m (clean up, typos fixed: lenght → length, a offline → an offline) |
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The [[transformer]] for a [[flyback converter]] is used as the converters [[inductor]] as well as an isolation transformer. |
The [[transformer]] for a [[flyback converter]] is used as the converters [[inductor]] as well as an isolation transformer. |
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=Variables and acronyms= |
=Variables and acronyms= |
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*Universal constants |
*Universal constants |
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− | ** Permittivity of free space <math>\mu_o</math> (Wb A<sup> |
+ | ** Permittivity of free space <math>\mu_o</math> (Wb A<sup>−1</sup> m<sup>−1</sup>) |
− | ***<math>\mu_o = 4\pi 10^{-7}</math> (Wb A<sup> |
+ | ***<math>\mu_o = 4\pi 10^{-7}</math> (Wb A<sup>−1</sup> m<sup>−1</sup>) |
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*Core parameters |
*Core parameters |
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− | ** |
+ | ** ''EC35, PQ 20/16, 704, etc'', Core type (mm) |
** <math>K_g</math>, Geometrical constant (cm<sup>5</sup>) |
** <math>K_g</math>, Geometrical constant (cm<sup>5</sup>) |
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** <math>K_{gfe}</math>, Geometrical constant (cm<sup>x</sup>) |
** <math>K_{gfe}</math>, Geometrical constant (cm<sup>x</sup>) |
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** <math>l_m</math>, Magnetic path length (cm) |
** <math>l_m</math>, Magnetic path length (cm) |
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** <math>l</math>, or <math>l_g</math>, Air gap length (cm) |
** <math>l</math>, or <math>l_g</math>, Air gap length (cm) |
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− | ** <math>\mu</math>, Permittivity (Wb A<sup> |
+ | ** <math>\mu</math>, Permittivity (Wb A<sup>−1</sup> m<sup>−1</sup>) |
** <math>\mu_r</math>, Relative Permittivity (unitless) |
** <math>\mu_r</math>, Relative Permittivity (unitless) |
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***<math>\mu = \mu_o \mu_r</math> |
***<math>\mu = \mu_o \mu_r</math> |
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*MLT: mean length turn |
*MLT: mean length turn |
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*AWG: American wire gauge |
*AWG: American wire gauge |
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+ | |||
+ | =Initial calculations= |
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+ | |||
+ | ;Variables |
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+ | * <math>V_o</math> - output voltage [V] |
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+ | * <math>V_{in}</math> - input voltage [V] |
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+ | * <math>V_D</math> - diode voltage drop [V] |
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+ | * <math>V_{Rds}</math> - transistor on voltage [V] |
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+ | * <math>N</math> - turns ratio [unitless] |
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+ | * <math>D</math> - duty cycle [unitless] |
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+ | |||
+ | ;Calculate turns ratio |
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+ | <math>\frac{ V_o + V_D }{ V_{in} - V_{Rds} } = \frac{ 1 }{ N } * \left ( \frac{ D_{max} }{ 1 - D_{max} } \right )</math> |
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+ | |||
+ | * Diode |
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+ | ** Rectifier: <math>V_D = 0.8V</math> |
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+ | ** Schottky diode: <math>V_D = ?</math> |
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=Inductance calculations= |
=Inductance calculations= |
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<math> |
<math> |
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\Delta i = 0.5 * I |
\Delta i = 0.5 * I |
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− | </math |
+ | </math> |
+ | |||
+ | |||
;Solve for <math>L_m</math>: |
;Solve for <math>L_m</math>: |
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</math><br /> |
</math><br /> |
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− | The permittivity of free-space is so much larger than the permittivity the transformer material, that the magnetic path length, <math>l</math>, can be estimated to be the air gap |
+ | The permittivity of free-space is so much larger than the permittivity the transformer material, that the magnetic path length, <math>l</math>, can be estimated to be the air gap length, <math>l_g</math>. so <math>l = l_g</math> and<br /> |
<math> |
<math> |
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L_m=\frac{\mu_o A_c n_1^2}{l_g} |
L_m=\frac{\mu_o A_c n_1^2}{l_g} |
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;Solve for <math>n</math>: |
;Solve for <math>n</math>: |
