Expert Design and Empirical TestStrategies for Practical Transformer            Development               Victor W. Quinn ...
Outline• Units• Design Considerations• Coil Loss• Magnetic Material Fundamentals• Optimal Turns• Empirical Shorted Load Te...
New Product Development PremiseComponent Verification                !                        Application Validation•   Tr...
UNITS: Rationalized MKS+                       VoltElectric Field "                       Meter       Webers          Webe...
Design ConsiderationsCross Sections and Operating Densities                  Ip                       Is            J     ...
Faraday’s Law•    When a voltage E is applied to a     E +     winding of N Turns                                         ...
Flux Density Considerations                                                                         i(t)•     Voltage driv...
Ampere’s Law•     When a current i is applied to a       Ip      Is      winding of N Turns       3 H / dl            $ ie...
Transformer VA Rating• Faraday’s Law and Ampere’s Law imply that  instantaneous Volt/Turn and Amp-Turn are  constant.• The...
Fundamental Transformer Equation• Derive a relationship between Volt-Ampere rating  and transformer parameters:   VA Ratin...
Current Density (J ),Window Utilization Factor (KCu )and Coil Loss                                   11
Coil Loss  •    At low frequencies, for uniform conductor resistivity and uniform mean       lengths of turn, minimum wind...
Window Utilization Factor (KCu )                              Coil Insulation Penalty                                     ...
Example of KCu Estimate (PQ 20/20)                                                      "x                                ...
Window Utilization Penalties                                                                                           Typ...
Other Design Considerations AffectingWindow Utilization: KCu            Eddy           Current                 Leakage    ...
Low Frequency Example Calculation of Loss                H ( z ) x 7 RH 0 RMS x                        ˆ            ˆ     ...
Qualitative Example            Severe Skin / Proximity Effects            J0 2 1 J   ( H0 2 1 H ) cos(Bt ) x              ...
Dissipation And Energy As Function Of B                      (single layer) Hs1 $ 0, Hs2 $ Hs         2.5                 ...
Loss Equivalent and Energy EquivalentThicknesses (Single Layer Portion)                                          1z(HS1 7 ...
Define Normalized Densitiesfor General Sine Wave Boundary Conditions                      1 x1 y(                         ...
Complex Winding CurrentsDissipation For Frequency Dependent Resistor  V $ IR                                       V      ...
Nonsinusoidal Excitation                     I dc $ D 0 I rms                   I rms1 $ D1 I rms                   I rmsk...
Nonsinusoidal Currents andMulti-Layer Winding PortionDerive equivalent power density function           p0 equiv >R, B1 ,0...
Portion Utilization                                                                                            Sum of 10 H...
Sum of 10 HarmonicsPortion Utilization                                                                                    ...
Loss Equivalent ThicknessSine Wave, No Insulation                                                     Loss Equivalent Port...
Fourier Decomposition Of Theoretical Waveshapes                                       @                      f (t ) $ 5 a ...
Fourier Decomposition Of Theoretical Waveshapes                                         @                       f (t ) $ 5...
Loss Equivalent ThicknessComplex Wave, No Insulation                                                           Loss Equiva...
Loss Equivalent ThicknessComplex Wave, No Insulation                                                           Loss Equiva...
Core Loss Introduction                         32
Magnetic Material           •   One Oersted is the value of applied field strengthIex               which causes precisely...
MagnetizationMicroscopic Effects                      •   Soft magnetic material                          provides increas...
Optimal Transformer Turns                            35
Design Considerations AffectingCurrent Density: J                                     Coil Loss D ( J )          Customer ...
Design Considerations AffectingFlux Density: !B       Saturation     Bpeak        Bpeak            OCL                    ...
Selection Of Transformer Parameters:J , !B , KCu , KFe                   J                                          !B•   ...
Selection Of Transformer Parameters•    For given conductor and core regions, the normalized expression for low     freque...
Determination Of Fcoil                                                                2                                   ...
Determination Of Fcore               K0 Vp         B$              fN p Acore         If Core Loss $ VolumeFe K core @B A ...
Empirical Test: Verify                         42
Transformer RealitiesWinding loss               Ip                        Is    !leakage                                  ...
Coupled Coils                               M,k                       ip(t)              is(t)            +               ...
Finding k and M Empirically                       ip(t)             is(t)                  +             vp(t)        Lp  ...
Leakage Inductance                               M,k                      ip(t)                      is(t)          +     ...
Lumped Series Equivalent Test Method                        Rp          Rs              Primary    Lp    Ls        Seconda...
Empirical Shorted Load Test                       ip(t)           is(t)              +5 I n (nf )                    Lpn  ...
Core Loss Test Method Challenges• Core magnetization is nonlinear process with  nonlinear loss effects so Fourier Decompos...
Sine Voltage Loss Measurement Challenge                                                                         Measured L...
