic based on winding design factor. The Central Composite Design (CCD) is employed to obtain equations for the leakage inductance, stray capacitances, and resistance output voltage and output current 52, 55. 1.3. Finite Element Method Introduction
The Finite Element Method (FEM) and its hybrid versions (finite element-boundary integral, finite element-absorbing boundary condition, Finite element-mode matching, etc.) are the most successful frequency domain computational methods for low and high frequency electromagnetic simulations. From its earlier introduction for electrical machine modelling, its applications now cover antennas, microwave circuits, propagation and large scale scattering from non-metallic structures. Finite elements solve by breaking up a problem into small regions and solutions are found for each region taking into account only the regions that is right next to the one being solved. In the case of magnetic fields where FEM is often used, the vector potential is what is solved for in these regions. Magnetic field solutions are derived from the vector potential through differentiating the solution. This can cause problems in smoothness of field solutions. Theoretically, any partial differential equation class of problem can be solved using FEM (although some types will do better than others). FEM is a numerical technique for solving models in differential form. For a given design, the FEM requires the entire design, including the surrounding region, to be modelled with finite elements. A system of linear equations is generated to calculate the potential (scalar or vector) at the nodes of each element. Therefore, the basic difference between these two techniques is the fact that FEM only needs to solve the unknowns on the boundaries, whereas FEM solves for a chosen region of space and requires a boundary condition bounding that region. While, FEM can solve nonlinear problems, the nonlinear contribution requires a volume mesh. Putting a volume mesh in begins to diminish the benefits of FEM listed above. In fact, for a saturating nonlinear magnetic problem, the saturation characteristic is best solved with FEM. There are generally two types of analysis that are used in industry: 2-D modelling, and 3-D modelling. While 2-D modelling conserves simplicity and allows the analysis to be run on a relatively normal computer, it tends to yield less accurate results. 3-D modelling, however, produces more accurate results while sacrificing the ability to run on all but the fastest computers effectively. Within each of these modelling schemes, the programmer can insert numerous algorithms (functions) which may make the system behave linearly or non-linearly. Linear systems are far less complex and generally do not take into account plastic deformation. Non-linear systems do account for plastic deformation, and many also are capable of testing a material all the way to fracture. FEM uses a complex system of points called nodes which make a grid called a mesh. This mesh is programmed to contain the material and structural properties which define how the structure will react to certain loading conditions. Nodes are assigned at a certain density throughout the material depending on the anticipated stress levels of a particular area. Regions which will receive large amounts of stress usually have a higher node density than those which experience little or no stress. Points of interest may consist of: fracture point of previously tested material, fillets, corners, complex detail, and high stress areas. The mesh acts like a spider web in that from each node, there extends a mesh element to each of the adjacent nodes. This web of vectors is what carries the material properties to the object, creating many elements. A wide range of objective functions (variables within the system) are available for minimization or maximization: Mass, volume, temperature Strain energy, stress strain Force, displacement, velocity, acceleration Synthetic (User defined) Basic step for finite element analysis are summerised here: 1. Discrete the quantum: for a continuous domain there is no natural subdivision, so the mesh pattern will appear somewhat arbitrary. The continuum would be replaced by a series of simple, interconnected elements whose force-displacement characteristics are relatively easy to compute.
2. Determination of the element type: FEM describe the behaviour of the continuous objects based on the smaller unit shapes called element type which differs with the type of simulation.
3. After determination of the element types the field variable in the domain of the element is approximated with the nodes. Finally a series of equations introduce the system behaviour as the nodes values.
4. Apply the boundary condition.
1.3.1. FEM Introduction in Electrostatics Problems
The fundamental equation of electrostatic are forms of Faraday’s equation and Gauss, Law.
E 0 (1.3) .(E) V
The electrical field can be expressed in the terms of a gauge condition involving a scalar quantity(r) E (r) (1.4) For electrostatics the scalar quantity is a voltage (φ(r) =V(r)) and the sources are volume charges (f(r) =-ρv(r)), hence the equation changes to this following one:
.[V (r)] r (1.5) v Solution of the (1.3), subject to appropriate boundary condition (Dirichlet, Neumann, or impedance condition), to solve the original Maxwell’s equations. Solution of (1.3) is often accomplished either in closed form or numerically .Closed form solutions are available for only a limited number of boundary conditions. Hence it is usually more practical to employ a numerical method such as the finite element or boundary element methods. The potential attributed to a volume charge is given by the integral relation: (r ' ) V i (r) v G3D (r,r ' )dV ' (1.6)
Where the three –dimensional static Green function is given by
1 1 G3D (r,r ' ) (1.7) 4 | r r ' | 4r
For two –dimensional situations (e.g, in the sources of excitation run from z=- to z= and are invariant with respect to z), the following potential integrals is appropriate (r ' ) V i (r) s G 2D (r,r ' )ds' (1.8)
2D Where ρs denotes surface charges and G is the two-dimensional static Green’s function
1 1 G2D (r,r ' ) ln (1.9) ' 2 | r r | These integral relations are used to determine the potential Vi, at some point in space due to an impressed charge distribution. The parameters are shown in Fig.1.4 which are used to derive integral equations for the total potential due to an impressed source subject to boundary conditions on surfaces within the domain. Such an integral equation (for surface problems) is given by
V (r ' ) G(r,r ' ) V (r) V i (r) G(r,r ' ) V (r ' )ds' (1.10) ' ' n n
^ ^ ' ^ ' ^ Where V (r) / n n.V (r) , G(r,r ' ) / n' n .'G(r,r ' ) n .G(r,r ' ) and n'
^ denotes the outward normal to the integration surfaces S. note that n' n(r ' ) implies
^ ^ that the unit normal is a function of the integration variables, where n n(r) is a function of the observation variables.
z R=r-r’ V
r’ r ζ
y
x
(a)
z
V rˆ r’ ζ rˆ y r cos
x (b)
Fig1.4: Illustration of the geometrical parameters associated with field representation (a) Near zero setup (b) Far zone setup
For perfect election conductors (1.8) can be rewritten in terms of known surface
^ ^ charges. Specially, by making use of (1.2) .and relation / n.E n.V (r) s we obtain the usual expression
' i ' s (r ) ' V (r) V (r) G(r,r ) ds (1.11) Where, G represents either (1.5) or (1.7) as appropriate37.
1.3.2. Magnetostatic Equations The solution of Maxwell’s equation for stationary magnetic field is similar to the procedure given above for electrostatics. In the case Ampere and Gauss magnetic law are
H J (1.12) .B 0 Where the static field density is assumed to be related to the magnetic field intensity by the expression
B H (1.13) Note that in (1.10), it’s not assumed a fictitious magnetic charge density. Rather, the fundamental sources of static field are current, J. A magnetic vector potential could be defined in terms of these currents
A(r) J(r ' )G(r,r ' )dV ' (1.14) v Where the Green’s function is the same three dimensional function used for electrostatic or two dimensional function. For the latter case, the integral must be reduced to a two-dimensional one over the domain of J. with the introduction of this vector potential, solution of (1.10) with (1.11) yields the expression
B A J(r ' )*G(r,r ' )dV ' (1.15) V The derivation of (1.13) can be found in most introductory electromagnetic texts, and similar expressions are possible for two-dimensional currents where the integration is taken over surface rather than a volume52.
1.4. Instruction to ANSYS (Mechanical APDL)
ANSYS software applies to solve the FE models in this research, since the most portion of the problem was related in finding the capacitive coupling between the layers. For calculation and extracting the capacitive coupling between the conductors there is two solvers in ANSYS which are described abstractly in this section. The first possible solver in mechanical, ANSYS Parametrical Design Language, APDL is the Electrostatic Field Analysis. This analysis uses the Trefftz method to find the capacitive matrix in the whole system. It mean that an enough far surface is defined somewhere around the design objects which zero potential is defined there. There is a total steps which are constant for solving all the problems with this analysis method:
1. The first step all objects should be drawn in a CAD environment which could be readable in ANSYS. The CAD software which is used in this research is Solid works.
2. The final file which is export from CAD to ANSYS has the suffix of PARA. The GUY method is opted to explain the instruction rather than of programming. In the preference section the electromagnetic and electrical would be chosen respectively to fulfil the electrostatic analysis.
3. The element types of the object are specified by relating the exact types of the analysis object to the conductors and insulation. From the library element type for the electrostatic 3D brick 122 and 2D tetra 123 are selected. An element type is identified by a name (8 characters maximum), consisting a group label and a unique number. The element is selected from the library for use in the analysis inputting its name
4. In the material model part the relative permittivity of the insulation between the conductors should be defined.
5. The underlying method of the FEM is based on the fact that large domain could be dived in to small regions. With solving the differential equations in these regions and assembling them the whole system could be solved. These small regions are called mesh. The smaller the mesh sizes the higher simulation accuracy. In this stage the desired design would be meshed. In reality, these elements are connected to each other along their boundaries but in order to perform a theoretical approximation, the assumption is made that the elements are connected only at their nodes.
6. In this step a Trefftz node should be defined which includes all the graphic objects. Obviously the dimension values related to this surface should meet the criteria of Trefftz node.
7. Applying the boundary condition is the task in this stage. Trefftz node should obtain the infinite voltage.
8. Applying the loads could be three categories of excitation, flags and Comp. Force. For solving electrostatic problems the flag is applied to infinite surface.
