# DC-DC Flyback magnetics selection (esp, inductance)

K

#### [email protected]

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?

L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)

L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

L_p = sqrt(L_s^2 / (N_s/N_p) )

L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

R

#### RHRRC

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?

L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)

L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

L_p = sqrt(L_s^2 / (N_s/N_p) )

L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

If it is a flyback then, by definition, there is no secondary current
whilst the primary is 'charging'.
The primary inductance is give by: L=N^2.AL

K

#### [email protected]

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?
L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)
L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

L_p = sqrt(L_s^2 / (N_s/N_p) )
L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

If it is a flyback then, by definition, there is no secondary current
whilst the primary is 'charging'.
The primary inductance is give by: L=N^2.AL

Ofcourse current in secondary is only present when current in primary
is removed. But rather when the current is present in the different
windings that they follow the formulas pointed out.
I'm looking howto find out which inductance to look for rather than
how the inductance of a specific transformer coil is calculated.

L

#### legg

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?

L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)

L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

This is an oddly arranged formula with some ambiguous terms.
I_s and I_r would have to be defined in peak or rms values
in a particular circuit branch. The fact that a maximum
discharge period is used doesn't make much sense, except that
it would include the worst-case flux excursion in an IET
ie continuous current application. There is really no such
thing as a minimum duty cycle in a flyback circuit, until
a lot of other parameters have been rigged.You should maybe
quote the text and page number if you want further advice on
its application.

The secondary inductance determines the slope of the output
current waveform during energy discharge. As L reduces, the
closer the circuit runs towards CET or discontinuous operation,
the lower the voltage stress during the charging period and
the higher the peak to average current will be in output
components and windings.

The discharge period is minimum (at low line - hence
T_s(1-Dmax).
L_p = sqrt(L_s^2 / (N_s/N_p) )

L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

When power transfer alone is considered, secondary and primary
inductance are not inherently dependant due to decoupling
in the power transfer.

The primary inductance can store the required power if it
can be induced to sufficient peak current to satisfy the
formula:

W = Lmax x Iminpk^2 x f / 2

W = required power Watts
Lmax = maximum permissible primay inductance Henries
Iminpk = minimum primary current required Amps
f 0perating frequency in Hertz

(from e = L.I^2.f/2 energy formula)

This is most difficult at low line

Vmin = Lmax x Ipk x f / Dmax

Vmin = minimum primary voltage during the storage period.Volts
Lmax = inductance limit to achieve necessary current. Henries
f = operating frequency Hertz
Dmax = maximum duty cycle before enforced limiting

(from v = L.di/dt induction formula)

Note that both formulas can be stated in terms of
either L or Ipk. Through substitution, a quadratic
equation is possible for fixed power, voltage, frequency
and duty cycle for the primary winding.

RL

S

#### [email protected]

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?
L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)
L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

This is an oddly arranged formula with some ambiguous terms.
I_s and I_r would have to be defined in peak or rms values
in a particular circuit branch. The fact that a maximum
discharge period is used doesn't make much sense, except that
it would include the worst-case flux excursion in an IET
ie continuous current application. There is really no such
thing as a minimum duty cycle in a flyback circuit, until
a lot of other parameters have been rigged.You should maybe
quote the text and page number if you want further advice on
its application.

The secondary inductance determines the slope of the output
current waveform during energy discharge. As L reduces, the
closer the circuit runs towards CET or discontinuous operation,
the lower the voltage stress during the charging period and
the higher the peak to average current will be in output
components and windings.

The discharge period is minimum (at low line - hence
T_s(1-Dmax).
L_p = sqrt(L_s^2 / (N_s/N_p) )
L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

When power transfer alone is considered, secondary and primary
inductance are not inherently dependant due to decoupling
in the power transfer.