51                                                                           or                                           ...
Rectangular Voltage Loss Measurement Challenge                                                Rectangular Voltage Loss Mea...
Rectangular Voltage Loss Measurement Challenge                                 Loss Measurement Error vs Uncompensated Tim...
Linear System Assumption                                                                                          i(t)Illu...
Modified Core Loss Estimation                                55
Notions for Modified Core Loss     Calculation Method•   Characterize a given piecewise                                   ...
Further Loss WeightingIf instantaneous loss is presumed to                                                                ...
Compare Three Core Loss Estimation Methods• iGSE   – Improved Generalized Steinmetz Equation [1]• FHD   – Fourier Harmonic...
Comparison of Core Loss Calculation MethodsTriangular Flux ShapeFixed Equivalent Core Loss Resistance$=#=2                ...
Comparison of Core Loss Calculation MethodsTriangular Flux ShapeEddy Current Shielded Lamination$=1.5 , #=2               ...
Comparison of Core Loss Calculation Methods              Triangular Flux Shape                                            ...
Comparison of Core Loss Calculation MethodsTriangular Flux Shape3C85 Ferrite$=1.5 , #=2.6                                 ...
Harmonic Decomposition Problem                       $=1.5 , #=2.6                                                        ...
Observations of Loss Methods•   iGSE and SED deliver consistent loss estimates from    Steinmetz parameters since both met...
Evaluate Loss using Harmonic CoilLoss Analysis and SED Core LossEstimating Method                                    65
Example Of Coil Harmonic Loss Testing                                                   Sum of 10 Harmonics               ...
Loss Summary  168 W Forward Converter                           8 V, 21 A, 300 kHz                 3.5                    ...
Other Observed Core Loss Factors• Fundamental variables (peak field density, frequency,  temperature)• Biased operating ap...
Expert Design & Empirical Test Strategies for Practical Transformer Development
Expert Design & Empirical Test Strategies for Practical Transformer Development
Expert Design & Empirical Test Strategies for Practical Transformer Development
Expert Design & Empirical Test Strategies for Practical Transformer Development
Expert Design & Empirical Test Strategies for Practical Transformer Development
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Expert Design & Empirical Test Strategies for Practical Transformer Development

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Expert Design & Empirical Test Strategies for Practical Transformer Development presented by Mr. Victor QUINN of RAF Tabtronics LLC at the 2012 Applied Power Electronics Conference (APEC).

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Expert Design & Empirical Test Strategies for Practical Transformer Development

  1. 1. Expert Design and Empirical TestStrategies for Practical Transformer Development Victor W. Quinn Director of Engineering / CTO RAF Tabtronics LLC 1
  2. 2. Outline• Units• Design Considerations• Coil Loss• Magnetic Material Fundamentals• Optimal Turns• Empirical Shorted Load Test• Core Loss Estimation and Recommended Empirical Test Method (iGSE,FHD,SED)• Example Application• Summary Victor Quinn victor.quinn@raftabtronics.com 1-585-243-4331 Ext 340 2
  3. 3. New Product Development PremiseComponent Verification ! Application Validation• Transformer developers strive to design, develop and consistently manufacture transformers based on in depth understanding of application conditions and implementation of best practice design, production and test methods.• The initial first article transformer must be carefully validated in the respective application circuit to ensure the scope of the component development was sufficient for the end use.• Based on the challenges of accurate measurement of transformers in complex circuit applications, calorimetric (temperature rise) measurements are often used to characterize transformer power dissipation levels.• The transformer developer may work closely with the power system developer to correlate loss and thermal measurements under specific conditions.• Once the transformer design is validated, the transformer developer must implement tight QA controls on component materials and processes to ensure consistent results. 3
