Examensarbete Hogskoleingenjor Elektroteknik

Design of a planar transformer for a series loadedresonant converter

Forfattare:Andreas Bodegardandreas.bodegard@gmail.com

Handledare:Per Nilsson

per.nilsson@scandinovasystems.com

Department of Electrical EngineeringJune 17, 2020

Teknisk- naturvetenskaplig fakultet UTH-enheten Besöksadress: Ångströmlaboratoriet Lägerhyddsvägen 1 Hus 4, Plan 0 Postadress: Box 536 751 21 Uppsala Telefon: 018 – 471 30 03 Telefax: 018 – 471 30 00 Hemsida: http://www.teknat.uu.se/student

Abstract

Design of a planar transformer for a series loadedresonant converter

Andreas Bodegård

This report presents a project that has been made to present the design of a planartransformer as a part of a series loaded resonant DC/DC converter in a power unit.The design is based on an existing transformer that is not planar and so thecharacteristics of the transformer is translated into a planar version. A multilayerprinted circuit board (PCB) design was made to fit a chosen magnetic ferrite core thatwas chosen based on the magnetic characteristics of the old core. Calculations weremade for the loss of both core and windings and the final results show that it ispossible to design a planar transformer from a traditional transformer.

ISRN UTH-INGUTB-EX-*-20**/00-SEExaminator: Johan AbrahamssonÄmnesgranskare: Mats EkbergHandledare: Per Nilsson

Preface

This bachelor thesis of 15 credits have been done by me, Andreas Bodegardwith the purpose of completing my bachelor’s degree in electrical engineeringfrom Uppsala University. The thesis has been made at ScandiNova AB inUppsala. I want to thank to my supervisor Per Nilsson who has been a greathelp during this project. I also want to thank my subject reviewer MatsEkberg.

The project was made during the pandemic of COVID-19 which had a neg-ative impact on the outcome of the project. All work that has been done onthis project has been made from my home which affected the work flow aswell as the resources at hand.

Conclusion

This report will present the calculations and design made for the windings ofa planar transformer to be used in a DC/DC series loaded resonant converterwithin a power supply. The goal is to redesign an existing 3D transformerinto a planar 2D transformer to improve cost and to simplify manufacturing.The project is purely theoretical and no tests have been made on a physicalproduct.

Uppsala University

Abbreviations

V - VoltageI - CurrentR - ResistanceN - Number of revolutionsT - Period in secondsr - RadiusW - WattDC - Direct currentDC/DC - Direct current to direct current converterPCB - Printed circuit boardSLRC - Series loaded resonant converterMOSFET - Metal oxide semiconductor field effect transistorE-CAD - Electronic computer-aided designVDC - Voltage direct currentLitz wire - Wires with a small cross area that are wound together to reduceskin effect and electrically insulate against each otherRcu - Resistance copperPcu - Loss copperCreepage - Clearance -

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Contents

1 Introduction 3

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Theory 5

2.1 Transformer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 DC/DC converter . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Series loaded resonant converter . . . . . . . . . . . . . 5

2.3 Planar transformer . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3.1 Magnetic characteristics . . . . . . . . . . . . . . . . . 7

2.3.2 Losses in windings . . . . . . . . . . . . . . . . . . . . 8

2.3.3 Leakage inductance . . . . . . . . . . . . . . . . . . . . 8

2.3.4 Isolation between windings . . . . . . . . . . . . . . . . 9

2.4 Altium Designer . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Method 10

3.1 Evaluation of existing data . . . . . . . . . . . . . . . . . . . . 10

3.1.1 Existing data . . . . . . . . . . . . . . . . . . . . . . . 10

3.1.2 Calculations for existing transformer . . . . . . . . . . 11

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3.2 Translation to planar transformer . . . . . . . . . . . . . . . . 11

3.2.1 Applying to PCB . . . . . . . . . . . . . . . . . . . . . 12

3.2.2 PCB size . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Results 14

4.1 Results from calculations . . . . . . . . . . . . . . . . . . . . . 14

4.2 Choosing core . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.3 Winding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.4 Total loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4.5 Descriptions of layers . . . . . . . . . . . . . . . . . . . . . . . 19

5 Discussion 25

6 Conclusions 27

7 References 28

8 Appendix 29

8.1 Appendix 1: Data of existing transformer . . . . . . . . . . . . 29

8.2 Appendix 2: Datasheet Planar E core . . . . . . . . . . . . . . 31

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1 Introduction

The itroductory chapter will present the background to the project, the prob-lem, purpose and some limitations that exists, as well as an introduction toScandiNova.