The primary inductance can store the required power if it
can be induced to sufficient peak current to satisfy the
formula:

W = Lmax x Iminpk^2 x f / 2

W = required power Watts
Lmax = maximum permissible primay inductance Henries
Iminpk = minimum primary current required Amps
f 0perating frequency in Hertz

(from e = L.I^2.f/2 energy formula)

This is most difficult at low line

Vmin = Lmax x Ipk x f / Dmax

Vmin = minimum primary voltage during the storage period.Volts
Lmax = inductance limit to achieve necessary current. Henries
f = operating frequency Hertz
Dmax = maximum duty cycle before enforced limiting

(from v = L.di/dt induction formula)

Note that both formulas can be stated in terms of
either L or Ipk. Through substitution, a quadratic
equation is possible for fixed power, voltage, frequency
and duty cycle for the primary winding.

RL

Go to www.fairchildsemi.com and look for a flyback assistance software
that they have there. Is really good.

I use the N67 material from Epcos.

design.

L

#### legg

Jan 1, 1970
0
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?
L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)
L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]

This is an oddly arranged formula with some ambiguous terms.
I_s and I_r would have to be defined in peak or rms values
in a particular circuit branch. The fact that a maximum
discharge period is used doesn't make much sense, except that
it would include the worst-case flux excursion in an IET
ie continuous current application. There is really no such
thing as a minimum duty cycle in a flyback circuit, until
a lot of other parameters have been rigged.You should maybe
quote the text and page number if you want further advice on
its application.

The secondary inductance determines the slope of the output
current waveform during energy discharge. As L reduces, the
closer the circuit runs towards CET or discontinuous operation,
the lower the voltage stress during the charging period and
the higher the peak to average current will be in output
components and windings.

The discharge period is minimum (at low line - hence
T_s(1-Dmax).
L_p = sqrt(L_s^2 / (N_s/N_p) )
L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary

When power transfer alone is considered, secondary and primary
inductance are not inherently dependant due to decoupling
in the power transfer.

The primary inductance can store the required power if it
can be induced to sufficient peak current to satisfy the
formula:

W = Lmax x Iminpk^2 x f / 2

W = required power Watts
Lmax = maximum permissible primay inductance Henries
Iminpk = minimum primary current required Amps
f 0perating frequency in Hertz

(from e = L.I^2.f/2 energy formula)

This is most difficult at low line

Vmin = Lmax x Ipk x f / Dmax

Vmin = minimum primary voltage during the storage period.Volts
Lmax = inductance limit to achieve necessary current. Henries
f = operating frequency Hertz
Dmax = maximum duty cycle before enforced limiting

(from v = L.di/dt induction formula)

Note that both formulas can be stated in terms of
either L or Ipk. Through substitution, a quadratic
equation is possible for fixed power, voltage, frequency
and duty cycle for the primary winding.

RL

Go to www.fairchildsemi.com and look for a flyback assistance software
that they have there. Is really good.

I use the N67 material from Epcos.

design.

I'm pretty well acquainted with most versions of this kind of SW.

The OP has not ventured to question the best methods for establishing
gap or turns on his transformer. This would be the next logical
question.

Using SW-assisted magnetic design GUI's can produce rubbish, if the
basics behind them aren't understood by the end-user. This is
particularly true if the software is formulated around a specific
application IC or schematic. This is one of the reasons why I asked
the OP where his original formula came from.

With a basic understanding of the flyback transformer's application
and some simple, universally applicable relationships, you'd likely
not need the GUI. It looks better in your lab notes as well, being
traceable, checkable and reusable.