  4. 4. UNITS: Rationalized MKS+ VoltElectric Field " Meter Webers WeberB" 2 # 1 2 $ 1Tesla $ 10 Gauss 4 Meter Meter Ampere % Turn ATH" # 1 $ 1.257 & 10% 2 Oe Meter M Ampere 1 Oe = 2.02 AT/inchJ" Meter 2 1 1 ( . 0.676)- % inch (Cu @ 20 Celsius) $ " ( Ohm % Meter Henry H)0 $ 4* & 10%7 $ 1.257 & 10%6 (permeability constant) Meter M H G % 12 Farad ) 0 . 3.19 /10 %8 . 0.5 inch+ 0 $ 8.85 & 10 (permittivity constant) inch A Meter ( F,$ , where f = frequency in Hertz + 0 . 0.225 / 10%12 *)0 f inch 2.6 ,. inch (Cu @ 20 Celsius ) f 4
  5. 5. Design ConsiderationsCross Sections and Operating Densities Ip Is J !B ! JPrimary Secondary !B Core Core cross section [Acore] Coil cross section [Awindow] constrained by aperture constrained by aperture of of coil. core. 5
  6. 6. Faraday’s Law• When a voltage E is applied to a E + winding of N Turns Np Ns d0E $ (% ) N - dt (Instantaneous Volt/Turn Equivalence) t1 2 T Voltage 3E t1 p dt 10 $ E 2Np 0 Time t1 2 T 1 E $ T 3 t1 E dt (Average Absolute Voltage) 6
  7. 7. Flux Density Considerations i(t)• Voltage driven coil t1 2 T 3t1 E p dt E v(t) + L 10 $ Np 2Np -• Line filter inductorCurrent v(t) + Time i(t) LVoltage - Time (Two induced consecutive, additive voltage pulses) 7
  8. 8. Ampere’s Law• When a current i is applied to a Ip Is winding of N Turns 3 H / dl $ ienclosed Np Ns Curve C• For ideal core having infinite permeability, Hc=0 Curve C N p I p $ Ns I s Is Ip Hc (Instantaneous Amp-Turn Equivalence) The Amp-Turn imbalance is precisely the excitation required to achieve core flux density. Magnetic material reduces the excitation current for a given flux density. 8
  9. 9. Transformer VA Rating• Faraday’s Law and Ampere’s Law imply that instantaneous Volt/Turn and Amp-Turn are constant.• Therefore the winding Volt-Ampere product is independent of turns and is a useful parameter to rate transformers.• Since core flux excursion is based upon average absolute winding voltage E and winding dissipation is based upon RMS current i RMS , define: Transformer VARating $ 5i Ei 4 i RMSi 9
  10. 10. Fundamental Transformer Equation• Derive a relationship between Volt-Ampere rating and transformer parameters: VA Rating 6 Acore 4 Awindow 4 freq 4 J 4 1 B 4 K Fe 4 KCu VA Rating VAP 7 Acore 4 Awindow 6 4 freq 4 J 4 1 B 4 K Fe 4 KCu• Therefore, by increasing frequency, current density, flux density, or utilization factors, the area product can be reduced and the transformer can be made smaller. 10
  11. 11. Current Density (J ),Window Utilization Factor (KCu )and Coil Loss 11
  12. 12. Coil Loss • At low frequencies, for uniform conductor resistivity and uniform mean lengths of turn, minimum winding loss is achieved when selected conductors yield uniform current density throughout the coil. • For uniform current density J: Low Frequency Coil Loss $ ( / Cond Vol / J 2 2 = : or Low Frequency Coil Loss $ - / ;5 NI i 8 < i 9 where ( / 1y ( / 1y -$ $ 1x / Thicknesscu K Cu / Core Window Area Window Utilization Factor 12
  13. 13. Window Utilization Factor (KCu ) Coil Insulation Penalty Core Window• Conductor Coatings• Insulation Between Windings• Insulation Between Layers• Margins• Core Coatings or Bobbin / Tube Supports These considerations can total more than half of the available core window limiting utilization to less than 35%! 13
  14. 14. Example of KCu Estimate (PQ 20/20) "x tol 2IW 2IW "z support tol margin tolK Cu x $ @!x % 2>tol? % 2(margin or bobbin flange)A $ @0.55 - 2(0.003) - 2(0.036)A $ 0.858 !x 0.55 *K Cu shape ( round versus square) $ $ 0.785 4K Cu insul ( heavy film solid wire) $ 0.85K Cu z $ @!z % 2>tol? % (support) - 2(2IW)A $ @0.169 % 2>0.010? % (0.035) - 2(0.01)A $ 0.556 !z 0.169 So, KCu . K Cu x / K Cu shape / K Cu insul / K Cu z $ 0.318 14