1.1 Background

This project is a bachelor thesis that has been made at and in cooperationwith ScandiNova AB and Uppsala University. ScandiNova is a company thatis world leading in pulse power systems. The company was founded in 2001by Mikael Lindholm, David Woodburn and Walter Crewson. ScandiNovahas since then grown to more than 70 employees and conducts installationsand services around the globe. A few examples of areas where the pulsepower systems are used in are; particle accelerators, radar, radio therapyand industrial x-ray. [1]

As of today, ScandiNova produces four different series of products; the K-series, M-series, PG-series and the E-series. The K-series is a klystron mod-ulator with a peak power of up to 100 MW. The M-series is a magnetronmodulator with a peak power of up to 5 MW, but with what the magnetronlacks in power it compensates with being significantly smaller in size. ThePG-series are pulse generators. These can produce pulses of up to 36 MWpower. The E-series are E-gun modulators that have a high reliability andhave a wide variety of uses such as; radio therapy, cargo inspection andindustrial X-ray. [2]

1.2 Problem

A crucial component of the pulsed power systems that ScandiNova developsare their own design of a DC/DC power unit. They are constantly lookingfor improvements for components and found that a planar transformer couldbe used instead of their present transformer. The transformer plays the partof acting as the inductive part of the resonant circuit through the leakageinductance and as the part that increases the voltage of the power unit. As

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so it plays a crucial part of the power unit. The transformer that is used nowtakes a long time to construct and has a low reproducability.

1.3 Purpose

The purpose of the project is to evaluate the characteristics of an existingwire3D transformer and recalculate the values to fit a planar 2D transformer de-sign. Furthermore, PCB windings should be designed for the planar core thatis chosen based on the magnetic characteristics of the existing transformercore.

1.4 Questions

• Can a planar transformer be designed using the existing transformercharacteristics?

• What design should be used to create the needed leakage inductance?

1.5 Limitations

The work is be limited to a theoretical design and the work doesn’t includedesigning a transformer but to redesign the existing transformer.

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2 Theory

This chapter will introduce the theory behind the design of the planar trans-former windings. Formulas as well as pictures together with explanations arepresented for a deeper understanding of choices made in the project.

2.1 Transformer

A transformer is a component that has the objective of changing currentand/or voltage levels. The transformer utilizes magnetic properties to trans-fer a specific current and voltage level using windings around a magneticcore. The primary windings induce a magnetic flow in the core that in turninduces a current in the secondary windings. The ratio of primary windingsto secondary windings can be used to calculate the ratio of voltage betweenthe primary and secondary side of the transformer. [3]

VpVs

=Np

Ns

=IsIp

= ratio (1)

p notion for primary and s notation for secondary

2.2 DC/DC converter

A DC/DC converter is used to change the voltage of a source to a higheror lower voltage. This can be done in multiple ways, the DC/DC converterthat will be used within this project is a SLRC or a series loaded resonantconverter.

2.2.1 Series loaded resonant converter

A series loaded resonant converter utilizes a switch technology in series witha resonant circuit, where the coil of the resonant circuit is the primary sideof a transformer, which in turn is connected to a full-wave rectifier.The switch technology consists of 4 MOSFET connected in an h-bridge that

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converts the DC voltage into a square wave. The square wave is then con-verted into a sinusiodal signal using a resonant circuit, which can then beamplified using a transformer. The transformer is connected to a rectifierthat converts the signal back to a DC voltage which has now been amplifiedby the ratio of the primary and secondary side windings.

Figure 2.2.1 Schematic of the H-bridge DC/DC converter

2.3 Planar transformer

A planar transformer is a component that has the same functions as a regulartransformer. The advantages of a planar transformer is that the windingsare made with circuit board technology. Hereby the transformer becomescompact, has good thermal characteristics, has simplicity in manufacturingand good power density.

