ETC AN-17

®
Flyback Transformer Design For
TOPSwitch® Power Supplies
Application Note AN-17
When developing TOPSwitch flyback power supplies,
transformer design is usually the biggest stumbling block.
Flyback transformers are not designed or used like normal
transformers. Energy is stored in the core. The core must be
gapped. Current effectively flows in either the primary or
secondary winding but never in both windings at the same
time.
Why use the flyback topology? Flyback power supplies use the
least number of components. At power levels below 75 watts,
total flyback component cost is lower when compared to other
techniques. Between 75 and 100 Watts, increasing voltage and
current stresses cause flyback component cost to increase
significantly. At higher power levels, topologies with lower
voltage and current stress levels (such as the forward converter)
may be more cost effective even with higher component counts.
Flyback transformer design, which requires iteration through a
set of design equations, is not difficult. Simple spreadsheet
iteration reduces design time to under 10 minutes for a transformer
VDIODE
D2
UG8BT
L1
3.3 µH
7.5 V
ISEC
VR1
P6KE200
C1
33 µF
(CIN)
L2
22 mH
IPRI
VDRAIN
C6
0.1 µF
R2
68 Ω
C3
120 µF
25 V
C2
680 µF
25 V
U2
NEC2501-H
D1
UF4005
BR1
R1
39 Ω
VR2
1N5995B
6.2 V
RTN
D3
1N4148
C5
47µF
DRAIN
SOURCE
CONTROL
L
U1
TOP202YAI
C7
1000 nF
C4
Y1
0.1 µF
CIRCUIT PERFORMANCE:
Line Regulation - ±0.5%
(85-265 VAC)
Load Regulation - ±1%
(10-100%)
Ripple Voltage ± 50 mV
Meets VDE Class B
N
J1
PI-1787-021296
Figure 1. ST202A Power Supply Operates from Universal Input Voltage and Delivers 15 Watts.
June 1996
AN-17
that usually works the first time. This method, used for
continuous mode as well as discontinuous mode designs, has
three distinct steps:
1) Identify and estimate a set of independent variables
(input) depending on application details, transformer
core, and selected TOPSwitch.
2) Identify and calculate a set of dependent parameters
(output).
3) Iterate specified independent variables until selected
dependent parameters fall within defined limits for a
practical flyback transformer.
A simple PC spreadsheet (available from Power Integrations
for Excel or compatible spreadsheet programs) automates the
transformer design method presented in this application note.
(Note: this improved version has been completely revised and
may give slightly different answers compared to earlier versions.
Refer to the last page of this application note for a complete
description of the changes.)
A new parameter, the ratio of primary ripple current to peak
current (KRP), is introduced to describe the TOPSwitch drain
current waveform shape and simplify subsequent calculations
such as RMS current and AC flux density.
Application specific independent variables include minimum
and maximum AC input voltage, line frequency, TOPSwitch
switching frequency, output and bias voltages, output power,
bridge rectifier conduction time, size of input energy storage
capacitor, power supply efficiency and power loss allocation
between primary and secondary circuitry. Variables depending
on the transformer core and construction include effective core
cross sectional area and magnetic path length, ungapped
effective inductance, bobbin physical winding width, margin
width (for creepage distance and safety isolation), number of
primary layers, and number of secondary turns. Variables
depending on TOPSwitch include switching frequency, reflected
output voltage, ripple to peak current ratio, and TOPSwitch
voltage drop.
For a given application and transformer core, 20 of these 23
independent variables will be calculated or estimated once and
then remain fixed during iteration. Only three variables,
number of secondary turns NS, ripple to peak current ratio KRP,
and number of primary winding layers L will be changed during
the iteration process.