  15. 15. Window Utilization Penalties Typical Core Window Utilization Coil Loss 100% 14 12 75% 10 Loss (W) 8 6 50% 4 2 Ideal 25% 0 0 5 10 15 20 Window Utilization Frequency (kHz) 0% 100% 90% Insulation occupies 80% 70% more than 50% of core window. Utilization 60% 50% 40% 30% 20% Eddy current 10% losses can further 0% 0 5 10 15 20 reduce effective Frequency (kHz) conductor area by more than 50%. 15
  16. 16. Other Design Considerations AffectingWindow Utilization: KCu Eddy Current Leakage Losses Inductance Maximum Kcu Insulation Requirements Corona / DWV Number Of Capacitance Requirements Windings 16
  17. 17. Low Frequency Example Calculation of Loss H ( z ) x 7 RH 0 RMS x ˆ ˆ ˆ J ( z) y 1z z ! H ( z ) x 7 H 0 RMS x ˆ ˆ Ampere s Law # (R - 1)H 0 RMS 1x $ iRMS iRMS R$ 21 H 0 RMS1x dH 1H ( R % 1) H 0 RMS iRMS x ! J y RMS $ $ $ $ dz 1z 1z 1 x1 z y ! ( 1y iRMS 2 Loss $ (1x1z 3 J y RMS dy $ 2 y 1 x1 z Effective conductor thickness 17
  18. 18. Qualitative Example Severe Skin / Proximity Effects J0 2 1 J ( H0 2 1 H ) cos(Bt ) x ! 2 J0 1J i 1z CC , H0 cos(Bt ) x !% J0 1x CC 1z Circulating 2 2 Current J0 $ H0 , 1 J $ 1H , , " " i 3 H 4 dl $ i # 1 H cos(Bt ) $ lw curve1 18
  19. 19. Dissipation And Energy As Function Of B (single layer) Hs1 $ 0, Hs2 $ Hs 2.5 2.5 Single layer with one surface field at zero is 2 forgiving of design 2Dissipation errors. Dissipation However, other Average Energy 1.5 constructions can 1.5 yield lower loss.1x1y( 2 1 x1 y)0,Hs 2 HS 1 1 2, 8 0.5 0.5 Average Energy 0 0 0.5 1.5 2.5 3.5 4.5 1z 7B Minimum Dissipation @ B="/2 , 19
  20. 20. Loss Equivalent and Energy EquivalentThicknesses (Single Layer Portion) 1z(HS1 7 0 and HS2 7 HS with B 7 ) , e2 B % e %2 B 2 2 sin(2B) [ 2 B %2 B ] (1y e 2 e % 2 cos(2B) (1yPower $ (NIRMS ) 2 / $ (NIRMS ) 2 / Thkequivloss 1x , 1x )0 1y 3 e2 B % e%2 B % 2 sin(2B) ) 1yEnergy $ (NIRMS ) / [ 2 B %2 B 2 ], $ 0 (NIRMS ) 2 / Thkequivmagnetic 61x 2 e 2 e % 2 cos(2B) 61x 20
  21. 21. Define Normalized Densitiesfor General Sine Wave Boundary Conditions 1 x1 y( Dimensionless densities (p0 , e0) Power $ H 2 p 0 (R, B , 0 ) , 0RMS Magnetic Energy $ 1x1y) 0, H 0RMSe 0 (R, B, 0 ) 2 • !x !y represents the surface area of the conductor layer • H0RMS=RMS value of sinusoidal magnetic field intensity at one boundary • R=Ratio of magnetic surface field Intensities • B=Ratio of conductor thickness to " (conductor skin depth) • "=Shift of magnetic surface field phases 21
  22. 22. Complex Winding CurrentsDissipation For Frequency Dependent Resistor V $ IR V _ P$ I R 2 + 2 Pave $ 1 T 3I Rdt T I Power 1 2 Pave $ R 3 I dt TT For complex waveshape and frequency Pave $ R * Irms 2 dependent resistor, Harmonic Orthogonality => 1 2 Irms $ 3 I dt TT Pave total $ 5 n R( f n ) * Irmsn 2 22
  23. 23. Nonsinusoidal Excitation I dc $ D 0 I rms I rms1 $ D1 I rms I rmsk $ D k I rms • I rmsk is the RMS current value at the kth. harmonic • I rms is the RMS value of the complex waveshape • D k is the ratio of the RMS value of the kth harmonic to the RMS value of the complex waveshape 23
  24. 24. Nonsinusoidal Currents andMulti-Layer Winding PortionDerive equivalent power density function p0 equiv >R, B1 ,0 ? $ D 0 2 >1 % R ?2 2 E i D 2 p >R, i / B1 ,0 ? i 0 B1 iWhere B1 is the ratio of conductor thickness to skin depth for the first harmonicSum results to derive equivalent winding thickness and effective window utilization ,Loss Equivalent Winding Portion Thickness $ 2 nl Kn H F p0 equiv K1 % , B1 ,0 H 1 5 I In F I J n F G n $1 J l G 1K Cu $ 2 nl Kn H F p0 equiv K1 % , B1 ,0 H 1 nl B1 5 I In F I F n $1 J l G J n G 24
  25. 25. Portion Utilization Sum of 10 HarmonicsSine Wave, No Insulation 2 Amplitude (normalized) 1.5 1 0.5 0 Conductor Utilization In Portion -0.5 0 -1 2 4 6 8 10 12 14 -1.5 No Insulation -2 Phase (radian) 100.0% 90.0% 1 For portions less than 80.0% 2 3 skin depths thick, 70.0% 3 utilization increases 4 with increasing layers. 60.0% KCuz 5 50.0% 6 Layers 40.0% 7 30.0% 20.0% 10.0% 0.0% 0.00 1.00 2.00 3.00 4.00 5.00 6.00 Portion Thickness (in skin depths) 25