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Figure 2.3 Picture of a planar transformer [4]

2.3.1 Magnetic characteristics

The magnetic characteristics of the transformer core will decide the losses ofthe transformer. Shape, volume, cross area and material are all importantparts in designing a transformer. The change in cross area will decide themagnetic flux density which is directly related to the interlinkage of theprimary and secondary windings. The magnetic flux density together withthe volume of the core has a direct connection to the loss of the core. A toohigh level of magnetic flux density will make the core reach a saturated levelbefore the frequency has a time to change direction. If that happens the corewould have to have an increase in opposing magnetic force to take it out ofa saturation, which would lead to an increase in loss.

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Figure 2.3.1 Graph depicting the loss of transformer core as a function ofvolume [5]

2.3.2 Losses in windings

The losses in the windings are due to the resistive properties of the winding.This means that they are entirely dependent on the material, thickness andskin effect. For the 3D transformer a Litz wiring is used. Litz wires is usedto increase the conductive area of the wire by using several smaller wires thatare woven and isolated from each other. For the planar 2D transformer therewill be no Litz wiring, therefore no reduction in skin-effect will be present.

2.3.3 Leakage inductance

Leakage inductance is a product of the magnetic flux that is not picked upfrom primary windings to secondary windings. One can see the leakage induc-tance as an imperfectly interlinked flux from primary winding to secondarywinding. To achieve a specific leakage inductance one need to design a trans-former with a gap between primary and secondary windings. The larger gapthe more leakage flux and therefore the more leakage inductance. For thisspecific transformer the leakage inductance is used as the coil in the resonantconverter to convert the square wave to a sinusoidal wave, therefore a specificleakage inductance is desired. The square wave is converted to a sinusoidalwave by choosing a capacitor that matches the leakage inductance. When

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there is a flow through the resonant circuit the capacitor and inductancereacts to each other to transform the instantaneous rise of the square waveto a slow rise and the top of the square wave to a peak. The top of the peakis when resonance frequency is reached between the components. [6]

2.3.4 Isolation between windings

With a voltage of up to 1500 VDC, isolations between the windings has avery important part to play in the design. To avoid voltage jumps betweenwindings and short circuits in the design a sufficient distance of both creepageand clearance is necessary. A simplified explanation of creepage and clearanceis; creepage is the route that an ant would take from winding to winding andclearance is the route that a bird would take from winding to winding. Forthis assignment creepage and clearance will be seen as the same since therewill be no cutouts in the design for the windings. [7]

Figure 2.3.4 Picture showing creepage and clearance [7]

2.4 Altium Designer

The design of the planar windings and DC/DC converter was made in Altiumdesigner 20 which is a E-CAD program developed for PCB design. [8]

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3 Method

The following chapter will explain the work flow and the methology behindthe project. Evaluation of the existing data, calculations for the transformerdesign and the process behind choices will be presented.

3.1 Evaluation of existing data

The evaluation of the data from the existing transformer that was to be re-constructed into a planar transformer started with calculating the relevantdata such as magnetic flux of the core to translate into a planar core andcalculating the cross section area of both primary and secondary windingsto be able to translate into PCB windings. Another important part was totranslate the leakage induction from the transformer into the planar trans-former. How this was made came into the design aspect of the transformerand will be taken up later in the report.

3.1.1 Existing data

For original document, see Appendix 1: Data of existing transformer. (inswedish)Primary voltage: 400 VDCSecondary voltage: 1500 VDCTemperature class: Class B < 130 CIsolation test: 4000V 1 minCore: Ferroxcube article: E71/33/32-3C95Bobin: TME, WEISSER WE3759Primary windings: 12 turns, Litz wire 10x33x0.125 mm2 CuSecondary windings: 46 turns, Litz wire 225x0.071 Rupalit V155 CuLeakage inductance: 9.82 µH

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3.1.2 Calculations for existing transformer

Magnetic flux density of the old core E71/33/32-3C95 (from now on referredto as old core) was calculated. The magnetic flux was calculated by usingthe relation between windings, primary voltage V and cross section area Ac

of the transformer core:

N =V ∗ TAc ∗ ∆B

(2)

Ac for cross section area of core

The frequency 125 kHz gives the period T as 4µsBoth primary and secondary current and current density were to be keptthe same which meant that the total cross section area had to be directlytranslated to the PCB windings. Therefore a simple geometric calculationwas made for the windings to get the total cross section area.