RL

K

#### [email protected]

Jan 1, 1970
0
On Thu, 01 Nov 2007 11:59:11 -0700, [email protected] wrote:
When choosing magnetics for a flyback type DC-DC converter with
Vin=36-57V Imax=400 mA DC to 3,3V, with a Pmax=12,95W. Is the
inductance of the pulse transformer calculated as below..?
If not, how does one calculate it ..?
L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)
L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]
The discharge period is minimum (at low line - hence
T_s(1-Dmax).
L_p = sqrt(L_s^2 / (N_s/N_p) )
L_p - Inductance primary [H]
L_s - Inductance secondary [H]
N_s - Turns secondary
N_p - Turns primary
The primary inductance can store the required power if it
can be induced to sufficient peak current to satisfy the
formula:
W = Lmax x Iminpk^2 x f / 2
W = required power Watts
Lmax = maximum permissible primay inductance Henries
Iminpk = minimum primary current required Amps
f 0perating frequency in Hertz
(from e = L.I^2.f/2 energy formula)
This is most difficult at low line
Vmin = Lmax x Ipk x f / Dmax
Vmin = minimum primary voltage during the storage period.Volts
Lmax = inductance limit to achieve necessary current. Henries
f = operating frequency Hertz
Dmax = maximum duty cycle before enforced limiting
(from v = L.di/dt induction formula)
Note that both formulas can be stated in terms of
either L or Ipk. Through substitution, a quadratic
equation is possible for fixed power, voltage, frequency
and duty cycle for the primary winding.

Go towww.fairchildsemi.comand look for a flyback assistance software
that they have there. Is really good.
I use the N67 material from Epcos.
design.

I'm pretty well acquainted with most versions of this kind of SW.

The OP has not ventured to question the best methods for establishing
gap or turns on his transformer. This would be the next logical
question.

Using SW-assisted magnetic design GUI's can produce rubbish, if the
basics behind them aren't understood by the end-user. This is
particularly true if the software is formulated around a specific
application IC or schematic. This is one of the reasons why I asked
the OP where his original formula came from.

With a basic understanding of the flyback transformer's application
and some simple, universally applicable relationships, you'd likely
not need the GUI. It looks better in your lab notes as well, being
traceable, checkable and reusable.

RL, I got the formula from a degree thesis written about DC-DC in the
300W class. What I'm trying to determine is the proper parameters for
the transformer magnetics in a flyback converter. Not how to build the
transformer magnetics. So parameters like L [Henries], N [Ratio], Ipk
[Ampere] etc.. are the one's I'm seeking.
I found the energy principle lately a good way to analyze this lately.

Another puzzle is how to analyze the input filter choke, there's a
inductor with 10uH in series and then a 26,7 uF capacitor (48V). I
calculate I need only about 1uF. So is the inductor choke there to
handle the transient surge that the capacitor can't handle due
ESR ..?, because there's simple not enough energy in the inductor to
take the load of charging the transformer primary.

L

#### legg

Jan 1, 1970
0
On Mon, 05 Nov 2007 03:50:12 -0800, [email protected] wrote:

L_s = (V_ut*T_s*(1-d_min)) / (2*I_s*I_r)
L_s - Inductance on secondary [H]
V_ut - Output voltage [V]
T_s - Cycle time
d_min - Minimum duty cycle
I_s - Power through secondary [A]
I_r - Allowed ripple [A]
Go towww.fairchildsemi.comand look for a flyback assistance software
that they have there. Is really good.
I use the N67 material from Epcos.
design.

I'm pretty well acquainted with most versions of this kind of SW.

The OP has not ventured to question the best methods for establishing
gap or turns on his transformer. This would be the next logical
question.

Using SW-assisted magnetic design GUI's can produce rubbish, if the
basics behind them aren't understood by the end-user. This is
particularly true if the software is formulated around a specific
application IC or schematic. This is one of the reasons why I asked
the OP where his original formula came from.

With a basic understanding of the flyback transformer's application
and some simple, universally applicable relationships, you'd likely
not need the GUI. It looks better in your lab notes as well, being
traceable, checkable and reusable.

RL,

I got the formula from a degree thesis written about DC-DC in the
300W class. What I'm trying to determine is the proper parameters for
the transformer magnetics in a flyback converter. Not how to build the
transformer magnetics. So parameters like L [Henries], N [Ratio], Ipk
[Ampere] etc.. are the one's I'm seeking.
I found the energy principle lately a good way to analyze this lately.