Dependent parameters are divided into four groups: DC input
voltage, primary current waveform shape, transformer design,
and voltage stress. DC input voltage parameters are simply the
minimum and maximum DC input voltage after the AC mains
have been rectified and filtered. Primary current waveform
2
C
6/96
shape parameters include maximum duty cycle, average current,
peak current, ripple current, and RMS current to completely
define transformer primary current and determine operation in
either continuous or discontinuous mode. Transformer design
parameters include primary inductance, number of primary
turns, number of bias winding turns, gapped effective inductance,
maximum flux density, AC flux density, ungapped core relative
permeability, estimated gap length, effective bobbin width,
insulated primary wire diameter, insulation thickness, bare
conductor cross section, primary current capacity, and secondary
design parameters. Voltage stress parameters determine the
maximum TOPSwitch off-state drain voltage and output rectifier
peak inverse voltage.
Of all these dependent parameters, only three require examination
and comparison within limits during iteration. Maximum flux
density BM, gap length LG , and primary current capacity CMA
are checked with each iteration until all three parameters are
within specified limits. The remaining dependent parameters
are either intermediate calculations or parameters used by the
manufacturer for construction or the designer for specifying
components.
Understanding primary and secondary current waveform shape
in both continuous and discontinuous mode operation is
necessary before beginning transformer design.
Figure 1 shows a typical flyback power supply using the
TOP202 TOPSwitch from Power Integrations, Inc. TOPSwitch
combines an integrated high voltage MOSFET switch with a
complete switching power supply controller and protection
circuitry in a single 3 pin TO220 package. The TOPSwitch
power supply operates from 85 to 265 VAC and delivers 15
Watts at 7.5 Volt output. AC power is rectified and filtered by
BR1 and C1 (CIN) to create the high voltage DC bus applied to
the primary winding of T1. The other side of the transformer
primary is driven by TOPSwitch. D1 and VR1 clamp voltage
spikes caused by transformer leakage inductance. D2, C2, L1,
and C3 rectify and filter the power secondary. TOPSwitch bias
voltage is provided by D3 and C4 which rectify and filter the
bias winding. EMI filter components L2, C6, and C7 reduce
conducted emission currents. Bypass capacitor C5 filters
internal TOPSwitch gate charge current spikes and also
compensates the control loop. Regulation is achieved when the
output voltage rises sufficiently above Zener diode voltage
(VR2) to cause optocoupler photodiode current to flow.
Optocoupler phototransistor current flows into the TOPSwitch
control pin to directly control the duty cycle and output voltage.
R1 together with series impedances of VR2 and TOPSwitch
determine the control loop DC gain. R2 and VR2 provide a
slight preload to improve regulation at light loads.
Figures 2 and 3 show typical voltage and current waveforms
taken from the same power supply delivering 15 Watts from
110 VAC input voltage but with different flyback transformer
0V
IP
0A
20
IR
500 mA
IP
0 mA
0 mA
10 V
0V
-10 V
-20 V
5A
5A
0
10
Time (µs)
ISEC
10
Time (µs)
0
ISEC
5A
0V
500 mA
VDIODE
VDIODE
0 mA
10 V
0V
-10 V
-20 V
200 V
IPRI
500 mA
IPRI
IR
PI-1527-051695
200 V
VDRAIN
PI-1526-091395
VDRAIN
AN-17
0A
20
Figure 2. Voltage and Current Waveforms for Transformer
Primary and Secondary in Discontinuous Mode.
Figure 3. Voltage and Current Waveforms for Transformer
Primary and Secondary in Continuous Mode.
primary inductance. TOPSwitch turns on to effectively apply
the DC input voltage across the transformer winding with the
“dot” side at lower potential than the “no-dot side”. Primary
current IPRI increases linearly with a rate of change (di/dt) that
varies directly with DC input voltage and inversely with primary
inductance. Ripple current IR is defined as the incremental
linear current rise (di) over the entire TOPSwitch on time (tON).