  26. 26. Sum of 10 HarmonicsPortion Utilization 2 Amplitude (normalized)Sine Wave, Insulation Penalty 1.5 1 0.5 0 -0.5 0 2 4 6 8 10 12 14 -1 Conductor Utilization In Portion -1.5 -2 Phase (radian) IL=0.5 ! IW =0.5 ! 50.0% Maximum conductor 40.0% utilization is achieved 1 with single layer portions, but a large 2 30.0% number of portions is KCuz 3 required. 4 20.0% 5 6 10.0% 7 Layers 0.0% 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Portion Thickness (in skin depths) 26
  27. 27. Loss Equivalent ThicknessSine Wave, No Insulation Loss Equivalent Portion Thickness Sum of 10 Harmonics IL=0.0 ! IW =0.0 ! 2 3.0 Amplitude (normalized) 1.5 1 Layers 0.5 0 2.5 -0.5 0 2 4 6 8 10 12 14 -1 -1.5 Equivalent Thickness (in skin depths) -2 7 Phase (radian) 2.0 6 5 4 1.5 3 2 1.0 1 0.5 0.0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Portion Thickness (in skin depths) 27
  28. 28. Fourier Decomposition Of Theoretical Waveshapes @ f (t ) $ 5 a cos(nBt ) 2 b sin( nBt ) n n A nAmplitude an $ 0 8Ip n* Ip bn $ sin( DC) 2 * Ip DC* n 2 2 2 n $ 1, 3, 5, ... radian 4 Ip n* an $ sin( DC) Ip * n 2 2 * Ip bn $ 0 n $ 1, 3, 5, ... - DC / * / 2 DC / * / 2 (1 - DC/2) / * 2 /* 28
  29. 29. Fourier Decomposition Of Theoretical Waveshapes @ f (t ) $ 5 a cos(nBt ) 2 b sin( nBt ) n n A nAmplitude an $ 0 2 Ip Ip bn $ sin(n* DC) 2 * Ip DC (1 - DC) * n2 2 n $ 1, 2, 3, ... radian 2 Ip an $ sin( n * DC) Ip * (1- DC) * n Ip bn $ 0 - Ip * (DC) n $ 1, 2, 3, ... - DC / * DC / * (2 - DC) / * 2 /* 29
  30. 30. Loss Equivalent ThicknessComplex Wave, No Insulation Loss Equivalent Portion Thickness IL=0.0 ! IW =0.0 ! 3.5 7 Layers Sum of 10 Harm onics 3.0 2 6 1.5 Amplitude (normalized) 1 Equivalent Thickness (in skin depths) 0.5 2.5 5 0 -0.5 0 2 4 6 8 -1 4 -1.5 2.0 -2 Phase (radian) 3 1.5 2 1.0 1 0.5 0.0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Portion Thickness (in skin depths) 30
  31. 31. Loss Equivalent ThicknessComplex Wave, No Insulation Loss Equivalent Portion Thickness IL=0.0 ! IW =0.0 ! 7 Layers Sum of 10 Harmonics Amplitude 2 6 3.5 0 0 2 4 6 8 5 -2 3.0 Equivalent Thickness (in skin depths) Phase 4 2.5 3 2.0 2 1.5 1.0 1 0.5 0.0 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 Portion Thickness (in skin depths) 31
  32. 32. Core Loss Introduction 32
  33. 33. Magnetic Material • One Oersted is the value of applied field strengthIex which causes precisely one Gauss in free space. • Permeability is the relative gain in magnetic induction provided by magnetic material. ! • Magnetic Material consists of matter spontaneously magnetized. – Magnetic Material in demagnetized state is divided into smaller regions called domains. – Each domain spontaneously magnetized to saturation level. – Directions of magnetization are distributed so there is no net magnetization. – Crystal anisotropy and stress anisotropy create preferential orientation of spontaneous magnetization within each domain. – Magnetostatic energy is associated with induced monopoles on surface. – Exchange energy resides in domain wall as a result of nonparallel adjacent atomic spin vectors. – Domain structure evolves to achieve relative local minimum of total stored energy. 33
  34. 34. MagnetizationMicroscopic Effects • Soft magnetic material provides increased magnetic induction from induced alignment of dipoles in domain structure. B • Magnetization process converts material to single domain state magnetized in Br same direction as applied field. • Magnetization process involves domain wall motion Hc then domain magnetization rotation. H • Low frequency magnetization characteristics for magnetic material display energy storage and dissipation effects. • Material voids and inclusions =>irreversible magnetization (Br, Hc) 34
  35. 35. Optimal Transformer Turns 35
  36. 36. Design Considerations AffectingCurrent Density: J Coil Loss D ( J ) Customer Limit 2 Considering insulation and eddy current penalties Maximum J Electrical Requirements (regulation, efficiency) Maximum Winding Loss Maximum Temperature Rise 36