Aw = nwire ∗ r2 ∗ π (3)

Where n = number of wires within the Litz wire and Aw is the cross sectionarea of the wire

3.2 Translation to planar transformer

The translation of the parameters for the transformer was made by takingthe calculated magnetic flux density of the old core and matching that toa group of planar cores to get close to the same value. So with the sameprimary windings, the same primary voltage and the same magnetic fluxdensity all that had to be done was to calculate the magnetic flux density ofthe planar cores and get value that matches the old core.

When calculating the PCB windings was made with a copper thickness of 2oz.This was chosen as it is a usually used standard for PCB traces. This value

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Part Ac [m2] V [mm3] height [mm] width [mm] Flux [T]C5810 0.000308 24.6 10.54 21.4 0.4329C6410 0.000516 41.4 10.2 21.8 0.258409938 0.00054 79.8 20.3 36 0.2469

Table 1: Planar cores

combined with the total cross area of the old windings made the calculationsfor the new windings width possible.

Widthp =Awp

Cu(2oz.)(4)

Awp is cross section area primary winding,Aws secondary winding andCu(2oz.) is the thickness of the copper on the board

Widths =Aws

Cu(2oz.)(5)

Awp is cross section area primary winding,Aws secondary winding andCu(2oz.) is the thickness of the copper on the board

3.2.1 Applying to PCB

Isolatory distance as clearing distance and creepage distance was applied toreduce the chance for short circuiting. The distancing was applied accordingto UL-61010-1 safety standard. All values presented in Table 2 are in mm.

Center leg-P P-P P-S S-S S-Outer edgeOuter layer 1 2 8 2 4

Internal layer 1 0.2 0.4 0.4 4

Table 2: Isolation distances. P=Primary, S=Secondary

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With the isolation distances decided, a total width could be calculated forthe primary windings as well as secondary windings. This in turn leads tothe decision on how many layers were to be used for the PCB for all thewindings to fit. A decision was made to use a 7 layer PCB design based onthe choice to creat an as compact design as possible with windings accordingto Table 3.

Layers 1 2 3 4 5 6 7 TotalPrimary 1 2 2 2 2 2 1 12

Secondary 6 6 7 8 7 6 6 46

Table 3: Number of revolutions per layer

3.2.2 PCB size

The PCB size was restricted by the window width of the core, the isola-tion requirements and the need for a gap between primary and secondarywindings to acquire the leakage induction. A direct translation from theold transformer was applied for the distance between primary and secondarywindings, which was a 22 mm gap. See Table 1 or Appendix 2: DatasheetPlanar E core for window width of the core.

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4 Results

The results in this report presents the calculations that have been made through-out the project, and presents the finished drawing of the PCB design in Altiumdesigner.

4.1 Results from calculations

Primary SecondaryCurrent 30A 7.5AVoltage 400V 1500V

Windings 12 46Width 4.383mm 0.277mm

Thickness 0,07 0,07A/mm2 8,149 8,419

Rcu 9,5*10−6 9,1*10−6

Pcu 8,54*10−3 5,09*10−3

Table 4: Results from calculations

4.2 Choosing core

The core that was chosen was the largest planar E core, the 09938EC core.This core was calculated to have a magnetic flux density of 0,24 T whichwas closest to the existing planar core that had a magnetic flux density of0,2 T, together with the chosen P material which was the material with thepermeability that leads to the magnetization not reach a saturated state.Figure 4.2 shows the B-H loop of different temperatures for this specific core.

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Figure 4.2 graph showing B-H loop for the core [9]

The loss calculations for the core was made with Figure 2.3.1 by . This graphshows the losses with a specific magnetic flux density. From this graph onecan read that the losses for the core is 1000 mW/cm3. With cm3 being thevolume of the core. This translates to a loss of 0,0798 W. The datasheet forthe chosen core can be found in Appendix 2: Datasheet Planar E core.