9. The last step would be solving the problem and determining the capacitive coupling matrix between the conductive objects.
Another method for finding the capacitive coupling between the objects is applying the magnetostatic and edge based analysis. The difference between this method and the above mentioned method is that the element type would be differing to 3D brick 117. this time for applying the load ,the excitation part is opted. It means that voltage excitation with different values. After running the simulation the desired output data would be the total energy between the conductive surfaces (W), and defined voltage difference between them (V) the capacitive coupling would be achieved from the following equation 57:
2W C (1.15) V 2
2. Planar Inductors Impedance Characteristic
2.1. Introduction
Planar inductors are applicable in Switched Mode Power Supplies (SMPS) as a low volume replace for the previous wiring type of inductors. However, as mentioned in the first section, the relative high ratio of dv/dt due to the high switching frequencies in the power electronic switches causes the leakage currents which distort the output current of the convertor. Since the distorting current has the straight relation with the capacitive coupling between these planar layers, any devise changes in planar structure which results in reduction of these capacitive coupling would be effective. In switching frequency each planar layer could be modelled with an inductor with a capacitive coupling with the other planar layer. Fig.2.1 illustrates a boost convertor with a MOSFET switch in high frequency gate pulse. In this circuit a planar element modelled as an inductor which is parallel with the potential capacitive coupling existed in the planar structure.
iCL
iS CL
iL L
VS + VL - Cout Rout
Fig.2.1: A boost convertor circuit with a planar element and the circuit current
The input current iS which should have the similar shape as the iL would be distorted by the capacitive coupling CL. Fig.2.2 shows the spike currents which are generated due to the CL, appears in the source current iS.
VL
iL
iCL
iS
Fig.2.2: Voltage and current is the boost convertor which includes a planar inductor.
As displayed in Fig.2.2 the current spikes carried with the source current increase the electrical dissipation, decrease the circuit efficiency and could damage the insulation between the planar layers as well. Physical parameters have their own special effects on the impedance characteristic of the planar magnetic elements. In this section it is aimed to investigate the effect of these physical parameters which includes shifting percentage of the layers, distance between the tracks and the insulation thickness on the electrical resistance of the planar elements and capacitive couplings. The next step is to analyse the electrical resistance behaviour of the planar layers in higher frequencies. Moreover, the current orientation in different layers could influence the resistance behaviour of the layers.
2.2. Capacitive Coupling in Planar Elements
Changing the physical structure, affects the capacitive coupling between the planar layers. In this research the special attention is paid to the relative shifting of the planar layer positions. Simply two planar tracks could be supposed. Relative shifting of these planar tracks as shown in Fig.2.3 reduces the common surface area between them without considering the fringing effects. It reduces the capacitive coupling between them. Shifting the layers would be desired as far as it wouldn’t influence the volume of the planar element that much.
Common surface area
(a)
Common surface area
(b)
Fig.2.3: a) Effective common surface area between two none-shifted planar tracks b) Effective common surface area between two shifted planar tracks
A planar structure with two layers and two tracks in each layer is shown in Fig.2.4. The track width is w; distance between the tracks is d and with the relative displacement of the layers together, sh.
Fig.2.4: A planar structure with two layer and two tracks in each layer
Based on the planar structure in Fig.2.4, shifting percentage is defined as below:
sh shift(%) w d (2.1)
2.2.1. Calculation of the Capacitive Coupling between the Planar Tracks
The first step is calculate the capacitive coupling between the adjacent tracks in the similar layer which is presented in Fig.2.5
CAB
A B
Fig.2.5: Capacitive coupling between the two planar horizontal adjacent tracks
The problem is supposed in the cylindrical coordinates. Since the track materials in the planar are the metal the problem could be solved through the boundaries conditions. Laplace equation for scalar electric potential V in cylindrical coordinate is: 1 v 1 2v 2v r 2 2 2 0 r r r r z (2.2)
In this particular problem which consists of the two pages with the potential of 0 and
V0 , and with the angle of Ө between them, the potential equation is function of Φ and independent of the r and z the Laplace equation changes to the :
1 2v 2 2 0 r (2.3)
After solving the partial equivalences the potential function is found:
v c1 c2 (2.4)
With the boundary condition which rules that for {Φ =0, V=0} substitute these values to the above equation results that c2=0, after finding the c1, from the second boundary condition which is {Φ=π, V=V0}:
v v 0 (2.5)
Q V E , E Vdl ,C V (2.6)
1 1 V Q rE 0 , E 0 , Eds r r r r r 0 (2.7)
ld 2 V lV lV w d 2 Q w 0 dr 0 ln(d 2 w) ln d 2 0 ln r d 2 d 2 0 (2.8)
2l 0 w d 2 C ln d 2 (2.9)
In the above formula w represents the track width and d stands for the distance between the tracks. . 2.2.2 2D FEM Analysis of Capacitive Coupling in Planar Elements
In this stage for investigation about the capacitive coupling trend as a result of the physical changes, a planar structure in Fig.2.7 is introduced. This structure consists of three planar layers with three tracks in each layer.
C12
1 2 3 C17 4 5 6 C39 7 8 9
Fig.2.7: Three layer planar structure with three tracks in each layer
2.2.3. Shifting Effect on the Capacitive Coupling Between the Tracks
In this section the capacitive coupling between the tracks of the layers in Fig.2.7 when the insulation thickness is 0.2mm and track width is 5mm, are simulated with 2D FE method. In these simulations the last conductive track, with the number of nine is considered as the grounded track which has the electric potential of zero. In these simulation results there are three noticeable categories of capacitive couplings compared to the other negligible values. In this structure shifting is defined as the movement of the middle layer compared to the fixed structure of the upper and lower layers. This movement in relation to the initial structure is called shifting. The first category is about the capacitance coupling between the adjacent tracks in the similar layer (ex.C12, C56, C78...) which are roughly constant within the shifting range and generally have the smaller values for larger distance between tracks. Fig.2.8 shows some capacitive coupling instances (pF) within the shifting range for different distances between the tracks. Another point is that, C78 has the larger values compared to C12 due to the shielding effect of the middle layer in this structure which decreases the electrical fluxes between the conductors of C12. While in the case of C78, the closing path of the electrical fluxes is under the related layer which couldn’t be effected by the middle layer shielding so that C78 has a larger average total εr compared to C12 . C12 25 20 15 10 5 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C56 20 15 10 5 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C78 40 30 20 10 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C89 40
30
20
10
0 noshift 25% 50%
1mm 2mm 3mm 4mm
Fig.2.8: Capacitive coupling between two adjacent tracks in one layer over the shifting range for various distance between tracks.
The second category of these graphs includes the capacitive coupling between the tracks in two adjacent layers which have the whole common surface area between them (ex.C14, C25, C58), thus have the biggest values in this structure. Here in this structure track width have the constant value of 5mm .These capacitive couplings are decreased within the increase in shifting range. The Fig.2.9 shows instances of these capacitive coupling changes for different cases of distance between the tracks.
C14 160 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C25 160 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C69 160 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
Fig.2.9: Capacitive coupling between two tracks with whole common surfaces, which is decreased within the shafting range in various cases of distance between the tracks.
The third category belongs to the tracks in adjacent layers with no common surface between them at none shifted position. Within the rise in shifting range the common surface area between them would increase consequently the capacitive coupling (ex.
C24, C35, C48). Their changing trend is against the capacitive coupling in previous cases. Fig.2.10 shows their changes over the shifting range for different distances between the tracks. C24 60 50 40 30 20 10 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C35 60 50 40 30 20 10 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C48 60 50 40 30 20 10 0 noshift 25% 50%
1mm 2mm 3mm 4mm
C59 60 50 40 30 20 10 0 noshift 25% 50%
1mm 2mm 3mm 4mm
Fig.2.10: Capacitive coupling between two tracks in two immediate layers with no common surface area in none shifted mode but this area would increase within shifting range.
2.2.4. Insulation Thickness and Capacitive Coupling
The distance between the tracks which are related to the insulation thickness (h), affect the capacitance coupling among the tracks. The first series of simulation have been carried out for the insulation thickness of 0.2mm while the second category, simulated for 2mm insulation thickness within the distance changes between the tracks. As can be seen, the insulation thickness increased to ten times while the capacitance coupling has the reverse relation with the distance between the conductive tracks and it decreased almost seven times. It means that the reduction in the capacitive coupling is less than expected. The reason refers back to the fringing effect which explains the leakage fluxes which increases the electrical capacitance value.
C14,d=1mm 160 140 120 100 80 60 40 20 0 noshift 25% 50%
h=2mm h=.2mm
C14,d=2mm 160 140 120 100 80 60 40 20 0 noshift 25% 50%
h=2mm h=.2mm
C14,d=3mm
160 140 120 100 80 60 40 20 0 noshift 25% 50%
h=2mm h=.2mm
C14,d=4mm 160 140 120 100 80 60 40 20 0 noshift 25% 50%
h=2mm h=.2mm
Fig.2.11: Capacitive coupling of C12, within the shifting range for various distances between tracks in h=.2mm and h=2mm
As Fig.2.11 shows the relevant simulation results, for more distance between the tracks the fringing effect increases since the shielding provided by neighbouring tracks reduces. Fig.2.12 shows the difference between the fringing fluxes of C14 for two different distances between the tracks in the similar insulation thickness.
