No edit summary |
m (clean up, typos fixed: lenght → length, a offline → an offline) |
||
(31 intermediate revisions by 2 users not shown) | |||
Line 1: | Line 1: | ||
− | {{ |
+ | {{incomplete}} |
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. |
||
Line 5: | Line 5: | ||
=Variables and acronyms= |
=Variables and acronyms= |
||
*Universal constants |
*Universal constants |
||
− | ** 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>) |
Line 27: | Line 27: | ||
*Core parameters |
*Core parameters |
||
− | ** |
+ | ** ''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>) |
||
** <math>K_{gfe}</math>, Geometrical constant (cm<sup>x</sup>) |
** <math>K_{gfe}</math>, Geometrical constant (cm<sup>x</sup>) |
||
Line 35: | Line 35: | ||
** <math>l_m</math>, Magnetic path length (cm) |
** <math>l_m</math>, Magnetic path length (cm) |
||
** <math>l</math>, or <math>l_g</math>, Air gap length (cm) |
** <math>l</math>, or <math>l_g</math>, Air gap length (cm) |
||
− | ** <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) |
||
***<math>\mu = \mu_o \mu_r</math> |
***<math>\mu = \mu_o \mu_r</math> |
||
Line 43: | Line 43: | ||
*MLT: mean length turn |
*MLT: mean length turn |
||
*AWG: American wire gauge |
*AWG: American wire gauge |
||
+ | |||
+ | =Initial calculations= |
||
+ | |||
+ | ;Variables |
||
+ | * <math>V_o</math> - output voltage [V] |
||
+ | * <math>V_{in}</math> - input voltage [V] |
||
+ | * <math>V_D</math> - diode voltage drop [V] |
||
+ | * <math>V_{Rds}</math> - transistor on voltage [V] |
||
+ | * <math>N</math> - turns ratio [unitless] |
||
+ | * <math>D</math> - duty cycle [unitless] |
||
+ | |||
+ | ;Calculate turns ratio |
||
+ | <math>\frac{ V_o + V_D }{ V_{in} - V_{Rds} } = \frac{ 1 }{ N } * \left ( \frac{ D_{max} }{ 1 - D_{max} } \right )</math> |
||
+ | |||
+ | * Diode |
||
+ | ** Rectifier: <math>V_D = 0.8V</math> |
||
+ | ** Schottky diode: <math>V_D = ?</math> |
||
=Inductance calculations= |
=Inductance calculations= |
||
Line 50: | Line 67: | ||
<math> |
<math> |
||
\Delta i = 0.5 * I |
\Delta i = 0.5 * I |
||
+ | </math> |
||
+ | |||
+ | |||
+ | |||
+ | ;Solve for <math>L_m</math>: |
||
+ | let <math>n = \frac{n_2}{n_1}</math><br /> |
||
+ | |||
+ | <math> |
||
+ | I=\frac{n}{D'}I_{load} |
||
</math><br /> |
</math><br /> |
||
− | Derivation:<br /> |
||
<math> |
<math> |
||
− | + | \Delta i = \frac{nI_{load}}{2D'} |
|
− | \Delta i = \frac{nI_{load}}{2D'}\\ |
||
⚫ | |||
</math><br /> |
</math><br /> |
||
+ | <math> |
||
⚫ | |||
+ | </math><br /> |
||
<math> |
<math> |
||
− | L_m=\frac{\mu A_c |
+ | L_m=\frac{\mu A_c n_1^2}{l} |
− | </math> |
+ | </math><br /> |
+ | |||
+ | 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> |
||
+ | L_m=\frac{\mu_o A_c n_1^2}{l_g} |
||
+ | </math><br /> |
||
+ | |||
+ | ;Solve for <math>n</math>: |
||
+ | Minimize total power loss: <math>P_{tot} = P_{fe} + P_{cu}</math><br /> |
||
+ | 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 /> |
||
+ | The <math>\beta</math> and <math>K_{fe}</math> are in the core material's datasheets<br /> |
||
+ | |||
+ | =Core calculations= |
||
+ | |||
+ | ==Core selection== |
||
+ | |||
+ | ;Variables |
||
+ | * <math>P_{Fe}</math> - power loss in the core [<math>W</math>] |
||
+ | * <math>B_{sat}</math> - saturation flux density [<math>T</math>] |
||
+ | * <math>B_{max}</math> - max 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_e</math> - effective cross-setional area of the core [<math>cm^2</math>] |
||
+ | * <math>AP</math> - Area Product [<math>cm^4</math>] |
||
+ | * <math>K_u</math> - window utilization factor, or fill factor [unitless] |
||
+ | * <math>N_P</math> - number of turns on the primary [unitless] |
||
+ | * <math>N_S</math> - number of turns on the secondary [unitless] |
||
+ | * <math>N_B</math> - number of turns on the bias [unitless] |
||
+ | * <math>\mu_o</math> - permittivity of free space (air) <math>\mu_o = 2 \pi 10^{-7}</math> [H/m] |