  37. 37. Design Considerations AffectingFlux Density: !B Saturation Bpeak Bpeak OCL L Core Loss D (1B ) Steady State Transient Linearity Where exponent # is determined through empirical core loss testing Maximum 1 B Electrical Requirements (efficiency) Maximum Core Loss Maximum Temperature Rise 37
  38. 38. Selection Of Transformer Parameters:J , !B , KCu , KFe J !B• For given core and winding regions, J and !B function in a competing relationship. – Decreasing !B is equivalent to increasing turns of all windings by the same proportion. – Increasing turns of all windings by a given proportion generates proportionately higher current density.• For a linear transformer, selection of turns on any one winding, uniquely determines J and !B densities and therefore total loss for a specific application. 38
  39. 39. Selection Of Transformer Parameters• For given conductor and core regions, the normalized expression for low frequency winding loss can be extended and combined with an empirically Empirical tests derived core loss result to yield: characterize core material in Insulation and eddy current impacts Fcore application Total transformer loss $ Fcoil / N 2 L 2 conditions p Np• Fcoil and Fcore relate exponential functions of primary turns (Np) to coil and core losses respectively.• n is the empirically derived exponential variation of core loss with magnetic flux density.• Without a constraint of core saturation, minimum transformer loss is achieved with primary turns: L / Fcore Core Loss 2 Np $ L 22 $ 2 / Fcoil implying => Winding Loss L 39
  40. 40. Determination Of Fcoil 2 = : Low Frequency Coil Loss $ - / ;5 NI i 8 < i 9 = VAsec : 5 NI i $ ; I p 2 V 8 N p i ; 8 < p 9 2 (1y = VAsec : Coil Loss $ ;I p 2 8 N p2 K Cu Awindow ; Vp 8 < 9 2 (1y = VAsec : Fcoil $ ;I p 2 8 K Cu Awindow ; Vp 8 < 9 Reflects insulation and eddy current loss penalties 40
  41. 41. Determination Of Fcore K0 Vp B$ fN p Acore If Core Loss $ VolumeFe K core @B A , L L = K0 Vp : 1 then Core Loss $ VolumeFe K core ; 8 ; fAcore 8 N pL < 9 L = K0 Vp : and Fcore $ VolumeFe K core ; 8 ; fAcore 8 < 9 Reflects empirical characterization of core loss for specific operating conditions and environment 41
  42. 42. Empirical Test: Verify 42
  43. 43. Transformer RealitiesWinding loss Ip Is !leakage !leakage ! Core Loss and Leakage Magnetic Energy magnetic applied to excite core flux 43
  44. 44. Coupled Coils M,k ip(t) is(t) + + vp(t) Lp Ls RL vs(t) - - Zi k is coupling coefficient M is mutual inductance di p dis dip disv p $ Lp %M vs $ M % Ls dt dt dt dt 44
  45. 45. Finding k and M Empirically ip(t) is(t) + vp(t) Lp Ls - Lsck $ 1% whe re L sc $ primary inductance with secondary shorted Lp M $ k Lp Ls 45
  46. 46. Leakage Inductance M,k ip(t) is(t) + + vp(t) Lp Ls RL vs(t) - - Zi L p = RL 2 jBLs (1 % k 2 ) : RLZ i ( jB ) $ ; 8 where Q p 7 Ls ;< 1 % jQ p 8 9 B Ls • Leakage inductance represented if Qp <<1 46
  47. 47. Lumped Series Equivalent Test Method Rp Rs Primary Lp Ls SecondaryIf BLs CC Rs ,Primary Equivalent Leakage Inductance $ ( 1 % k 2 )Lp LpPrimary Equivalent Resistance $ R p 2 k 2 Rs Ls 47
  48. 48. Empirical Shorted Load Test ip(t) is(t) +5 I n (nf ) Lpn - Zi AC Winding Loss . 5n Measured Winding Loss[ I n (nf )] Average Energy . 5n Measured Average Energy[ I n (nf )] Coil Loss . AC Winding Loss 2 DC Winding Loss 48
  49. 49. Core Loss Test Method Challenges• Core magnetization is nonlinear process with nonlinear loss effects so Fourier Decomposition may be problematic• Application waveshapes are difficult to generate – Rectangular voltage – Triangular current – Commercial impedance test equipment is based on sinusoidal testing at low amplitude• Accurate loss measurement for complex waveshapes is challenging 49
  50. 50. Sine Voltage Loss Measurement Challenge Measured Loss Error from Uncompensated Phase Shift vs Inductor Q Sine Wave 180 160 Power Measurement Error Multiplier (x % phase error) 140 120 Q of 10 rror 100 0c ~ e 80 au 158 se x 60 s p ph ow ase 40 er me error 20 as ure 0 0 20 40 60 80 100 120 me Q nt 50