(a)
(b) Fig.2.12: Comparison of the electrical fringing fluxes between two planar tracks for different distance between the tracks
Other simulation groups belong to the C24, which is increased over the shifting range for both insulation thickness of .2mm and 2mm in various distance between the tracks which are illustrated in Fig.2.13.
C ,d=1mm 24 60
50
40 30 20
10
0 noshift 25% 50%
h=2mm h=.2mm
C24,d=2mm 40 35 30 25 20 15 10 5 0 noshift 25% 50%
h=2mm h=.2mm
C24,d=3mm 30 25 20 15 10 5 0 noshift 25% 50%
h=2mm h=.2mm
C24,d=4mm 30 25 20 15 10 5 0 noshift 25% 50%
h=2mm h=.2mm
Fig.2.13: Simulation results for C24, over the shifting range for various distances between the tracks in insulation thickness of 2mm and .2mm
2.3. Electrical Resistance in Planar Elements
As partly explained in the literature review section, planar tracks use the most of their surfaces for current conduction in high frequencies. Hence, the electrical resistivity which is in reverse relation with the cross section of the conductor would reduce compared to the conventional wire conductive. The skin effect phenomenon could be defined more in detail. In higher frequencies the current layers inside the conductor volume interact with each other, producing an alternative field. This AC field generates the eddy currents inside the conductor which push the electron charges flowing toward the outer layers near the conductor surfaces. The depth of conductivity from the outer surface of the conductor is called skin depth. It’s clear that for higher frequencies the skin depth would reduce and would be defined with this formula which ρ is the conductor resistivity, µ is magnetic permeability and ω is the frequency of the alternative field:
2 In a planar conductor track since the thickness is negligible, at high frequencies most of conductor surface is used to carry the current that’s why planar tracks are more efficient than round cross section wires. Fig.2.13 illustrates a planar track current density in three frequencies of 100 Hz, 1 KHz and 1MHz.As can be understood, in low frequencies the current density distribution over the whole surfaces is monotonous while in higher frequencies the current is pushed around the rectangular periphery, reducing the conductive surface.
(a)
(b)
(c) Fig2.13: Current density in three frequencies (a) 100Hz (b) 1MHz (c) 10 MHz
Another phenomenon appears in high frequency is the proximity effect, which is the effect of the one conductive electromagnetic field on the current density distribution of the neighbour conductors. It means that in high frequencies a conductive current not only depends on its own characteristic but the outer electromagnetic fields as well.
(a)
(b)
(c)
(d) Fig.2.14: a) Current density in two planar conductive at 1MHz with opposite current direction b) Current density in two planar conductive at 1MHz with similar current direction c) Current density in two planar conductive at 10MHz with opposite current direction d) Current density in two planar conductive at 1MHz with similar current direction.
As shown in Fig.2.14, depends on the field direction the current density would differ. As this field could have similar direction and causes currents in both conductions to get away. The opposite direction of the electrical fields would cause the currents to attract each other. The next step in this part is comparison between the electrical resistance of the three cases at the frequency of 1MHz.The first case is the one planar track in Fig.2.13 has the width of 10mm .The second case is two planar tracks with the structure of the Fig.2.14.b with the similar width and distance of 3mm .Finally the third case is a 50% shifted structure with similar characteristic, operated at frequency of 1MHz.
(a)
(b) Fig.2.15: (a) Current density in two shifted planar tracks at the frequency of 1MHz (b) Current density in two shifted planar tracks at the frequency of 10MHz
Table 2.I contains the electrical resistance values of the above described three cases at the frequencies of 1MHz and 10MHz. As can be understood the electrical resistance of an alone track is half of the second case which includes two adjacent tracks with whole common surface area as a result of proximity effect between these two conductors in the mentioned frequency. In fact the second conductor leads the current distribute even more to the outer surfaces and edges of the first conductor. The third case which includes the 50% shifted tracks shows the resistance values between two other cases. Since the common surface of the conductors halved and the proximity effects have less effect compared to the second cases. As can be seen in Fig.2.15 the current density distribution is more concentrated around the conductor edges and the common surface area roughly contains no current. Table 2.I: Electrical resistance of a planar track in the three cases
Electrical Frequency Frequency resistance(mΩ) 1MHZ 10MHZ
One planar 25 49
Two planar 44 86 tracks Two shifted 35 70 planar tracks
2.3.1 .Relation between current direction and Resistivity
The objective of this section is to understand the effect of the current direction on the resistivity of the planar tracks. Current direction changes the electromagnetic field and the force direction between the adjacent conductive tracks. This influence which is recognized as proximity effect changes the current density in the conductive area of the tracks and interferes with resistivity of the planar inductors.
R11 110
105
100
95
90 no shift shift25% shift50%
+++ +-+ ++-
R22 120 115 110 105 100 95 no shift shift25% shift50%
+++ +-+ ++-
R33 115 110 105 100 95 90 85 no shift shift25% shift50%
+++ +-+ ++-
R44 120 115 110 105 100 95 90 no shift shift25% shift50%
+++ +-+ ++-
R55 125 120 115 110 105 100 95 no shift shift25% shift50%
+++ +-+ ++-
R66 115 110 105 100 95 90 no shift shift25% shift50%
+++ +-+ ++-
R77 110
105
100
95
90 no shift shift25% shift50%
+++ +-+ ++-
R88 120 115 110 105 100 95 no shift shift25% shift50%
+++ +-+ ++-
R99 115 110 105 100 95 90 85 no shift shift25% shift50%
+++ +-+ ++-
Fig.2.15: Electrical resistance of the tracks in a planar structure for different current direction over the shifting range at the frequency of 1MHz
The above graphs in Fig2.15, illustrate the trend of current direction effect on the planar tracks resistivity over the shifting range in the operation frequency of 1MHz. For current direction three cases are assumed for these three layers .When all the layers conduct the similar current direction the case would be represented by(+++). The second mode occurs when the middle layer conduct the current in different direction from the outer layers and signed by (+-+). The last option happens when the middle layer is in the similar current direction with only one of the outer layers and shown with (++-). From the graph it would be understood that in this frequency at the first situation which the all layers, have the similar current directions the track resistance increase compared to the other cases. The reason is that when the current direction is not similar in the three layers the overall electromagnetic force on each conductive tracks, increases the effective conductive area on the periphery of the tracks, resulting the resistance to decrease compared to the first mode. Repeating these simulations for frequency less than 1 MHz reveals that there is negligible difference between these possible cases of the current direction from the resistance values point of view. In order to simulate a real planar element case, the summation of the all N*I should be zero. Therefore, in the above example, the first and third layer could conduct a current with similar value and direction, whilst the middle layer with the half turn number conducts the current in opposite direction and the twice value. At different frequencies, for calculation of the resistance, the first and third layer is grouped to consist one conductive layer called r1 and the middle layer is considered the second conductive layer called r2. Electromagnetic 2D, FE simulation provides the values of these resistances. It is aimed to find out the effect of the different current direction on the current density and finally the resistors. Table 2.II shows the values of these in special frequencies.
Table 2.II: Conductive resistance of a planar structure for different current direction in some frequencies
r and r 1 2 100Hz 1MHz 10MHz resistance(mΩ)
(++) 17 35 108
(+-) 17 35 106
As can be observed in Table 2.II, current direction does not have much effect on the resistance of the planar element conductive layers. In primary analysis it might be expected that in the mode of different current direction, the proximity effect of the opposite currents in both sides of the middle layer causes the increase of the conductive cross section area. However, the current density observation in these cases explains that the current accumulation in planar layers is not, as expected. Instead of current distribution on the track length, the majority of the current accumulates to the edges. This phenomenon prevents from appearance of the proximity effect regarding to the current direction. Fig 2.16 (a) shows the edge of a planar track and in Fig.2.15 the current density distribution is figure out. As can be seen the middle part has less current compared to the upper and lower parts. Fig2.16(c, d) is the current density distribution in vertical direction of the middle part in a planar track. It is concluded that the major current density is accumulated in the edge section rather than the middle parts.
(a)
(b)
(c)
(d) Fig2.16. (a, b) current density distribution in the vertical direction of the planar track edge (c, d) current density in the vertical direction of the middle part in a planar track
Fig.2.17 (a, b) shows the current density in the edge section of the middle track in a three layer planar structure in vertical direction when all current have the similar directions. Thus, the current get away from the up and bottom part, accumulates in the middle section of the edge. In Fig.2.17(c, d) shows the current density on the edge of the middle track when the current direction in middle track is in the opposite direction with the two other tracks, so that the current density attracts to the upper and bottom of the edge.
(a)
(b)
(c)
(d) Fig.2.17: a, b) Current density distribution along the specified array when all the tracks have similar current direction c, d) Current density distribution along the specified array when the middle track has opposite current direction
Fig.2.18 (a, b) illustrates the current density along the vertical array in the middle section of the mid layer when all tracks have similar current direction. While Fig.2.18(c, d) shows the current density along the vertical array in the middle section of the mid layer when the middle track has the opposite current direction. As the following graphs figure out, the majority of the current distribution occur in the track edges of the planar layers, thus the current direction diversion and the proximity effect doesn’t affect the resistance of the conductive tracks much even in high frequencies which is more than the operating frequencies of the conventional SMPS.