Peak primary current IP is the final value occurring as TOPSwitch
turns off. Energy, proportional to the square of peak current IP,
is stored by magnetic field in the transformer core as if the
primary winding were a simple inductor. The secondary
winding carries a reflected voltage proportional to primary
voltage by turns ratio with the same “dot” polarity. While
TOPSwitch is on, output diode D2 and bias diode D3 are reverse
biased which prevents secondary current flow. When TOPSwitch
turns off, the decreasing magnetic field induces an abrupt
voltage reversal on all transformer windings such that the “dot”
side is now higher potential than the “no-dot” side. Diode D2
and D3 become forward biased and secondary current rises
quickly to a peak value (proportional by the inverse turns ratio
to primary peak current IP). Primary current immediately drops
to zero. TOPSwitch drain voltage quickly rises to a voltage
equal to the sum of the DC input voltage and reflected output
voltage. Secondary winding current now linearly decreases at
a rate that varies directly with output voltage and inversely with
secondary inductance. Duty cycle is defined as the ratio of
TOPSwitch on time tON to switching period T. D can also be
calculated from tON and switching frequency f S as shown.
The stored energy is completely delivered to the load. TOPSwitch
drain voltage VDRAIN relaxes and rings back towards the DC bus
voltage when no current is flowing in either primary or secondary.
D=
t ON
= t ON × f S
T
Figure 2 shows TOPSwitch and output diode triangular current
waveforms which define “discontinuous” mode of operation
resulting from low primary inductance. The secondary current
linearly decreases to zero before TOPSwitch turns on again.
Figure 3 shows trapezoidal current waveforms which define
“continuous” mode of operation resulting from high primary
inductance. Secondary current is still flowing when TOPSwitch
turns on at the beginning of the next cycle. The stored energy
is not completely delivered to the load. Energy (due to non-zero
magnetic field) remains in the core when TOPSwitch turns on
again which causes the initial step in TOPSwitch current. Note
that TOPSwitch drain voltage VDRAIN stays at a high value equal
to the sum of the DC input voltage and reflected output voltage
until TOPSwitch turns on again.
Current never flows in the primary and secondary winding at
the same time. Neither primary or secondary current is actually
continuous. In flyback power supplies, continuous/
discontinuous mode refers to magnetic field continuity in the
transformer core over one complete switching cycle. (The
flyback power supply is an isolated version of the simple buckboost converter where continuous and discontinuous modes are
easily defined by inductor current continuity.)
Each primary current waveform has a peak value (IP), a ripple
current value (IR), an average or DC value (I AVG), and an RMS
value (IRMS). IP determines the number of primary turns and the
core size necessary to limit peak flux density and must also be
below TOPSwitch peak current limit. IAVG is the average or DC
primary current (as well as the power stage DC input current)
which is proportional to output power. IRMS causes power losses
due to winding resistance and TOPSwitch RDSON. The ratio
(KRP) of ripple current IR to peak current IP defines the continuous
or discontinuous waveform. KRP also simplifies subsequent
calculations. Transformers designed for discontinuous operation
have a higher peak current and a ripple current to peak current
ratio KRP of one. Practical continuous designs have lower peak
C
6/96
3
AN-17
currents and a ripple to peak current ratio KRP of less than one
but typically greater than 0.4. KRP is inversely proportional to
primary inductance so a continuous design with lower KRP will
have a higher inductance. Continuous transformer designs
have a practical primary inductance upper limit approximately
four times that of a discontinuous design at the same input
voltage and output power due to the difference in peak currents
and value of KRP.
The primary current waveforms shown in Figures 2 and 3
deliver the same output power and therefore (assuming equal
efficiency) must have equal IAVG. The discontinuous current
waveform has a higher peak value and therefore must have a
higher RMS current value. Discontinuous mode requires less
inductance and reduces transformer size but operates with
higher losses and lower efficiency due to higher RMS currents.
Continuous mode requires higher inductance and larger
transformer size but offers improved efficiency and lower
power losses. The trade-off between transformer size and
power supply efficiency depends on the packaging and thermal
environment in each application.