  51. 51. 51 or ci t pa s ca losEmpirical Open Load Test nt te n a ra t so ccu en l re a em lle es ur ra itat as Pa acil me f ip(t) Lp ir(t) Zi + -
  52. 52. Rectangular Voltage Loss Measurement Challenge Rectangular Voltage Loss Measurement Potential Time Delay 1.5 Time Delay 1 Voltage Loss Impact 0.5 Current Normalized Amplitude 0 -0.5 -1 -1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (Period) 52
  53. 53. Rectangular Voltage Loss Measurement Challenge Loss Measurement Error vs Uncompensated Time Delay 0.5 Duty Cycle (Q ~ 31.83) 100 Rectangular Voltage Loss Measurement 80 Potential Time Delay 1.5 60 1 Loss Measurement Error (%) 40 Voltage 0.5 Current Normalized Amplitude 20 0 0 0. Time Delay 05 -0.5 20 % -20 % pe lo r io -1 -40 ss d m tim ea e -60 -1.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 su de Time (Period) -80 re la m y en ca -100 t e us rro es -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Time Delay (% of Period) r 53
  54. 54. Linear System Assumption i(t)Illustrates Loss Variation(Function of Duty Cycle) + Normalized Rectangular Wave Loss vs Duty Cycle v(t) R L calculated from fixed core loss resistance ("=#=2) - 10 9 8 No es nl pi t d in e 7 Reverse Voltage ea lin r l ea os r Increase Normalized Loss 6 Fixed Voltage s sy Fixed ET Fixed ET va st ria em 5 tio n 4 Duty Cycle Increase 3 2 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Duty Cycle 54
  55. 55. Modified Core Loss Estimation 55
  56. 56. Notions for Modified Core Loss Calculation Method• Characterize a given piecewise Sinusoidal Equivalent Derivative flux excursion using a sinusoidal SED equivalent derivative which 1 provides same peak flux and 0.8 Sinusoidal Equivalent Derivative SED average slope over the interval 0.6 Linear Flux Trajectory• The resultant induced loss by this 0.4 sinusoidal equivalent derivative will Normalized Amplitude 0.2 be weighted by the effective duty 0 cycle of the induced loss -0.2• Leverage benefits of sinusoidal -0.4 empirical test methods -0.6• Facilitate consistent and application relevant transformer -0.8 [1] core loss test results -1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Time (Period) – Correct peak flux density – Consistent piecewise flux derivative 56
  57. 57. Further Loss WeightingIf instantaneous loss is presumed to Ratio of Sine Wave Loss to Square Wave Loss vs Alpha " vary with the power of the flux derivative [1]: 1.5 D 1.45 dB P(t ) fixed peak flux density 6 1.4 dt 1.35 Normalized Ratiothen a further weighting factor can be 1.3 determined to scale the 1.25 measured sinusoidal loss 1.2 1.15 calorimetricNote that for an exponent greater 1.1 calorimetric than 1, sine wave voltage 1.05 generated loss is greater than 1 square wave voltage generated 1 1.2 1.4 1.6 1.8 2 2.2 2.4 Alpha " loss as demonstrated historically 57
  58. 58. Compare Three Core Loss Estimation Methods• iGSE – Improved Generalized Steinmetz Equation [1]• FHD – Fourier Harmonic Decomposition• SED – Sinusoidal Equivalent DerivativeInitial comparisons will be based on Steinmetz power law representation as established for specific domains of sinusoidal excitation. 58
  59. 59. Comparison of Core Loss Calculation MethodsTriangular Flux ShapeFixed Equivalent Core Loss Resistance$=#=2 Methods consistently calculate loss for linear system Calculated Core Loss: Triangle Wave Calculated Core Loss: Quasi Triangle Wave (normalized to peak flux equivalent sine wave at fundamental frequency) (normalized to peak flux equivalent sine wave at fundamental frequency) ("=#=2) ("=#=2) 4.5 6 4 5 3.5 3 4Normalized Loss Normalized Loss 2.5 iGSE iGSE 3 FHD FHD 2 SED SED 1.5 2 1 1 0.5 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Duty Cycle Duty Cycle Duty Cycle Duty Cycle Duty Cycle = 1.0 Duty Cycle = 1.0 59
  60. 60. Comparison of Core Loss Calculation MethodsTriangular Flux ShapeEddy Current Shielded Lamination$=1.5 , #=2 Calculated Core Loss: Quasi Triangle Wave Calculated Core Loss: Triangle Wave te stima (normalized to peak flux equivalent sine wave at fundamental frequency) (normalized to peak flux equivalent sine wave at fundamental frequency) ("=1.5 #=2) ("=1.5 #=2) ndere ds U 2.5 8 Metho mpacts ased ing I tive B x Crowd 7 Deri va Flu 2 6 iGSE 5 Normalized LossNormalized Loss 1.5 FHD iGSE SED 4 FHD SED 1 3 2 0.5 1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Duty Cycle Duty Cycle Duty Cycle Duty Cycle Duty Cycle = 1.0 Duty Cycle = 1.0 60