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Minimize total power loss: <math>P_{tot} = P_{fe} + P_{cu}</math><br /> |
Minimize total power loss: <math>P_{tot} = P_{fe} + P_{cu}</math><br /> |
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− | Core loss: <math>P_{fe} = K_{fe} |
+ | Core loss: <math>P_{fe} = K_{fe} \Delta B^\beta A_c l_m</math><br /> |
<math>B_{ac} = \frac{L_m \Delta i}{n_1 A_c}</math><br /> |
<math>B_{ac} = \frac{L_m \Delta i}{n_1 A_c}</math><br /> |
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The <math>\beta</math> and <math>K_{fe}</math> are in the core material's datasheets<br /> |
The <math>\beta</math> and <math>K_{fe}</math> are in the core material's datasheets<br /> |
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− | |||
=Core calculations= |
=Core calculations= |
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* <math>B_{sat}</math> - saturation flux density [<math>T</math>] |
* <math>B_{sat}</math> - saturation flux density [<math>T</math>] |
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* <math>B_{max}</math> - max flux density [<math>T</math>] |
* <math>B_{max}</math> - max flux density [<math>T</math>] |
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− | * <math>\Delta B </math> - change in flux density [<math>T</math>] |
+ | * <math>\Delta B </math> - change in flux density [<math>T</math>], aka <math>B_{ac}</math> |
* <math>A_w</math> - winding area [<math>cm^2</math>] |
* <math>A_w</math> - winding area [<math>cm^2</math>] |
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* <math>A_e</math> - effective cross-setional area of the core [<math>cm^2</math>] |
* <math>A_e</math> - effective cross-setional area of the core [<math>cm^2</math>] |
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;Calculate minimum number of primary and secondary turns |
;Calculate minimum number of primary and secondary turns |
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− | *<math>N_{P-min} = \frac{ L_p * I_{pk} * 10^4 }{ B_{max} * A_e }</math |
+ | *<math>N_{P-min} = \frac{ L_p * I_{pk} * 10^4 }{ B_{max} * A_e }</math> |
*<math>N_{S-min} = \frac{ N_{P-min} }{ N }</math> |
*<math>N_{S-min} = \frac{ N_{P-min} }{ N }</math> |
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;AC current |
;AC current |
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<math>I_{rms}=\sqrt{ I_{rms}^2 - I_{dc}^2 }</math> |
<math>I_{rms}=\sqrt{ I_{rms}^2 - I_{dc}^2 }</math> |
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+ | |||
+ | |||
+ | =Power Loss= |
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+ | <math>P_{tot}=P_{fe}+P_{cu}</math> |
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=References= |
=References= |
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* [http://www.irf.com/technical-info/appnotes/an-1024.pdf IRF - Flyback Transformer Design] - nice description of howto wind the transformer |
* [http://www.irf.com/technical-info/appnotes/an-1024.pdf IRF - Flyback Transformer Design] - nice description of howto wind the transformer |
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* [http://focus.ti.com/lit/ml/slup127/slup127.pdf TI - Magnetics Design 5 - Inductor and Flyback Transformer Design] - describes various converters DCM and CCM |
* [http://focus.ti.com/lit/ml/slup127/slup127.pdf TI - Magnetics Design 5 - Inductor and Flyback Transformer Design] - describes various converters DCM and CCM |
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− | * [http://www.st.com/stonline/books/pdf/docs/7310.pdf OFFLINE FLYBACK CONVERTERS DESIGN METHODOLOGY WITH THE L6590 FAMILY] - very good, full description of designing |
+ | * [http://www.st.com/stonline/books/pdf/docs/7310.pdf OFFLINE FLYBACK CONVERTERS DESIGN METHODOLOGY WITH THE L6590 FAMILY] - very good, full description of designing an offline flyback converter |
* [http://focus.ti.com/general/docs/lit/getliterature.tsp?literatureNumber=slua086&fileType=pdf Isolated 50 Watt Flyback Converter Using the UCC3809] |
* [http://focus.ti.com/general/docs/lit/getliterature.tsp?literatureNumber=slua086&fileType=pdf Isolated 50 Watt Flyback Converter Using the UCC3809] |
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* [http://www.powerdesignindia.co.in/STATIC/PDF/200903/PDIOL_2009MAR19_SUPPLY_AN_01.pdf?SOURCES=DOWNLOAD TOPSwitch Flyback Transformer Construction Guide] |
* [http://www.powerdesignindia.co.in/STATIC/PDF/200903/PDIOL_2009MAR19_SUPPLY_AN_01.pdf?SOURCES=DOWNLOAD TOPSwitch Flyback Transformer Construction Guide] |
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+ | [[Category:Electronics]] |
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+ | [[Category:Howto]] |
Latest revision as of 16:22, 17 December 2013
Warning: This page it's very incomplete, use this article, particular has very caution! Please help finish it this page! |
The transformer for a flyback converter is used as the converters inductor as well as an isolation transformer.