(a)
(b)
(c)
(d) Fig.2.18: (a, b) Current density distribution along the specified array when All the tracks have similar current direction (c, d) Current density distribution along The specified array when the middle track has opposite current direction
2.3.2. Effect of Shifting on the Resistance in Different Distance between the Tracks
The planar structure which is assumed here has the structure of the Fig.2.7. Through the magnetostatic 2D Finite Element analysis the electrical resistance of these planar conductive tracks would be calculated. The characteristic is: track width (w):5mm, h=.1mm, frequency: 1MHz, distance between the tracks is changed between 1mm to 5mm. Whilst the first and third layers are kept constant the position of the second is changed with increasing the shift percentage. The following graphs illustrate the relation between the shifting percentage and the electrical resistance of each planar track in different distance between the tracks (d). R11 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R22 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R33 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R44 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R55 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R66 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R77 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R88 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
R99 140 120 100 80 60 40 20 0 noshift 25% 50%
1mm 2mm 3mm 4mm
Fig2.19: Electrical resistance of the tracks in three layer structures over The shifting range for various cases of distance between the tracks
The above graph shows the resistivity of each track (mΩ) over the range of shifting percentage in four distances between the tracks. By and large, the electrical resistance decreases with the increase in shifting range. Moreover, for the larger values of the distance between the tracks, electrical resistance of the tracks decreases. Therefore, reduction of the resistance loss happens in the expense of boosting the volume in the planar elements.
2.3.3. Relation of the Insulation Thickness and Planar Track Resistance
This section is devoted to investigate the effect of insulation thickness on the electrical resistance of the planar layers.
R11,d=4mm 100
95
90
85
80
75 no shift 25% 50%
h=2mm h=.2mm
R22,d=4mm 105
100
95
90
85
80 no shift 25% 50%
h=2mm h=.2mm
R33,d=4mm 100 95 90 85 80 75 no shift 25% 50%
h=2mm h=.2mm
R44,d=4mm 105 100 95 90 85 80 no shift 25% 50%
h=2mm h=.2mm
R55,d=4mm 150
100
50
0 no shift 25% 50%
h=2mm h=.2mm
R66,d=4mm 100
95
90
85
80 no shift 25% 50%
h=2mm h=.2mm
R77,d=4mm 100 95 90 85 80 75 no shift 25% 50%
h=2mm h=.2mm
R88,d=4mm 105 100 95 90 85 80 no shift 25% 50%
h=2mm h=.2mm
R99,d=4mm 100 95 90 85 80 75 no shift 25% 50%
h=2mm h=.2mm
Fig.2.20: Electrical resistance of tracks in a three layer planar element over the shifting range for insulation thickness of 2mm and .2 mm
The red graphs in the above Fig.2.19 and Fig.2.20 are related to the planar track resistance in the insulation thickness of .2mm, when this value becomes ten times, 2mm, then the resistance values are decreased. With the increase in the shifting percentage this reduction becomes stronger.
3. Shifting Effect of Planar Tracks on Total Capacitive Coupling of Two Layer Planar Element
In the previous chapter the capacitive couplings between the tracks in some different planar structures have been calculated using 2D FEM. The aim of this chapter is to analyse the effect of shifting the layers to reduce total capacitive coupling in a two layer planar element. 2D and 3D FE simulations are carried out and the results are compared.
3.1. 2D and 3D FE Analysis of Shifting in Two Layer Planar Elements
2D model for the planar layers are developed by plotting the cross section area of the tracks in different cases, positions the tracks with respect to each other. It is aimed to investigate the relation between the shifting rates and its quantity effect on the capacitive coupling between the layers.
(a) l
w d
h
sh (b) Fig.3.1: a) Physical parameters of a planar layer b) Capacitive coupling between a two layer planar element and its physical parameter
The inductor parameters: the track width (w) distance between the tracks in one layer (d) the insulation thickness (h) Turn number (n) are kept constant in all simulations. The mean length of the conductor in one layer is defined as (l). All these parameters are illustrated in Fig.3.1. In several cases, the bottom layer is shifted and 2D simulation is carried out to calculate capacitive couplings for each case and the results are used to analyse the shifting effect. The approximate amounts of these capacitances between two plates A can be calculated with a simple formula: C h
A
h
Fig.3.2: Two infinite plate with commo surface area of A and vertical distance of h
Table 3.I, contains the structure parameters of two layer planar elements which are used in the following simulations:
Table 3.I: Physical parameters of the two layer planar structure
Track width(w) 15mm
Distance between tracks(d) 10mm
Insulation thickness(h) .18mm Copper thickness .05mm Relative permittivity of the 1.88 insulation(εr)
Due to the fringing effect and asymmetrical geometry of the planar structure it is important to perform 3D Finite Element to achieve the exact values of capacitive coupling.
Fig.3.3: 2D and 3D, FE simulation results over the shifting range and comparison with calculation result
Therefore, the leakage flux that has not been included in the formula has a significant effect on the capacitance value. As can be seen in Fig.3.3, at the shift of 50 % the capacitive coupling is minimized. Since in the real case, the number of tracks on each layer is more than 2, shifting more than 50% generates repeated cases, meanwhile increases the volume of the magnetic element. Table 3.II contains the amounts of the coupling capacitors between the two relatively shifted layers. As shown in the table with increasing the shifting amount, the common surface between the layers would decrease. Since shifting more than 50% is equal to the volume boost, this amount is raised up to the 50%.
Table 3.II: Capacitive coupling values over the shifting range in two layer structure from 2D & 3D, FE analysis
Capacitive Capacitive coupling Simplified Shift coupling results results in 2D Calculated in 3D (%) simulation (pF) capacitance simulation(pF) results from the formula(pF) 0 1265 1307 1312 9 1096 1136 1115 15 979 1015 984 18 912 939 918 24 803 815 798 30 687 692 656 36 569 589 525 42 483 520 415 50 402 460 330
In Fig.3.4 (a, b), from the electrostatic simulation the electrical field distribution in the none-shifted and shifted structure of this two layer planar structure is shown in the insulation thickness of 0.18mm and in Fig.3.4 (c, d) this field is figured out for the insulation thickness of 1mm. Comparison between these figures reveals that in low insulation thickness the electric field concentrates more around the track edges.
(a) (b)
(c)
(d)
(e) Fig.3.4: a, b) Electrical field (E) in two layer planar shifted and none shifted structure with insulation thickness .18mm c, d) In two layers planar shifted and none shifted Structure with insulation thickness’ of 1mm (e) Colour code for E magnitude
3.2. 2D and 3D FE Analysis of Distance Between the Tracks in Two layer Planar
At the this stage, for a few different distances between the tracks in each layer (d) and with the optimum 50% shift, the 2D simulation results are illustrated in Fig. 3.4. For the case of d=15mm which has no common surface area between the two layers, a capacitive coupling still exists because of the fringing effect. This time the formula graph is under the 2D simulation graph with a parallel slope, due to applying the same shifting amount in all points. Table 3.III contains the simulation and calculation results of this section. As it is expected, increasing the distance between the tracks results in reduction of the common surface and thus the capacitive coupling.
Table 3.III:2D & 3D FE simulation results of a two planar layer for different distances between the tracks
Distance Capacitive Capacitive Calculated between the coupling results in coupling results in capacitance tracks(mm) 2D simulation(pF) 3D simulation (pF) results from the formula(pF) 1 997 1010 847
2 942 980 780
5 755 770 705
10 492 460 302
15 125 159 0
3.3. An Introduction to Spectrum Analyser
Spectrum Analyser is a device which shows the impedance and power spectrum of a signal (usually RF signal) in the frequency domain rather than time. A Spectrum Analyser can illustrate the amplitude and phase of a signal in different kinds of measuring systems. Fig.3.5 illustrates the Spectrum Analyser of the Laboratory which is applicable for the spectrum frequency range of 9 KHz to 3GHz.
Fig.3.5: Spectrum analyser used in this research for measuring the planar elements impedance
The first step for measuring with the Spectrum Analyser is calibration. In this regard the import kit is used for calibration purposes. Import kit contains the parameters for new calibration. For a set up calibration standards is selected and measured over the required sweep range for many calibration types of magnitude and phase response of each calibration standard. The analyser compares the measurement data of the standards with their known ideal responses. The difference is used to calculate the system errors. Using a particular error model (calibration type) it derives a set of system error correction. The system error correction data is used to compare the measurement results of DUT that is measured instead of the standards. Calibration is always channel- specific. because it depends on the hardware setting, in particular on the sweep range. The calibration types depend on the number of the test ports of the analyser. Fig.3.6 shows an image from the calibre kit which is applied for calibration of the above Spectrum Analyser.
Fig3.6: Calibre kit used in this research for measurement calibration of spectrum analyser
For calibration purpose, first the key of “cal” on the Analyser is pressed then the desired port to calibrate is selected. The number of the data samples should be entered in advance which is usually set to 2000 point. The Calibration is performed in these three stages:
Short circuit calibration Open circuit calibration 50 Ω impedance calibration
After calibration the main window should be divided in two windows, one for the impedance phase and the other for impedance amplitude. There is a Z option which
transforms to S11 or S22, depending on the applying port. The next step is verifying the frequency range in which the impedance is measured. The planar inductor experiment set-ups, in this research mostly indicates their capacitive characteristic in frequency range of 1MHz to 15MHz.
3.4. Experiment Results for Capacitive Coupling of Two Layer Planar Inductor
At the last stage some prototypes have been built to compare with the simulation results. These samples have the exact parameters of the ones used in the simulations.