4.3 Winding

With a total width of 52,594 mm for the primary and 12,726 mm for thesecondary a width per revolution was calculated to 4,383 mm and 0,277 mmrespectively. Which was calculated using Equation (3):

Awp = (10 ∗ 30) ∗ (0.125

2)2 ∗ π = 3, 682mm2

Aws = 225 ∗ (0, 071

2)2 ∗ π = 0, 891mm2

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Using Equation (4) and (5) the total width of the primary windings and totalwidth of the secondary windings could be calculated:

Total width primary =3, 682mm2

0, 07mm= 52, 594mm

Total width secondary =0, 891mm2

0, 07mm= 12, 726mm

Calculations were made to get the width per revolution for primary windingsand secondary windings:

Widthp =Total width primary

Np

=52, 594mm

12rev= 4, 383mm (6)

Where Widthp is the width per revolution for the primary winding

Widths =Total width secondary

Ns

=12, 726mm

46rev= 0, 277mm (7)

Where Widths is the width per revolution for the secondary winding

The calculated values of width per revolution and the isolation distances thenumber of layers needed could be calculated. A value for the total widthneeded for the top layer of a 7 layer card was calculated to 29,043 mm whichmakes the residual distance 6,957 mm. If the design was to be made with 6layers there would be a residual of -1,702 mm. Here the minus sign means thatwith 6 layers the PCB card would be to wide for the core between the centerleg and the outer leg. For a 6 layer card there would have to be 2 revolutionsof the primary winding and 7 revolutions of the secondary windings on thetop layer. For a 7 layer card there would have to be 1 revolution of theprimary windings and 6 revolutions of the secondary winding on the toplayer. Following Equations (8) and (9) show the total isolation distancesneeded for the two designs, using the values from Table 2:

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Widthiso,6layers = [Cl−P ]+(2∗[P−P ])+[P−S]+(6∗[S−S])+[S−Ol] = 27mm (8)

Where Cl is Center leg and Ol is Outer leg

Widthiso,7layers = [Cl−P ]+[P−S]+(5∗ [S−S])+[S−Ol] = 23mm (9)

Where Cl is Center leg and Ol is Outer leg

The Equations (10) and (11) below show the total width for 6 layers and 7layers using the isolation distances calculated in Equations (8) and (9) andthe calculated values from Equation (6) and (7):

Width6layers = Widthiso,6layers+(2∗Widthp)+(7∗Widths) = 37, 702mm (10)

Width7layers = Widthiso,7layers+Widthp+(6∗Widths) = 29, 043mm (11)

Comparing this with the width of the core window that is 36mm wide theonly option was to proceed with 7 layers.

The winding losses were calculated by using the resistive properties of coppertogether with the length and width of the conductors. The results are showin Table 4 above.

4.4 Total loss

The total loss of the transformer were calculated to be 0,934 W which wascalculated from the total loss of the copper windings with a resistivity of1.68*10−8 Ωm , the total length of the secondary windings and the primarywindings and the cross section area of the windings.

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Rcu = ρL

Ac

(12)

ρ is the electrical resistivity, L is the length, Ac is the cross section area

Pcu = I2 ∗Rcu (13)

Pcu is the copper loss, I is the current and R is the resistance

The core loss was calculated by reading the core loss value from the graphin Figure 2.3.1 and recalculating it to power W.

Figure 4.4 showing the used value

W = (mW

cm3∗ cm3)/1000 (14)

cm3 used is the volume of the chosen core

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4.5 Descriptions of layers

Figure 4.5.1 Picture of top layer

Layer 1 has connection points to the primary and secondary windings. Theprimary winding has one revolution and secondary winding has 6 revolutionsaround the center leg of the core.

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Figure 4.5.2 Picture of second layer

Layer 2 has via connections to the primary layer and via connections to thethird layer. The primary winding has two revolutions and the secondarywinding has six revolutions.

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Figure 4.5.3 Picture of third layer

Layer 3 has via connections to the second layer and via connections to thefourth layer. The primary has two revolutions and the secondary winding hasseven revolutions. Since this layer is an internal layer the isolation distancerequirements between primary and secondary layers are substantially lower,which is because the material of the internal layer is less conductive thenthat of the outer layers.

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Figure 4.5.4 Picture of fourth layer

Layer 4 has via connections to the third layer and via connections to thefifth layer. The primary has two revolutions and the secondary has eightrevolutions. Like the third layer, this layer is internal which means that theisolation distance requirements are lower here as well.

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Figure 4.5.5 Picture of fifth layer

Layer 5 has via connections to the fourth layer and via connections to thesixth layer. The primary has two revolutions and the secondary has sixrevolutions.

Figure 4.5.6 Picture of sixth layer

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Layer six has via connections to the fifth layer and via connections to theseventh layer. The primary has two revolutions and the secondary has sixrevolutions.