Variables and acronyms
- Universal constants
- Permittivity of free space (Wb A−1 m−1)
- (Wb A−1 m−1)
- Permittivity of free space (Wb A−1 m−1)
- Wire variables:
- , Wire resistivity (Ω-cm)
- , Total RMS winding currents (A)
- , Peak magnetizing current (A)
- , Max RMS current, worst case (A)
- , Allowed copper loss (W)
- , Cross sectional area of wire (cm2)
- Xformer/inductor design parameters
- , turns (turns)
- , Magnetizing inductance (for an xformer) (H)
- , Inductance (H)
- , Winding fill factor (unitless)
- , Core maximum flux density (T)
- Core parameters
- EC35, PQ 20/16, 704, etc, Core type (mm)
- , Geometrical constant (cm5)
- , Geometrical constant (cmx)
- , Cross-sectional area (cm2)
- , Window area (cm2)
- , Mean length per turn (cm)
- , Magnetic path length (cm)
- , or , Air gap length (cm)
- , Permittivity (Wb A−1 m−1)
- , Relative Permittivity (unitless)
- Acronyms
- RMS: root-mean-squared - (where denotes the arithmetic mean)
- MLT: mean length turn
- AWG: American wire gauge
Initial calculations
- Variables
- - output voltage [V]
- - input voltage [V]
- - diode voltage drop [V]
- - transistor on voltage [V]
- - turns ratio [unitless]
- - duty cycle [unitless]
- Calculate turns ratio
- Diode
- Rectifier:
- Schottky diode:
Inductance calculations
The inductance of the transformer, , controls the current ripple.
Say you want a current ripple 50% of average current.
- Solve for
let
The permittivity of free-space is so much larger than the permittivity the transformer material, that the magnetic path length, , can be estimated to be the air gap length, . so and
- Solve for
Minimize total power loss:
Core loss:
The and are in the core material's datasheets
Core calculations
Core selection
- Variables
- - power loss in the core []
- - saturation flux density []
- - max flux density []
- - change in flux density [], aka
- - winding area []
- - effective cross-setional area of the core []
- - Area Product []
- - window utilization factor, or fill factor [unitless]
- - number of turns on the primary [unitless]
- - number of turns on the secondary [unitless]
- - number of turns on the bias [unitless]
- - permittivity of free space (air) [H/m]
- Material specifications
Grade | [T] | Specific Power Losses @100 °C [W/cm3] | Manufacturer |
---|---|---|---|
B2 | 0.36 | THOMSON | |
3C85 | 0.33 | PHILIPS | |
N67 | 0.38 | EPCOS (ex S+M) | |
PC30 | 0.39 | TDK | |
F44 | 0.4 | MMG |
- Calculate minimal AP needed
[]
- should be less than , to avoid core saturation. for example , then for a conservative calculation use
-
- Generally and
- Using for off-line power supplies is a good estimate
- Calculate minimum number of primary and secondary turns
- Calculate actual number of turn on the primary and secondary to be used.
- : Round up to the nearest integer
- Calculate air gap
Current calculations
- Variables
- - Ripple current max peak
- - Ripple current min peak
- - pk-pk ripple current
- Peak current
- DC current
- RMS current
- AC current
Power Loss
References
- U of Colorado - Flyback transformer design
- TI - "Magnetics Design 4 - Power Transformer Design" - very good, long, description of transformers and design
- TDK ferrite materials
- IRF - Flyback Transformer Design - nice description of howto wind the transformer
- TI - Magnetics Design 5 - Inductor and Flyback Transformer Design - describes various converters DCM and CCM
- OFFLINE FLYBACK CONVERTERS DESIGN METHODOLOGY WITH THE L6590 FAMILY - very good, full description of designing an offline flyback converter
- Isolated 50 Watt Flyback Converter Using the UCC3809
- TOPSwitch Flyback Transformer Construction Guide