The insulation with εr=1.88 is used in these tests. For measuring the capacitive coupling, a Network Analyser is used to give the impedance of the sample in the specified range of frequencies. Fig.3.7 shows a planar structure prototype connected to Spectrum Analyser.
Fig.3.7: a) Prototype sample planar structure measured with spectrum analyser
After connection of the terminal to the probe and its related ground, at the desired frequency, the impedance of the 2000 point in that frequency range would be achieved. These data as the amplitude and phase in each frequency point could be saved as a .dat file which is retrieved with software MATLAB. The capacitive impedance could be derived from the phase and amplitude data information with a simple program in MATLAB. Fig.3.8 shows the magnitude and the phase values of the inductor impedance in the frequency range of 1MHz to 5MHz. The test result shows that in this frequency range the phase angle is pretty close to -90 . For instance a typical point at 2 MHz has the magnitude of 66 Ω and the phase of -86 . The samples have been taken for frequency ranges at which the spectrum analyser was calibrated. Then the coupling capacitor amounts are obtained from those ranges at which the planar element has capacitive impedances. A sample measurement from spectrum analyser is illustrated in Fig.3.8.
Fig.3.8: Magnitude and phase of a planar structure measured with Spectrum Analyser
Each sample results in any frequency range could contain up to 2000 points of frequency data, which includes information of magnitude and phase in these frequencies. With simple calculation at any of these frequencies the capacitance coupling could be retrieved for the planar magnetic sample of planar winding. The magnitude results of a typical sample from the Table 3.III, with d=1mm, is plotted in Fig.3.9 at the frequency range of 1MHz to 5MHz, which its capacitor
1 coupling in frequency of 3MHz could be obtained by this Equation: C . This 2f | Z | amount from the test result, confirms the simulation results on Table3.III and the impedance point is shown in Fig.3.9 (a). The first tests are about measuring the capacitive couplings for different amount of shifting. The graph in Fig.3.9 (b) shows the results of the test measurements. The test results are very close to the 3D simulation results. As the confirmation of the simulation, the more the shifting percentage in two layer planar inductor, the less its equal capacitive coupling from the terminals.
(a)
(b) Fig.3.9: a) A prototype capacitive impedance over the frequency range b) Test results for capacitive coupling of over the shifting range the two layers planar structure and comparison with simulation result
For verification of the second categories of the simulations which was about the effect of changing the distance between the tracks on the total capacitive coupling of the two layer planar elements, the impedance of some test set ups are measured and the results are illustrated in Fig.3.10. It proves that increasing the distance between the tracks reduces the total capacitive coupling.
Fig.3.10: Test measurements for capacitive coupling of the two layer shifted planar structure for various distance between the tracks (d) and comparison with simulation result
4. Total Capacitive Coupling in Multi Layer Structures
This section is devoted to investigate the different structure of multilayer (more than two layer) planar inductor. The structure which is considered is a four layer planar with four tracks in each layer. Through 3D Finite Element simulations all of capacitance couplings between the tracks could be calculated. Each layer could be modelled as an inductor which is connected to the next layer inductor with two capacitors .These capacitor amounts are half of the values calculated with FE analysis. Fig.4.1 (a) illustrates this model for two layer inductor. In this part it is aimed to compare the total capacitive coupling of the four layers simple structure with the 50% shifted one. Fig.4.1 (b) illustrates a structure with 50% shift and the relevant parameters. The shifting definition is based on the Eq.2.1.
C1ab
a b
L1
C12a C12b
L2 a b
C 2ab (a) d w 1 h shift C12 2
3 C34
4 (b) Fig.4.1: a) Capacitance-inductance model for two layer planar element b) A four layer shifted structure model and the relevant parameters.
The physical parameters in this case are: The track width(w) is considered 5mm
Distance between the tracks (d) is 5mm
Distance between the layers (h) is 0.2mm Number of turn in each layer is four The small capacitive coupling values under 10 pF in the shifted structure (ex. the
C12, C24) are considered negligible. Table 4.I illustrates the capacitive coupling values of the shifted and none shifted structure. In this regard the capacitive coupling between each consecutive pair (ex. C12, C23, C34) is called X and the capacitive coupling between each every other layers (ex. C13) is called Y.
Table 4.I: Capacitive couplings in multi layer shifted and none-shifted structure
Capacitive None- shifted coupling(pF) shifted X 547 207 Y 3 175
Fig.4.2(a) shows a series connection of the shifted four layer planar inductor with the connection sequence of (1234), with the capacitive coupling of X and Y and Fig.4.2(b) illustrates the none-shifted four layer structure with the capacitive coupling X. At high frequencies with the condition of ZL ZX ,ZY it could be possible to consider the open circuit impedance of none-shifted structure. The small value of Y is neglected as well.
1 a1 b1
x x 2 2 y y a2 2 b2 2 2
x x 2 2 3 y a3 b3 y 2 2 x x 2 2
a4 4 b4
(a)
1 a1 b1
x x 2 2
a2 2 b2
x x 2 2
a3 3 b3
x x 2 2
a4 4 b4
(b) Fig.4.2: a) Series connection of the four layers planar in shifted structure b) Series connection of the none-shifted four layer planar structures.
The total capacitive coupling between the terminals would be achieved with simple calculations and results in this summarised formula:
111Y 3 X 118X 2Y 2 52X 3Y 36Y 4 8X 4 Ceq 3 3 2 2 72Y 24X 104X Y 150Y X (4.1)
The X values decrease with increasing the shifting percentage while the Y value rises within the shifting range. The total capacitive coupling when the shifting percentage is zero would be calculated from this formula:
2X Ceq0 3 (4.2) In this calculation the X value is decreased linearly and the Y value increases within the shifting range. Changing the values of X and Y the Fig.4.3 shows the variation of Ceq and its comparison with the zero shifting case. K is the parameter which X indicated the ratio, over the shifting range. From the graph in Fig.4.3 it is Y determined that for a specific amount of shifting a turning point occurs which from then the shifted structure would possess the less equivalent capacitive coupling than the none shifted structure. Of course in this solution the capacitive coupling have constant values.
Fig.4.3: Comparison between the ECC in none shifted and shifted planar structure with the formulas calculated values.
4.1. Shifting Effect on the Equivalent Capacitive Coupling
In the previous section it is proved that shifting technique is quite effective in reduction of a total Capacitive Coupling (CC) in two layer planar elements. To investigate this effect on the planar elements with more than two layers, a structure of four layers is assumed with the physical parameters similar to ones metioned above. X represents the CC between the two adjacent windings (ex.1 and 2), while Y represents the CC between one winding and the one just after the adjacent winding (ex.1 and 3).
(a)
(b)
(c)
Fig.4.4: a) Four layer planar structure b) Capacitive coupling between the layers c) Electrical field between the layers and shielding effect of the layers on its distribution and magnitude
Shifting a winding relative to its previous layer reduces the CC between them which is X. Fig 4.4, shows these capacitive coupling between the layers in this four layer element. However, the CC between a winding and one on the next two layers, (Y) increases simultaneously. This increase is due to the middle winding and lack of shielding between them. Since the effect of decreasing the X is almost neutralised due to increase in Y, the Equivalent Capacitive Coupling, ECC is roughly constant within the shifting range. Applying this shifting method for every other one layer in a planar magnetic with more than two layers results in a trivial changes in the ECC, over the shifting range. Since shifting the second layer with respect to the first layer removes the electric shields between the first and third layers, the total capacitive coupling would be affected. As can be seen in Fig.4.5 (a), over the shifting range, the ECC increases slightly until 40% shift and after that it starts to decrease. Thus, shifting method causes negligible change in equivalent capacitive coupling. In Fig.4.5.(b), the similar simulations have been done for various distances between the tracks (d) with the applied shifting percentage of 50% in every other one layer. The equal capacitive coupling has been changed negligibly over the d range. In the next section, a new structure for multi layer planar winding would be introduced which provides less ECC, compared to the simple multi layer structure.
(a)
(b) Fig.4.5: a) Changing the capacitive couplings of X, Y and ECC within the distance range and comparison between the shifted and none-shifted structure b) Changing the capacitive couplings of X, Y and ECC within the shifting range
4.2. The effect of Insulation Thickness on the Equivalent Capacitive Coupling
In this section the effect of insulation thickness on the ECC is investigated. The structure consists of four planar layers with four tracks in each layer. The simulation have been done for cases of h=.2mm and h=1mm for the various distance between the tracks and at the shifting point of 50%. From the Fig4.6.(a) it is found that for the distance less than 4mm the simple structure offers less ECC than the shifted structure while after 4mm distance point the trend divert and the shifted structure posses less ECC than the simple structure. Fig4.6. (b) shows these trends for the insulation thickness of 1mm. In this case for the whole range of the desired distance between the tracks, the simple structure is below the shifted ones. Thus for increasing the insulation thickness would increase the ECC.
(a)
(b) Fig.4.6: a) Comparison between the ECC for different distance (d) in Simple and shifted structure with the insulation thickness of .2mm b) Comparison between the ECC for different distance d) In simple and shifted structure with the insulation thickness of 1mm
4.3. Experimental Result for Comparison between the Different Structures in Multi Layer Planar
In this section it is understood that shifting the layers for multi layer structure is practically a failure since the simple structure offers less capacitive couplings for most cases. This experiment section is about comparing the effect of shifting in multi layers planar elements. In this regard, two planar inductors are compared, the first one is a ten layer inductor with the track width (w) of 5mm, the insulation thickness is .2mm and distance between the tracks are 5mm.All the layers are in the similar position connected series. The second structure is made of ten layers which are shifted 50% in every other one layer to investigate the effect of shifting in more than two layers structure. As can be expected from the simulation results this shifting is failed from the ECC reduction point of view. The ECC for shifted structure is 67pF and for the simple structure is 47 pF. Fig.4.7 (a, b), shows these two structures of ten layer planar windings.