Some control loop comments regarding continuous mode are in
order here. Most designers tend to avoid the continuous mode
whenever possible because the feedback control loop is more
difficult to analyze. Discontinuous mode power supplies are
modeled with a single pole response and are simple to stabilize.
Continuous mode offers improved efficiency, reduced losses,
lower component temperatures, or higher output power but
analysis is more difficult because a right half plane zero and
complex pole pair all shift with duty cycle. However, stabilizing
a continuous mode TOPSwitch power supply is quite
straightforward. Adequate phase margins are achievable over
all line and load combinations because the 70% maximum
TOPSwitch duty cycle DCMAX (from the data sheet) limits right
half plane zero and complex pole pair migration. Phase margin
is generally higher than expected once the damping effect of
effective series power path resistance and output capacitor ESR
is taken into account. Crossover bandwidths of 1 KHz (or
wider) are easily achievable with phase margins of at least 45
degrees. Refer to AN-14 for circuit techniques to use in
continuous mode designs.
Transformer core, winding, and safety issues must also be
discussed before beginning design.
Transformer core and construction parameters depend on the
selected core and winding techniques used in assembly. Physical
height and cost are usually most important when selecting
cores. This is especially true in AC mains adapter power
supplies normally packaged in sealed plastic boxes. Applications
allowing at least 0.75 inches of component height can use low
cost EE or EI cores from Magnetics, Inc., Japanese vendors
TDK and Tokin, or European vendors Philips, Siemens, and
4
C
6/96
Thomson. Applications requiring lower profile can benefit
from EFD cores available from the European vendors. EER
cores offer a large window area, require few turns, and have
bobbins available with high pin counts for those applications
requiring multiple outputs. ETD cores are useful in the higher
power designs when space is not a problem. PQ cores are more
expensive but take up slightly less PC board space and require
less turns than E cores. Safety isolation requirements make pot
cores, RM cores, and toroids generally not suitable for flyback
power supplies operating from the AC mains.
Flyback transformers must provide isolation between primary
and secondary in accordance with the regulatory agencies of
the intended market. For example, information technology
equipment must meet the requirements of IEC950 in Europe
and UL1950 in the U.S. These documents specify creepage
and clearance distances as well as insulation systems used in
transformer construction. 5 to 6 mm creepage distance is
usually sufficient between primary and secondary (check with
the appropriate agency and specification). Isolation is usually
specified by electric strength and is tested with a voltage of
typically 3000 VAC applied for 60 seconds. Two layers of
insulation (Basic and Supplementary) can be used between
primary and secondary if each layer exceeds the electric
strength requirement. Three layers of insulation (reinforced)
can also be used if all combinations of two layers (out of total
three layers) meets the electric strength requirement.
Figure 4a shows the margin winding technique used in most
flyback transformers. The margin is usually constructed with
layers of tape slit to the width of the desired margin and
wrapped in sufficient layers to match the winding height. The
margin is generally half the required primary to secondary
creepage distance (2.5 mm in this example). Cores and
bobbins should be selected large enough that the actual winding
width is at least twice the total creepage distance to maintain
transformer coupling and reduce leakage inductance. The
primary is wound between the margins. To reduce the risk of
interlayer voltage breakdown due to insulation abrasion,
improve layer to layer insulation, and decrease capacitance,
the primary layers should be separated by at least one layer of
UL listed polyester film tape (3M 1298) cut to fit between the
margins. Impregnation with varnish or epoxy can also improve
the layer to layer insulation and electric strength but does not
reduce capacitance. The bias winding may then be wound over
the primary. Supplementary or reinforced insulation consisting
of two or three layers of UL listed polyester film tape cut to the
full width of the bobbin may then be wrapped over the primary
and bias windings. Margins are again wound. The secondary
winding is wound between the margins. Another two or three
layers of tape is added to secure the windings. Insulation
sleeving may be needed over the leads of one or all windings
to meet creepage distance requirements at lead exits. Nylon or
AN-17
SECONDARY
SAFETY
INSULATION
TAPE
BIAS
PRIMARY
(Z WOUND)
SECONDARY
(INSULATED)
BIAS
(ALTERNATE
LOCATION)
BIAS
M
M
PRIMARY
(a) MARGIN WINDING
ALTERNATE
PRIMARY
WINDING
(b) C WINDING
PI-1521-091395
PI-1678-091395
Figure 4. Margin Wound Transformer.