  61. 61. Comparison of Core Loss Calculation Methods Triangular Flux Shape ct 0.001 Permalloy 80 Im pa ing $=1.71 , #=1.96 x Cr ow d Flu al tenti Calculated Core Loss: Triangle Wave Po Calculated Core Loss: Quasi Triangle Wave (normalized to peak flux equivalent sine wave at fundamental frequency) (normalized to peak flux equivalent sine wave at fundamental frequency) ("=1.71 #=1.95) ("=1.71 #=1.95) 3.5 10 9 3 8 2.5 7 iGSENormalized Loss Normalized Loss FHD 6 iGSE 2 SED 5 FHD 1.5 SED 4 3 1 2 0.5 1 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Duty Cycle Duty Cycle Duty Cycle Duty Cycle Duty Cycle = 1.0 Duty Cycle = 1.0 61
  62. 62. Comparison of Core Loss Calculation MethodsTriangular Flux Shape3C85 Ferrite$=1.5 , #=2.6 Calculated Core Loss: Triangle Wave Calculated Core Loss: Quasi Triangle Wave (normalized to peak flux equivalent sine wave at fundamental frequency) (normalized to peak flux equivalent sine wave at fundamental frequency) ("=1.5 #=2.6) ("=1.5 #=2.6) 2 8 1.8 7 1.6 6 1.4 iGSENormalized Loss 5 Normalized Loss 1.2 FHD iGSE 1 SED FHD 4 SED 0.8 3 0.6 FH 2 0.4 D un de 1 0.2 res 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 tim 1 0 ate 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Duty Cycle Duty Cycle s fer Duty Cycle rite Duty Cycle tria ng ula r lo ss Duty Cycle = 1.0 Duty Cycle = 1.0 62
  63. 63. Harmonic Decomposition Problem $=1.5 , #=2.6 Sum of 1 Harmonic Calculated Normalized Harmonic Loss: FHD 2 1.5 Amplitude (normalized) 1 1 0.9 0.5 0.8 0 -0.5 0 2 4 6 8 10 12 14Normalizeed to Total 0.7 -1 0.6 -1.5 -2 0.5 Presumed Significant Waveshaping Phase (radian) 0.4 with Minimal Incremental Loss Sum of 10 Harmonics 0.3 2 0.2 1.5 Amplitude (normalized) 1 0.1 0.5 0 0 1 2 3 4 5 6 7 8 9 10 -0.5 0 2 4 6 8 10 12 14 Harmonic Order -1 -1.5 -2 Phase (radian) 63
  64. 64. Observations of Loss Methods• iGSE and SED deliver consistent loss estimates from Steinmetz parameters since both methods presume instantaneous loss to be proportional to the power of the flux derivative• SED facilitates meaningful empirical test implementation beyond mathematical application of Steinmetz equation: – Evaluates core capacity for application driven flux density – Generates application rated average winding voltages – Generates rated instantaneous loss over flux excursion interval – Facilitates resonant test methods for accurate and consistent results in production environment 64
  65. 65. Evaluate Loss using Harmonic CoilLoss Analysis and SED Core LossEstimating Method 65
  66. 66. Example Of Coil Harmonic Loss Testing Sum of 10 Harmonics 2 Amplitude (normalized) 1.5 1 168 W Forward Transformer 300 kHz 0.5 3 Watt Maximum Winding Dissipation Losses By Harmonic: 16 V in 0 0 2 4 6 3.08 10 12 Losses By Layer 14 -0.5 Tabtronics: 568-6078, 16 V in, Radian Phase (radian) 53% Duty Cycle 2.5 0.6 Loss (Watt) 0.5 2.0 0.4 AC Loss (Watt) 0.3 0.2 DC 0.1 1.5 0.0 1 2 3 4 5 6 7 Layer Number 1.0 Calculated 0.5 Actual (5 harmonics) 0.0 DC 2 4 6 8 10 Harmonic Order Total 66
  67. 67. Loss Summary 168 W Forward Converter 8 V, 21 A, 300 kHz 3.5 Total 3 ACPower Loss (W) 2.5 Coil 2 AC 1.5 DC 1 Core Coil 0.5 0 Loss Summary 67
  68. 68. Other Observed Core Loss Factors• Fundamental variables (peak field density, frequency, temperature)• Biased operating application waveshape [2]• Flux density relaxation during circuit commutation intervals• Flux crowding from eddy current shielding• Designed air gap => fringing effects• Nonuniform core cross sections => nonuniform magnetic field densities => nonuniform loss density• Unintended micro-crack(s)• Mechanical Stress (magnetic anisotropy)• Irregular or mismatched core segment interfaces• Material manufacturing lot variances (unintended substitutions !) 68

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