(a) (b) Fig.4.7: a) Ten layer planar inductor with shifted structure b) Ten layer planar inductor none-shifted structure
5. A New Winding Structure to Decrease Capacitive Coupling for N-Layer Planar Magnetic Element
Introduction
In the previous chapter, after performing FE simulation and mathematical analysis on multi layer planar magnetic elements with shifted layers, we concluded that the method of shifting layers does not effectively reduce the equivalent capacitive coupling for a magnetic element with more than two layers. The cause is removal of the layer which acts as a shield between their upper and lower layers. To reduce the equivalent capacitive coupling on n-layer magnetic elements the winding structure should be designed in a way to maximize shielding effect of each layer while reducing the capacitive coupling between adjacent layers. Connections of several windings which make the magnetic element have a significant effect on the value of the equivalent capacitance. Table 5.I presents the equivalent capacitance of a four layer planar inductor for some possible series connections of four layers. As may be observed the first connection pattern gives the lowest equivalent capacitive coupling. Fig.5.1 shows the various series connection of the layers addressed in Table 5.I.
1234 1342 1324 1 1 1 2 2 2 3 3 3 4 4 4
2314 1243 1 1 2 2 3 3 4 4
Fig.5.1: Various series connection of the layers in a planar structure
Table 5.I: Capacitive couplings in simple structure Winding arrangement Equivalent capacitive sequence in two layer coupling planar element
(1,2,3,4) 100 (1,3,4,2) 142
(1,3,2,4) 135 (2,3,1,4) 138 (1,2,4,3) 110
The general conclusion from Table 5.I is that by connecting adjacent windings the equivalent capacitance reduces. For instance by connecting layers 1, 2, 3, and 4 in series the equivalent capacitance is less than the case where layers 1, 3, 2, and 4 are connected in series. The explanation is as a result of each connection some stray capacitors are short circuited and the stray capacitance between adjacent winding is the most significant. Therefore, by connecting closer windings, a larger capacitor is short circuited and overall the equivalent capacitor decreases more than other connections. Designing the winding for n-layer magnetic element, the rules of adjacent winding connection and maximum shielding should be used to achieve the best result.
5.1. New Winding Structure
Combining all the characteristics mentioned above, a new planar winding structure named “Split winding” structure is presented, simulated, experimented, and compared with a “Simple winding” structure as the final result of this research. Schematics of the Split winding and simple winding structures are presented in Fig.5. 1(b).
(a)
(b)
Fig.5.1: a) Two layer planar magnetic elements with 8 turn windings in simple structure b) Two layer planar magnetic with two windings in each layer with the turn number of eight in split structure.
The other parameter which influences the equivalent capacitance is the number of layers connected in series. The higher the number of layers more stray capacitances are connected in series and therefore lower the equivalent capacitance is. For instance to make a 20 round winding, connecting four 5-round layers gives a lower equivalent capacitance than connecting two 10 round layers. The number of layers in Fig.5.2 is two. However it may increase with the same structure. The number of turns in each layer is eight. In the Split structure, each layer contains two windings the distance between the tracks in each winding is 6mm, and the second winding is placed in the middle of the space between the tracks of the first winding. Now the distance between the tracks in one layer would be 0.5mm. With Finite Element (FE) analysis the capacitive couplings between each two windings are obtained and compared with the Simple structure. To have a clearer image of the Simple and Split structures a 2D schematic of both structures is presented in Fig.5. 2.
1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
(a)
1 1` 1 1` 1 1` 1 1`
2 2` 2 2` 2 2` 2 2`
3 3` 3 3` 3 3` 3 3`
4 4` 4 4` 4 4` 4 4`
(b)
Fig.5.2: a) Four layer with eight turn windings in the simple structure b) Split structure with four layers which is consisted of two, eight turn windings in each layer.
Using the connection rule, the connections between windings of both structures are presented in Fig.5. 3. It may be observed that the winding which have the most common area are connected in series to minimize the equivalent capacitive coupling. The terminals of each multi layer planer elements are shown with arrows.
Fig.5. 3: a) Connections of multi layer planar magnetic elements Simple structure b) Split Structure
5.2. Modelling the multi layer planar magnetic elements
To predict the resultant equivalent capacitive coupling, a simplified model of two planer layer which may be extended to develop a model for n-layer magnetic element is presented in Fig.5. 4. Each winding is modelled as an inductor and the capacitance between each winding and its adjacent windings is presented with two capacitors in both sides of the inductor. The model is presented for Simple (a) and Split structures (b).
C11`/2 1 C11`/2 1 1`
C /2 C12/2 C12/2 C12/2 C12/2 C1`2`/2 1`2`
2 2` 2
C22`/2 C22`/2 (a) (b) Fig.5. 4: a) winding connection of the simple structure b) Winding connection of the split structure
In Fig.5.4 (a) winding 1 is placed on layer 1 and winding 2 is placed on layer 2 and
C12 is the capacitive coupling between winding 1 and 2. In Fig.5.5 (b) windings 1 and 1` are placed in layer 1 and windings 2 and 2` are placed in layer 2. C12, C1`2` are the capacitive couplings between windings 1 and 2 and windings 1` and 2` respectively. C11` and C22` are capacitive couplings between windings 1 and 1` and windings 2 and 2` respectively. In the split structure, the capacitive coupling between the immediate windings which are placed exactly underneath of each other, and poses the total common surface area between them are called Cv . Comparing this capacitive coupling in both structures, it is revealed that the amount of this capacitor in Simple structure is almost twice as the split ones. That is because the common surface area is halved for the Split structure. Therefore, the capacitive coupling for
Simple structure is 2Cv. In Simple structure, the other capacitive couplings are neglected, thus the only capacitor amounts which are taken to accounts are the vertical capacitances, 2Cv. On the other hand, in Split structure there are the other important capacitive couplings, between the two windings in the same layers. These
CCs between the horizontal windings in outer layers are called Ch. However, these CCs between the horizontal windings in interior windings are reduced to small values under 10 pF. That’s because, for the internal layers the electric fluxes between the horizontal windings are shielded by the surrounding layers of up and down. In this case the CC between the horizontal windings in the interior layers is called Chm. Finally, the CC between the diagonal positioning windings to each other is named
Cd, these CC are also have the negligible values due to the zero common surface area between them. Cv, Ch, Chm and Cd are shown in Fig.5. 6.
Ch
Cv Chm
Cv Cd
Ch Fig.5. 5: Capacitances between two tracks
Having defined individual capacitances between windings, the next step to develop our model is to include connections. Fig.5.6 presents the simplified circuits resulted after including connections presented in Fig.5. 5.
1
Cv 1 2Cv/2=Cv Cv C C 2 v v 2
Cv Cv Cv Cv
n-1 Cv Cv n-1
Cv Cv Cv n n
(a) (b) 1
Cv/2 Cv/2
2
Cv/2
Cv/2 Cv/2
n-1
Cv
Cv/2 Cv/2 n C C C C Cv h h h h m m m m / / / / ( 2 2 2 2 Chm/2 C
Ch/2 Ch/2 v Chm/2 + C ( h m n` C Ch/2 Chm/2 Chm/2 ) v / Chm/2 Chm/2 Ch/2 + 2 C Cv/2 Cv/2 h m ) / 2 (n-1)`
Cv
Cv/2 Cv/2
2` Cv
Cv/2 Cv/2
1` Cv/2
(c) (d)
Fig.5.6: a) The capacitive-inductive model for n layer connection of series winding for simple structure b) Simplified connection of the winding connection c)The capacitive-inductive model for the series connection of winding in, n layer, d) Split structure simplified model of this structure
Fig.5.6 (a) shows the circuit model of a multi layer planar inductor with simple winding structure and series connection of windings. Fig5.6 (b) illustrates the capacitive circuit of Fig.5.6 (a). Fig.5.6 (c) is the circuit model of a multi-layer planar inductor with split winding structure and series connection of the windings. Fig5.6 (d) is the capacitive circuit of Fig.5.6(c). Since the equivalent capacitance is our focus, the value of this capacitance for n-layer structure has been calculated. The equivalent capacitance for n-layer planar magnetic element with simple winding structure is formulated in Eq5. 1.
n2 2Cv Cv 2Cv Cv _ simple Ceqsimple Cv Cv || ...|| Cv Cv || Cv || Cv || n 2 2 n 2 n 2 (5.1) Cv in Equation (1) is the vertical capacitance of split winding structure. The vertical capacitance of the simple structure (Cv-simple) is 2Cv. to calculate the equivalent capacitance of the planar magnetic inductor with spilt structure; a simple program has been used to calculate the equivalent capacitance by starting from the core capacitance in Fig.5.6 (d) which is (Cv+Chm)/4. As each layer is added a bridge develops. The equivalent capacitance has been calculated for each bridge. Then the results of simple and split structures are compared for different numbers of layers.