Figure 5. Triple Insulated Wire Wound Transformer.
Teflon sleeving with a minimum wall thickness of 0.41 mm
should be used to meet the safety agency requirements. Consider
the core as isolated dead metal (which means the core is
conductive but not part of any circuit and safely insulated from
the consumer). The sum of distance from primary winding (or
lead exits) to the core added to the distance from the core to the
secondary (or lead exits) must be equal to or greater than the
required creepage distance.
insulated wire. The double or triple insulated wire is then
wound. Another layer of tape is added to secure insulated
winding.
Both Z winding (Figure 4a) and C winding (Figure 4b) techniques
for multiple primary layers are shown. Note that the “dot” side
which connects to TOPSwitch is buried under the second layer
for self shielding to reduce EMI (common mode conducted
emission currents). Z winding decreases transformer
capacitance, decreases AC TOPSwitch losses, and improves
efficiency but is more difficult and costly to wind. The
C winding is easier and lower cost to wind but at the expense of
higher loss and lower efficiency.
Figure 5 shows a new technique using double or triple insulated
wire on the secondary to eliminate the need for margins (insulated
wire sources can be found at the end of this application note).
In double insulated wire, each layer is usually capable of
meeting the electric strength requirement of the safety agency.
In triple insulated wire, all three combinations of two layers
taken together must usually meet the electric strength
requirement. Special care is necessary to prevent insulation
damage during winding and soldering. This technique reduces
transformer size and eliminates the labor cost of adding margins
but has higher material cost and may increase winding costs.
The primary winding is wound over the full width of the bobbin
flange. The bias winding can be wound if desired over the
primary. One layer of tape is usually necessary between
primary or bias and secondary to prevent abrasion of the
Figure 5 also shows an alternate position for the bias winding
wound directly over the secondary to improve coupling to the
secondary winding and reduce leakage inductance (to improve
load regulation in bias winding feedback circuits). Note that
because the bias winding is a primary circuit, margin wound
transformers must have another layer of supplementary or
reinforced insulation between the secondary and alternate bias
winding.
Refer to AN-18 for more information regarding transformer
construction guidelines.
Flyback transformer design now begins by specifying the three
groups of independent variables shown in the spreadsheet
(Figure 6).
Application Variables:
Output power PO, output voltage VO , AC mains frequency fL,
TOPSwitch switching frequency f S (100KHz), minimum
(VACMIN), and maximum (VACMAX) AC mains voltage come
directly from the application.
For efficiency (η), start with an estimate based on measurements
in similar power supplies (or use a value of 0.8 if data is
unavailable).