Figure 4.5.7 Picture of seventh layer

The seventh layer has via connections to the sixth layer and connection pointsto the primary and secondary windings. The primary has 1 revolution andthe secondary has six revolutions.

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5 Discussion

The initial plan for the project was to deliver a finished physical product thatcould be tested on which would give a complete analysis of the functionalityof the product. Because of the current situation of the COVID-19 virus all thework had to be done from home and there were significant delays in the workbecause of difficulties with contact between student, supervisor and subjectreviewer. Even though the project has not produced a physical product thatcould be tested on, the project is a good start to lead to a complete planartransformer for a DC/DC converter.

To finish the product, the H-bridge, the resonant circuit and the rectifierwould have been added to the PCB design. With the PCB design finished itcould have been ordered together with the planar E core that had been cal-culated to fit the design. Then tests of voltage and current levels could havebeen tested to see that the calculated values were the same. Measurementswith the oscilloscope could have been made to assure that the signal in andout of the transformer were fitting the purpose. Tests for the sustainabilityof the transformer to see that the isolation distances were holding up to thethought out purpose, could also have been performed.

A change that could have been made to the transformer was to not have theprimary and secondary windings on the same layer but to rather have themon different layers with a separating layer that could work as isolation foran increase in leakage induction. This would have made the design of thePCB somewhat easier with a lower isolation distance per layer which wouldhave made the possibility of increasing number of revolutions around thecore possible. But a choice was made to keep the design of the transformeras close to the old transformer as possible to simplify the thought processthroughout the project.

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A few problems arouse during the project, the absence of which could havemade the work more effective. At the start of the project I got into reading alot of complicated academic documents that led me to several dead ends. Hadthe information been used in a more efficient way, the start of the projectwould have gone much faster. Another problem was that the calculationsof how many layers that should be used were complicated by the isolationdistances and some miscalculations. Designs were made for a 6 layers card,and a 3 layer card before reaching the conclusion that a 7 layer card was theright design.

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6 Conclusions

The possibility to convert a transformer from a 3D version to a 2D version isdefinitely possible. No conclusion could be drawn as for the leakage induc-tance that the design was supposed to have. Between designs it is probablethat the leakage inductance has changed since there is a significant differencebetween an air gap and a gap of the same length of PCB material. A 7 layerdesign was presented as being the most compact design possible, but somechanges could have been made to more efficently use all the space within thecore window.

The losses of the transformer is low with a loss of 0,934 W but sadly nomeasurements could be made on a prototype to back the results.

Some suggestions for future work would be to rethink the design parametersby utilizing the total core window area, the current design only uses a smallarea of the core window area and that could be seen as a waste. An optionto this would be to find an existing core that has a smaller height but thesame cross section area that would then fit the PCB design.

Another option would be to change the design to use layers of only primarywindings and layers of only secondary windings stacked on top of each otherwith a seperating layer of air or other material to ensure the correct leakageinductance.

The recalculations of the windings to include the skin-effect would be a mustfor any future work of this project.

Some added features could be to include the whole DC/DC converter circuitto the PCB design.

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7 References

[1]: https://scandinovasystems.com/about-scandinova/ Acquired 2020-06-13

[2]: https://scandinovasystems.com/products/ Acquired: 2020-06-15

[3]: https://en.wikipedia.org/wiki/Transformer Acquired: 2020-06-13

[4]: https://www.cettechnology.com/what-is-a-planar-transformer/ Acquired:2020-06-13

[5]: https://www.mag-inc.com/getmedia/5adcb1d1-20d1-4aa3-90e7-35000a37e9af/F-CORE-LOSS-VS-FLUX.JPG?width=398height=332 Acquired: 2020-06-07

[6]: https://en.wikipedia.org/wiki/Leakage inductance Acquired: 2020-06-07

[7]: https://resources.altium.com/p/high-voltage-pcb-design-creepage-and-clearance-distance Acquired: 2020-06-07

[8]:https://www.altium.com/ Acquired: 2020-06-13

[9]: https://www.mag-inc.com/Media/Magnetics/Datasheets/0P49938EC.pdfAcquired: 2020-06-08

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8 Appendix

8.1 Appendix 1: Data of existing transformer

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8.2 Appendix 2: Datasheet Planar E core

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