To have realistic data FE simulation has been performed and resultant values for Cv, Ch, and
Chm has been applied. Table 5.II and Table 5.III illustrate these results for simple and Split structures respectively.
Table 5.II: Capacitive coupling in simple structure
Capacitive coupling(Pf) Value in the Simple structure
2Cv (C12,C34) 966
C13,C24 7.8
C14 4.7
Table 5.III: Capacitive couplings in split structure Capacitive coupling (Pf) Value in the Split structure
Ch (C11’, C44’) 56
Chm (C22’,C33’) 4.8
Cd(C1’2,C12’,C2’3, ,C24’, C34’,C3’4) 6.3
Cv(C12,C1’4,C23,C2’3,,C34,C3’4’) 477
The parameters used for FE simulation are presented in Table 5.IV.
Table 5.IV: Physical characteristic of
the planar magnetic
Track width(w) 5mm Distance between the .5mm tracks(d) Insulation .21mm thickness(h) Relative permittivity 1.88 Insulation (εr) Cupper thickness .05mm Number of turn in a winding of 8 layer
The results of comparison between spilt and simple structure for different number of turns is presented in Fig.5.7. To deepen the analysis the effect of variation in Cv, Ch, and Chm has been investigated as well. As may be observed in Fig.5.7 (a), the equivalent capacitance of the simple structure is strongly dependant on the number of layers. With higher number of layer the equivalent capacitance of the simple structure reduces. Although the equivalent capacitance of the spilt structure reduces as well, it has lower dependency to the number of layers. As a result, for each set of capacitive parameters (Cv, Ch, Chm), there is a number of layers that for which and below the split structure shows lower equivalent capacitance than simple structure.
(a)
(b)
(c)
Fig.5. 7: a) Comparison between the equal capacitance for simple and split winding structures for different Cv b) Comparison between the equal capacitance for simple and split winding structures for different Ch , c) Comparison between the equal capacitance for simple and split winding structures for different Chm
The effect of each stray capacitance on the equivalent capacitance of the planar magnetic element has been investigated and results are shown in Fig.5.6. As may be observed in Fig.5.7 (a), increasing Cv-simple and Cv-split increases the equivalent capacitance. However, the interesting point is that it also changes the number of layers for which the simple structure becomes suggestible over split structure.
As may be seen in Fig.5.7 (b) Ch-split has a significant effect on the value of equivalent capacitance. As a result the number of turns that allows spilt structure to be favourite is strongly affected by value of Ch-split. On the other hand, as is illustrated in Fig.5. 8(c) the variation of Chm-split has not a significant effect on the equivalent capacitance of the split structure and it does not change the suggestible number of layers for spilt structure to be favourite.
Inspired by effectiveness of Ch-split and ineffectiveness of Chm-split, an improvement is expected if the value of Ch-split may be reduced for the cost of increasing the value of
Chm-split. The enhancement required in the structure of winding is to reduce the track width in top and bottom layer of the magnetic element. As a result, the value of Ch- spli will be reduced because of the increased distance between tracks and the value of the Chm-split will be increased as a result of reduction of shielding by top and bottom layer. This enhancement in the winding structure is shown in Fig.5. 8.
Ch
Cv Chm
Cv Cd
Ch
Fig.5. 8: Changing the outer layers width to reduce the equivalent capacitive coupling.
The result of this enhancement is presented in Fig.5. 9.
Fig.5. 9: The effect of outer track width on equivalent capacitance
The two winding per layer split structure explained in above section may be extended to a general split structure which has a higher number of windings per layer. The reduction in equivalent capacitive coupling after series connection of windings will be improved even more with a higher number of windings per layer. However, the practical problem of making the actual connections between layers may hassel the design of an split structure with three or four windings per layer.
5.3. Experimental Results
This section devoted to the experiment tests in order to verify the results of this chapter. The final experiments of this thesis compared the Split structure and Simple structure. For that purpose two model of windings are built. The first windings are composed of eight turns with the distance between tracks of 0.5mm. The second type consists of four turn windings with the track width of 5mm and distance between the tracks is 6mm. The windings in this second type make the Split structures. Therefore, in each layer the second winding is placed between the track distances of the first windings as explained on the simulation section. The windings are connected so that producing a series inductor as explained in section 5.2. The experiment is repeated with increasing the layer numbers to four. Fig.5.10 (a, b) shows the pictures for these two simple and split structures. Fig.5.11 compares the experiment and the simulation value results for both Simple and Split structures.
(a) (b)
Fig.5.10: a) Split structure of a four planar layers inductor b) A simple structure of a four a planar layer inductor
For given physical parameters of the planar inductor, below the four layers the ECC for Split structure is less than the Simple one. For more than four layers the trend is changed and the simple structure placed below the split ones. This result could be compared with the Fig.5.7 for Cv-split=500pF. Table 5. VI, Contains the measured value of the experiment samples.
Fig.5. 11: Test and simulation results of ECC for different winding layers for both
Table 5.VI: Capacitive coupling values for both simple and split structures in different layer numbers
Capacitance ECC ECC ECC Cv Ch values(pF) n=2 n=3 n=4
Simulation simple _ 143 120 100 500 values split 50 120 115 113
Experiment simple _ 145 120 90 385 values split 63 130 115 110
The capacitive coupling values in above table verifies the simulation results in previous section.For the vertical capacitive coupling, in simulation tests for CV=500 pF and Ch=50pF, the ECC has the higher values in simples structure compared to the split structure. However, this difference is reduced for more number of turns. For the similar values of designing in experiment tests the CV=380pF and Ch=63pF.experiment results shows that the ECC in simple samples are higher than the split samples .however ,this difference has been reduced within the rise in number of turns.
6. CONCLUSION
Planar magnetic elements are wildly applied in switched mode power supplies since they take less volume compared to the conventional rivals. The problem associated with these planar inductors is the current spikes generated at high frequencies, as a result of the relatively high capacitive couplings occur between the planar layers.
Different planar structures are analysed in this research in order to find a better configuration, which addresses the problem of capacitive coupling between planar layers. Since the capacitive couplings are tightly dependent on the physical parameters of the structure, various changes are carried out and many simulations are done to investiges these effects.
The Finite Element Method (FEM) is opted to electrostatic analysis of the capacitive coupling because of its high accuracy. Two dimensional (2D) FE, analysis in chapter two, shows that shifting the planar layers would increase the electrical resistance of the planar layers. Moreover, the effect of the other physical parameters such as the insulation thickness, track width and current direction is analysed.
In chapter 3, it is shown that the shifted structures could be effective in reduction of the equal capacitive coupling of the structures while keeping the volume constant. The results are verified with the experiment tests as well. Thus shifting method could fulfil the need for reduction of the capacitive coupling in two layer planar structure.
Shifting effect on the reduction of capacitive coupling in multi layer planar is investigated in chapter four simulation results show that within the desired dimension, shifting method would not satisfy the reduction of the equivalent capacitive coupling.
In chapter five a novel winding structure for planar elements has been introduced which is proved through the simulation results and experiment tests that offer the less capacitive coupling compared to the conventional planar elements.
7. Future Works and Further Research
The main objective of this research is to propose a better solution for planar structure to reduce the capacitive coupling. There are still problems for further research on the 3D-FE of the planar structure in the area of copper losses at different frequencies and the proper copper thickness to reduce the skin effect.
The new softwares of FE analysis provide the ability to couple the FE analysed element with the reminder of the electrical circuits to find out the operation of the desired object under the semi real test simulations. Thus, it could be possible to apply the proper softwares such as ANSOFT HFSS to observe the operation of a proposed planar structure in the designed converter circuits and under the range of wide frequency. This observation could include the current spikes as a result of the capacitive coupling in the planar structure or the heat dissipation on the efficiency of the circuit power.
Furthermore, a laboratory prototype based on the proposed planar structure could be applied in a switched mode power supply or a resonant converter to compare its characteristics and effects on the circuit current with a conventional planar structure.
Finally, the optimization design of planar magnetic with respect to the size, surface area and number of layers for the optimum achievements on the parasitic characteristic could be a further step of research.
REFERENCES
[1] www.ise.nl/products.
[2] A.Brockmeyer, “experimental evaluation of the influence of DC pre-magnetization on the properties of power electronic ferrites,” PhD thesis Aachen university of technology .
[3] H. Yan Lu, J. Guo Zhu, “Experimental determination of stray capacitances in high frequency transformers , IEEE Transactions Power Electronics on Volume 18, Issue 5, Sept. 2003
[4] Lu, H.Y. Zhu, J.G. Ramsden, V.S. Hui, S.Y.R,” Measurement and modelling of stray capacitances in high frequency transformers” Power Electronic specialists conferences,1999.PESC99.30th Annual IEEE Volume 2, 27.
[5] F. Wong, J. Lu, “High frequency planar transformer with helical winding structure”, Magnetic, IEEE Transaction on Volume 36, Issue5, Sep 2000
[6] H.Y. Lu, J.G. Zhu, V.S .Ramsden, “Comparison of experimental techniques for determination of stray Capacitances in high frequency transformers” Power Electronic specialist conference 2000,PESC, IEEE Volum18-23
[7] B.Ackermann, A.Lewalter, E.Waffenschmidt, “Analytical modelling of winding capacitances and dielectric losses for planar transformers”, Computers in Power Electronics, 2004. Proceedings 2004 IEEE Workshop AUG
[8] E. C. Snelling, “Soft Ferrites,Properties and Applications”, London,U.K.: Butterworth, 1988.