Efficiency can be used to calculate total power loss PL in the
power supply as shown below. Some power losses occurring in
series primary components such as the bridge rectifier, common
C
6/96
5
AN-17
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
B
C
INPUT
ENTER APPLICATION VARIABLES
VACMIN
85
VACMAX
265
fL
60
fS
100000
VO
7.5
PO
15
n
0.8
Z
0.5
VB
10.4
tC
3.2
CIN
33
D
OUTPUT
E
Volts
Volts
Hertz
Hertz
Volts
Watts
Volts
mSeconds
uFarads
ENTER TOPSWITCH VARIABLES
VOR
85
VDS
10
VD
0.4
VDB
0.7
KRP
0.92
Volts
Volts
Volts
Volts
F
Minimum AC Input Voltage
Maximum AC Input Voltage
AC Mains Frequency
TOPSwitch Switching Frequency
Output Voltage
Output Power
Efficiency Estimate
Loss Allocation Factor
Bias Voltage
Bridge Rectifier Conduction Time Estimate
Input Filter Capacitor
Reflected Output Voltage
TOPSwitch on-state Drain to Source Voltage
Output Winding Diode Forward Voltage Drop
Bias Winding Diode Forward Voltage Drop
Ripple to Peak Current Ratio (0.4 < KRP < 1.0)
ENTER TRANSFORMER CORE/CONSTRUCTION VARIABLES
EE22-Z
AE
0.41
cm^2
LE
3.96
cm
AL
2400
nH/T^2
BW
8.43
mm
M
0
mm
L
2
NS
5
Core Type
Core Effective Cross Sectional Area
Core Effective Path Length
Ungapped Core Effective Inductance
Bobbin Physical Winding Width
Safety Margin Width (Half the Primary to Secondary Creepage Distance)
Number of Primary Layers
Number of Secondary Turns
DC INPUT VOLTAGE PARAMETERS
VMIN
VMAX
9 3 Volts
3 7 5 Volts
Minimum DC Input Voltage
Maximum DC Input Voltage
CURRENT WAVEFORM SHAPE PARAMETERS
DMAX
IAVG
IP
IR
IRMS
0.51
0.20
0.74
0.68
0.32
Duty Cycle at Minimum DC Input Voltage (VMIN)
Average Primary Current
Peak Primary Current
Primary Ripple Current
Primary RMS Current
TRANSFORMER PRIMARY DESIGN PARAMETERS
LP
NP
NB
ALG
215
BM
BAC
959
ur
1845
LG
BWE
16.86
OD
INS
0.05
DIA
AWG
CM
102
CMA
6 2 3 uHenries
54
7
nH/T^2
2 0 8 5 Gauss
Gauss
0 . 2 2 mm
mm
0.31 mm
mm
0.26 mm
3 0 AWG
Cmils
3 2 1 Cmils/Amp
TRANSFORMER SECONDARY DESIGN PARAMETERS
ISP
7.95
ISRMS
3.36
IO
2.00
IRIPPLE
2.70
CMS
AWGS
DIAS
ODS
INSS
VOLTAGE STRESS PARAMETERS
VDRAIN
PIVS
PIVB
ADDITIONAL OUTPUTS
VX
12
VDX
0.7
NX
PIVX
1079
0.39
Amps
Amps
Amps
Amps
Amps
Amps
Amps
Amps
Primary Inductance
Primary Winding Number of Turns
Bias Winding Number of Turns
Gapped Core Effective Inductance
Maximum Flux Density (2000 < BM < 3000)
AC Flux Density for Core Loss Curves (0.5 X Peak to Peak)
Relative Permeability of Ungapped Core
Gap Length (Lg >> 0.051 mm)
Effective Bobbin Width
Maximum Primary Wire Diameter including insulation
Estimated Total Insulation Thickness (= 2 * film thickness)
Bare conductor diameter
Primary Wire Gauge (Rounded to next smaller standard AWG value)
Bare conductor effective area in circular mils
Primary Winding Current Capacity (200 < CMA < 500)
Peak Secondary Current
Secondary RMS Current
Power Supply Output Current
Output Capacitor RMS Ripple Current
Cmils
1 9 AWG
0.91 mm
1.69 mm
mm
Secondary Bare Conductor minimum circular mils
Secondary Wire Gauge (Rounded up to next larger standard AWG value)
Secondary Minimum Bare Conductor Diameter
Secondary Maximum Insulated Wire Outside Diameter
Maximum Secondary Insulation Wall Thickness
5 7 3 Volts
4 2 Volts
5 9 Volts
Maximum Drain Voltage Estimate (Includes Effect of Leakage Inductance)
Output Rectifier Maximum Peak Inverse Voltage
Bias Rectifier Maximum Peak Inverse Voltage
Volts
Volts
8.04
6 8 Volts
Auxiliary Output Voltage
Auxiliary Diode Forward Voltage Drop
Auxiliary Number of Turns
Auxiliary Rectifier Maximum Peak Inverse Voltage
Figure 6. Spreadsheet for ST202A Flyback Transformer Design.