||
+ | |||
+ | |||
+ | ;Material specifications |
||
+ | {|border=1 |
||
+ | !Grade |
||
+ | !<math>B_{sat}</math> [T] |
||
+ | !Specific Power Losses @100 °C [W/cm3] |
||
+ | !Manufacturer |
||
+ | |- |
||
+ | |B2 |
||
+ | |0.36 |
||
+ | |<math>P_{Fe} = 1.15 * 10^{-5} * \Delta B^{2.26} * f_{sw}^{1.11}</math> |
||
+ | |THOMSON |
||
+ | |- |
||
+ | |3C85 |
||
+ | |0.33 |
||
+ | |<math>P_{Fe} = 1.54 * 10^{-7} * \Delta B^{2.62} * f_{sw}^{1.54}</math> |
||
+ | |PHILIPS |
||
+ | |- |
||
+ | |N67 |
||
+ | |0.38 |
||
+ | | <math>P_{Fe} = 8.53 * 10^{-7} * \Delta B^{2.54} * f_{sw}^{1.36}</math> |
||
+ | |EPCOS (ex S+M) |
||
+ | |- |
||
+ | |PC30 |
||
+ | |0.39 |
||
+ | |<math>P_{Fe} = 1.59 * 10^{-6} * \Delta B^{2.58} * f_{sw}^{1.32}</math> |
||
+ | |TDK |
||
+ | |- |
||
+ | |F44 |
||
+ | |0.4 |
||
+ | |<math>P_{Fe} = 2.39 * 10^{-6} * \Delta B^{2.23} * f_{sw}^{1.26}</math> |
||
+ | |MMG |
||
+ | |} |
||
+ | |||
+ | |||
+ | |||
+ | ;Calculate minimal AP needed |
||
+ | <math>AP_{min} = 10^3 * \left ( \frac{ L_p * I_{Prms} }{ \Delta T^{ \frac{1}{2} } * K_u * B_{max} } \right )^{1.316}</math> [<math>cm^4</math>] |
||
+ | |||
+ | *<math>B_{max}</math> should be less than <math>B_{sat}</math>, to avoid core saturation. for example <math>B_{sat} > 0.3T</math>, then for a conservative calculation use <math>B_{max} = 0.25T</math> |
||
+ | |||
+ | *<math>\Delta T = T_{max} - T_{amb}</math> |
||
+ | *:Generally <math>T_{max} = 100C</math> and <math>T_{amb}=30C</math> |
||
+ | |||
+ | *Using <math>K_u=0.3</math> for off-line power supplies is a good estimate |
||
+ | |||
+ | ;Calculate minimum number of primary and secondary turns |
||
+ | *<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> |
||
+ | |||
+ | ;Calculate actual number of turn on the primary and secondary to be used. |
||
+ | *<math>N_S</math>: Round up <math>N_{S-min}</math> to the nearest integer |
||
+ | *<math>N_P = N * N_S</math> |
||
+ | |||
+ | ;Calculate air gap |
||
+ | <math>l_g = \frac{ \mu_o * N_P^2 * A_e * 10^{-2} }{ L_p }</math> |
||
+ | |||
+ | =Current calculations= |
||
+ | |||
+ | ;Variables |
||
+ | *<math>I_{pk}</math> - Ripple current max peak |
||
+ | *<math>I_{min}</math> - Ripple current min peak |
||
+ | *<math>\Delta I_{pp}</math> - pk-pk ripple current <math>I_{pk} - I_{min}</math> |
||
+ | |||
+ | ;Peak current |
||
+ | <math>I_{pk} = \left ( \frac{ I_{out-max} }{ N } \right ) * \left ( \frac{ 1 }{ 1 - D_{max} } \right ) + \frac{ \Delta I_L }{ 2 }</math> |
||
+ | |||
+ | ;DC current |
||
+ | <math>I_{dc}=D \frac{I_{pk}+I_{min}}{2}</math> |
||
+ | |||
+ | ;RMS current |
||
+ | <math>I_{rms}=\sqrt{ D \left ((I_{pk}+I_{min}) + \frac{1}{3} (I_{pk}+I_{min})^2 \right )}</math> |
||
+ | |||
+ | ;AC current |
||
+ | <math>I_{rms}=\sqrt{ I_{rms}^2 - I_{dc}^2 }</math> |
||
+ | |||
+ | |||
+ | =Power Loss= |
||
+ | <math>P_{tot}=P_{fe}+P_{cu}</math> |
||
=References= |
=References= |
||
− | * [http://ecee.colorado.edu/~ecen4517/materials/flyback.pdf Flyback transformer design] |
+ | * [http://ecee.colorado.edu/~ecen4517/materials/flyback.pdf U of Colorado - Flyback transformer design] |
+ | * [http://focus.ti.com/lit/ml/slup126/slup126.pdf TI - "Magnetics Design 4 - Power Transformer Design"] - very good, long, description of transformers and design |
||
+ | * [http://www.tdk.co.jp/tefe02/e140_1.pdf TDK ferrite materials] |
||
+ | * [http://www.irf.com/technical-info/appnotes/an-1024.pdf IRF - Flyback Transformer Design] - nice description of howto wind the transformer |
||
+ | * [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://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://www.powerdesignindia.co.in/STATIC/PDF/200903/PDIOL_2009MAR19_SUPPLY_AN_01.pdf?SOURCES=DOWNLOAD TOPSwitch Flyback Transformer Construction Guide] |
||
+ | [[Category:Electronics]] |
||
+ | [[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