[9] F. M. Tesche, M. V. Ianoz, and T. Karlsson, “EMC analysis and computational Models”, New York: Wiley, 1997.
[10] P.C.F.Lee, C.K. Hui, S.Y.R, “Stray capacitance calculation of coreless planar transformers including Fringing effects,” Nov.82007Volume: 43, Issue: 23.
[11] L. Heinemann, “Modelling and design of high frequency planar transformers” Power Electronics Specialists Conference, 1995, PESC '95 Record, 26th Annual IEEE Volume 2, 18-22 June 1995
[12] J.Li, Y.Shi, Z. Niu, D. Zhou, “Modelling, simulation and optimization design of PCB planar transformer” Volume 3, 29, Sept. 2005
[13] T. Filchev, D. Cook, P. Wheeler, J. Clare, “Investigation of high voltage, high frequency transformers voltage multipliers for industrial applications” Power Electronics, Machines and Drives, 2008 PEMD 4th IET Conference on2-4 April 2008
[14] R. Prieto, J.A. Oliver, J.A. Cobos, “1D magnetic component model for planar structures” Power Electronics Specialists Conference, 1999, ( PESC 99 )30th Annual IEEE Volume 1, 27
[15] S.C.Tang, S. Hui, H. Chung, “coreless printed circuit board (PCB) transformers with high power density and high efficiency”.
[16] Dai, N.; Lee, F.C. “Edge effect analysis in a high-frequency transformer” Power Electronics Specialists Conference, PESC '94 Record, 25th Annual IEEE20-25 June 1994
[17] Z. Azzouz, A. Foggia, L. Pierrat, G. Meunier, “3D finite element computation of the high frequency parameters of power transformer windings,” IEEE Trans. Magn., vol. MAG-29, pp. 1407–1410
[18] L. Dalessandro, F. S. Cavalcante, J. W. Kolar, “Self-capacitance of high-voltage transformers” IEEETrans. On Power Electron., vol.22, no.5, pp.2081–2092, Sept.2007.
[19] M. J. Prieto, A. Fernandez, J. M. Diaz, J. M. Lopera, J. Sebastian, “Influence of transformer parasitic in low-power applications,” in Proc. IEEE APEC, 1999, pp. 1175–1180.
[20] J. Biela, J. W. Kolar, “Using transformer parasitic for resonant converters,a review of the calculation of the stray capacitance of transformers,” IEEE Trans. Ind. Appl, vol. 44, no.1, Jan.-Feb. 2008.
[21] J.W. Hofsajer, K.Flicker , “reducing of EMI in planar transformer with charge balancing”, IEEE electronic letters Vol.38-No 25, DEC 2002.
[22] C.K. Lee, P.C.F. Chan, S.Y.R, Hui, “Alternating stacked inductor for Mega-Hertz power converter and filtering applications, in Proc. 39th Annual IEEE PESC ‗08, 15-19 June 2008, pp. 3021-3027.
[23] D. Van der Linde, C. A. M. Boon, J. B. Klaassens, “Design of a High-Frequency Planar Power Transformer in Multilayer Technology, IEEE Transactions on Industrial Electronics, Vol 38, Issue 2, April 1991, pp. 135-141
[24] C.K.Lee, S.Y.Hui, “printed spiral winding with wide frequency band width” power electronic IEEE transaction 2010, issue 29.
[25] R. Petkov, “Optimum design of a high-power, high-frequency transformer”, IEEE Trans. PowerElectron, vol.11, no.1, pp.33–42, Jan.1996.
[26] G.Bray ,EMI/EMC measurement and principles, IEEE, c1997.
[27] T. Rohan Gunewardena ,“designing planar transformer for reliability and thermal efficiency”.
[28] S.A. Mulder, “application note on the design of low profile high frequency transformers, Ferroxcube componenets”.
[29] H. Dixon, “Current Losses in Transformer, Windings and Circuit wiring”. www.cpdee.ufmg.br
[30] A. Stadler, M. Albach, “The influence of the winding layout on the core losses and the leakage inductance in high frequency transformers “IEEE transaction magnetic, VOL. 42, NO. 4, APRIL 2006.
[31] J. Liu, L. Sheng, J. Shi, Z. Zhang; X. He, “Design of High Voltage, High Power and High Frequency Transformer in LCC Resonant Converter”, APEC.2009.
[32] N. Dai and F. C. Lee, “An Algorithm of High-Density Low-Profile Transformers Optimization”, in Proc of IEEE Applied Power Electronics Conference and Exposition, 1997, pp. 918–924.
[33] G.skutt ,C.Lee,R. Ridley ,“leakage inductance effects in high power planar magnetic structures”.
[34] Y .Suzuki, I .Hasegawa, S. Sakabe, “Effective electromagnetic field analysis using finite element method for high frequency transformers with litz-wire”, Electrical Machines and Systems, 2008. ICEMS 2008, International Conference.
[35] J. Ferreira, “Improved analytical modeling of conductive losses in magnetic components,” IEEE Trans. on Power Electron., vol. 9, no. 1,pp. 127–131, Jan. 1994.
[36] Z.Ouyang, C.Thomas, M.Anderson, ”Optimal design and tradeoffs analysis for planar transformer in high Power DC-DC convertors” accepted to be published on IEEE Trans. Industrial Electronic 2010
[37] W. G. Hurley, E. Gath, J. G. Breslin, “Optimizing the AC resistance of multilayer transformer Winding with arbitrary current waveforms,” IEEE Trans. on Power Electron., vol.15, no.2, pp.369-376, Mar. 2008.
[38] C. Quinn, K. Rinne, T. O'Donnell, M. Duffy, C.O. Mathuna, “A review of planar magnetic techniques and technologies,” in Proc. IEEE APEC, 2001, pp. 1175–1183.
[39] A. Reatti, M. K. Kazimierczuk, “Comparison of various methods for calculating the AC resistance of inductors,” IEEE Trans. on Magn., vol.38, no.3, pp.1512–1518, May. 2002.
[40] A. D. Podoltsev, I. N. Kucheryavaya, B. B. Lebedev, “Analysis of effective resistance and eddy-current losses in multi-turn winding of high-frequency magnetic components,” IEEE Trans. on Magn., vol. 39, no.1, pp.539–548, Jan. 2002.
[41] W. G. Hurley, E. Gath, J. G. Breslin, “Optimizing the AC resistance of multilayer transformer windings with arbitrary current waveforms”, IEEE Trans. on Power Electron., vol.15, no.2, pp.369–376, Mar. 2008.
[42] X. Nan, C. R. Sullivan, “An improved calculation of proximity-effect loss in high-frequency windings of round conductors,” in Proc. IEEE PESC, 2003, pp.853–860.
[43] G.hayes, Neil Donovan,” inductance characterization of high leakage transformers”.
[44] M.C.Caponet,F. Profumo,R. De Doncker, “ Low stray inductance bus bar design and construction for good EMC performance in power electronic circuits,“ IEEE Transactions on Power Electronics, Volume 17, Issue 2, March 2002.
[45] L.Cláudio, P. Walter, “Determination of Magnetic Induction and Current Density Values for Planar Cores to Operate with Minimal Magnetic Losses” Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol. 8, No. 1, June 2009
[46] B.W.Carsten, “The low leakage inductance of planar transformers; fact or myth?” Applied Power Electronics Conference, 2001. APEC2001. Sixteenth Annual IEEE Volume 2, 4-8 March 2001
[47] V. A. Niemela, G. R. Skutt, A. M. Urling, and Y.-N.Chang, “Calculating the Short-Circuit Impedances of a Multi winding Transformer from its Geometry,” IEEE Power Electronics Specialists Conference 2004.
[48] F. Grover, “ Inductance Calculations: Working Formulas and Tables, D. Van Nostrand Company, New York, 1946.
[49] B. Carsten, “Low profile magnetic, geometry selection and optimization”, part of seminar 8 “Ferrites: Tips, traps, techniques and trends”, APEC 92, Boston, MA, February 23-27, 1992.
[50] H. Ni, “The Application of Planar Transformer in Switching Mode Power Supply”. The 15th China National Power Supply Technology Annual.2003.573-578
[51] F.Foo, X.H. Gong, “Determination of winding losses of high frequency planar-type transformer using Finite-Element Method”; Power Electronics and Variable Speed Drives, 1996. Sixth International Conference on (Conf. Publ. No. 429)
[55] S.Cove,M.Ordonez, ”Modelling of planar transformer parasitic using Design of Experiment Methodology” Electrical and Computer Engineering Conference Canada (CCECE) 2010
[53] W.Chen,Y. Yan, Y.Hu, Q. Lu, “ Model and design of PCB parallel winding for planar Transformer” on Volume 39, Issue 5, Part 2, Sept. 2003.
[54] D. C. Montgomery, “Design and Analysis of Experiments”, John Wiley and Sons, 2001.
[55] B.Feng, N. Zhong-Xia, S. Yu-Jie, Z. Dong-Fang, “EMI Modelling and Simulation of High Conference on 12-15 DEC, 2006.
[56] J.Volakis, Finite element method for electromagnetic: antennas, microwave circuits, and scattering Applications New York: IEEE Press, 1998.
[57] ANSYS® Academic Research, Release 12.0, Help System. Electromagnetic Field Analysis Guide, ANSYS, Inc.