Could you please quote the Author's name, the thesis title and year,
and the institution holding it on record?

There are increasingly severe restrictions affecting the simple
flyback topology at higher power levels, although I have used it with
some modifications, and seen similar work, above 3KW.

A study of higher power flyback applications that does not include a
physical iteration of the magnetic structure runs the risk of not
being taken seriously.

Minimization of core and copper losses, with rationalization of the
resulting stress affects on the surrounding components, would need to
consider, at least in passing, the physical turns count of the winding
and the flux densities anticipated in the core.
Another puzzle is how to analyze the input filter choke, there's a
inductor with 10uH in series and then a 26,7 uF capacitor (48V). I
calculate I need only about 1uF. So is the inductor choke there to
handle the transient surge that the capacitor can't handle due
ESR ..?, because there's simple not enough energy in the inductor to
take the load of charging the transformer primary.

If the self-resonant frequency of the filter components or parasitics
is anywhere near the operating frequency of the converter, there will
be undamped resonances that can interfere with normal or efficient
operation. Input filter inductors are not normally configured to enter
into the conversion process itself, in the flyback topology.

At 48V, a 300W flyback will be drawing large pulsating currents that a
1uF supply decoupling component might have difficulty handling, hence
a larger value.

The fact that the component is specified with 3 significant figures of
accuracy in capacitance is an indication that it's value does not
originate in a practical situation. Power electronic components are
seldom available in tolerances better than 5% at room temperature.

Theseseses often make interesting reading. Their value is often not in
the actual practical results recorded - in fact the best may describe
a complete experimental disaster and point to important errors in
innitial assumptions or quoted references.

RL

K

#### [email protected]

Jan 1, 1970
0
I got the formula from a degree thesis written about DC-DC in the
300W class. What I'm trying to determine is the proper parameters for
the transformer magnetics in a flyback converter. Not how to build the
transformer magnetics. So parameters like L [Henries], N [Ratio], Ipk
[Ampere] etc.. are the one's I'm seeking.
I found the energy principle lately a good way to analyze this lately.

Could you please quote the Author's name, the thesis title and year,
and the institution holding it on record?

There are increasingly severe restrictions affecting the simple
flyback topology at higher power levels, although I have used it with
some modifications, and seen similar work, above 3KW.

A study of higher power flyback applications that does not include a
physical iteration of the magnetic structure runs the risk of not
being taken seriously.

Minimization of core and copper losses, with rationalization of the
resulting stress affects on the surrounding components, would need to
consider, at least in passing, the physical turns count of the winding
and the flux densities anticipated in the core.
Another puzzle is how to analyze the input filter choke, there's a
inductor with 10uH in series and then a 26,7 uF capacitor (48V). I
calculate I need only about 1uF. So is the inductor choke there to
handle the transient surge that the capacitor can't handle due
ESR ..?, because there's simple not enough energy in the inductor to
take the load of charging the transformer primary.

If the self-resonant frequency of the filter components or parasitics
is anywhere near the operating frequency of the converter, there will
be undamped resonances that can interfere with normal or efficient
operation. Input filter inductors are not normally configured to enter
into the conversion process itself, in the flyback topology.

At 48V, a 300W flyback will be drawing large pulsating currents that a
1uF supply decoupling component might have difficulty handling, hence
a larger value.

The fact that the component is specified with 3 significant figures of
accuracy in capacitance is an indication that it's value does not
originate in a practical situation. Power electronic components are
seldom available in tolerances better than 5% at room temperature.

Theseseses often make interesting reading. Their value is often not in
the actual practical results recorded - in fact the best may describe
a complete experimental disaster and point to important errors in
innitial assumptions or quoted references.

The first paper gives the inductor for the secondary in equation 2.1,
but it seems to be half-forward topology (now that I looked again), I
had trouble finding the original document. But here it is:
ftp://ftp.elteknik.chalmers.se/Publications/MSc/Karlsson&RinnemoMSc.pdf
(in Swedish)

Here's another document I looked at for hints (ignore the CAN stuff):
http://courses.ece.uiuc.edu/ece445/projects/spring2004/project12_final_paper.dot
(in English)

My application is Uin between 36-57V, 48V DC nominal. Max 400mA. No
300W
Output 3,3V-12V depending on what turns ratio and voltage divider I
choose.
Topology: isolated flyback transformer.
So I'm looking for how to figure out the acceptable range for the
primary inductor Lp in [Henry]. Secondary inductance is also of
interest ofcourse.

L

#### legg

Jan 1, 1970
0
On Mon, 05 Nov 2007 12:28:24 -0800, [email protected] wrote:

The first paper gives the inductor for the secondary in equation 2.1,
but it seems to be half-forward topology (now that I looked again), I
had trouble finding the original document. But here it is:
ftp://ftp.elteknik.chalmers.se/Publications/MSc/Karlsson&RinnemoMSc.pdf
(in Swedish)
Well, I recommend you either study unfamiliar topics in a language
that you have no trouble with or stick to a topic you're familiar with
in an unfamiliar languages.

This paragraph preceding equation 2.1 states that a relationship will
exist between the primary and secondary inductances. It also assumes,
given the 300V intermediate bus being maintained by this
battery-backup port, that the secondary current will vary between 2.2
and 3A peak and that the 300uF capacitor, which just happens already
to by available, can handle the stress.

Equation2.1 simply states the expected relationship between the
primary and secondary inductances that the preceding paragraph
assumes, however the symbol 'r' in the original equation is intended
to be a dimensionless decimal number symbolizing a ratio of rms to
peak ripple current.

The equation predicts that the peak to average current ratios will
change as the inductance ratios or duty cycle limitations change. It's
not a cookbook formula to estimate either current or inductance.
Here's another document I looked at for hints (ignore the CAN stuff):
http://courses.ece.uiuc.edu/ece445/projects/spring2004/project12_final_paper.dot
(in English)

My application is Uin between 36-57V, 48V DC nominal. Max 400mA. No
300W
Output 3,3V-12V depending on what turns ratio and voltage divider I
choose.
Topology: isolated flyback transformer.
So I'm looking for how to figure out the acceptable range for the
primary inductor Lp in [Henry]. Secondary inductance is also of
interest ofcourse.

Because of the decoupling nature of the flyback circuit, the output
voltage is not closely dependant upon the turns ratio. You should
be able to make one transformer cover this output voltage range,
unless transformer size or component cost is critical.

A flyback circuit capable of producing 12V at a specific power level,
will likely produce a 3V3 output at the same power level, providing
that the rectifier current rating, output capacitor ripple current
rating and secondary winding copper cross-sectional area are suitable.
Flybacks are not the first choice for lower voltage circuits due to
the high peak to average ratio, which predicts a tendency to higher
rms losses in copper or other resistive circuit elements.

The 2A output at 12V will be less stressful than the 3V3 output at 7A.

I'm listing some web references that you might find useful:

SEM300 topic8 slup072
Switching Power Supply Design Review - 60 Watt Flyback Regulator
Raoji Patel and Glenn Fritz.
http://focus.ti.com/lit/ml/slup072/slup072.pdf

SEM400 topic2 slup076
Filter Inductor and Flyback Transformer Design for Switching Power
Supplies
Lloyd Dixon Jr.
http://focus.ti.com/lit/ml/slup076/slup076.pdf

Section 5 slup127 Inductor and Flyback transformer design
http://focus.ti.com/lit/ml/slup127/slup127.pdf

There are a lot of other archived app notes from the TI-Unitrode
seminars at their web site.
http://focus.ti.com/general/docs/training/trainingevents.tsp?familyId=2

notably the magnetics design handbook
http://focus.ti.com/docs/training/catalog/events/event.jhtml?sku=SEM401014

RL

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