6
C
6/96
AN-17
mode choke, and TOPSwitch are not associated directly with
energy stored in the flyback transformer core. The remaining
power losses, occurring in the output rectifier and clamp Zener
diode when energy is released from the flyback transformer, are
now defined as secondary loss PLS. Loss Allocation Factor Z,
defined below as the ratio of secondary loss PLS to total loss PL,
is a scaling factor which distributes the losses between primary
and secondary. Loss allocation factor Z is typically between 0.4
and 0.6 which means that secondary loss PLS is usually 40% to
60% of total power supply loss PL .
PL = PO × (
1−η
)
η
P
Z = LS
PL
Figure 7. Bridge AC Current, AC Voltage, and DC Voltage
Waveforms.
normally used and VD is typically 0.7 Volts.
Bias voltage VB is determined by the feedback control circuit
and is usually between 10 volts and 30 volts (see AN-16).
For bridge rectifier conduction time tC, 3 milliSeconds is typical
(measure on a similar power supply or set equal to zero for a
conservative first design).
For input filter capacitor CIN , start with a standard value in
microFarads between two and three times the output power in
Watts (appropriate for universal or 115 VAC input). For
example: 30µF to 45µF is a suitable capacitance range for a
15 Watt supply. 33µF is the lowest standard value within the
range.
TOPSwitch Variables:
Reflected output voltage VOR appears across the transformer
primary when TOPSwitch is off and current is flowing through
the secondary and output rectifier diode. Transformers optimized
for TOPSwitch applications should be designed with a maximum
reflected voltage VOR of 60V or less for the TOP1XX series and
135V or less for the TOP2XX series. For more information,
refer to AN-16.
VDS is the on-state TOPSwitch voltage from the data sheet
(typically 10 volts) at the specified value for peak TOPSwitch
drain current IP.
Output rectifier forward voltage drop VD depends on output voltage.
For lower output voltages (typically 8 Volts and below) a Schottky
diode is commonly used and VD is typically 0.4 Volts. In some cases,
a Schottky diode can be used for output voltages as high as 12V
depending on input voltage range and transformer turns ratio. For
higher output voltage, an ultrafast recovery PN junction diode is
Bias winding diode forward voltage drop (VDB) is also typically
0.7 Volts
Ripple current to peak current ratio KRP determines how far into
the continuous mode a flyback transformer will operate.
Continuous mode transformers optimized for TOPSwitch
applications operating from 100/115 VAC or universal input
voltage should have a minimum KRP of 0.4. Applications
operating from 230 VAC input voltage should have a minimum
KRP of 0.6. Discontinuous mode transformers optimized for
TOPSwitch applications always have a KRP equal to 1.0.
K RP =
IR
IP
Transformer Core/Construction Variables:
The following effective parameters are specified by the core
and bobbin manufacturer in data sheets: cross sectional area Ae
(cm2), path length Le (cm), ungapped inductance AL (specified
in either mH/(1000 turns)2 or nH/T2), and physical bobbin
winding width BW (mm).
Margin width M, determined by insulation methods and
regulatory requirements discussed above, is usually between
2.5 to 3.0 mm for margin wound or set to zero for insulated wire
wound transformers.
For number of layers L, one or two layers of primary winding
are normally used. Higher number of layers increase cost,
increase capacitance, reduce coupling, and increase leakage
inductance.
C
6/96
7
AN-17
Number of secondary turns NS is a key iteration variable. One
turn per Volt of output voltage is a good value to begin with for
NS (for example: start with 5 turns for a +5V output).
voltage VDS:
DMAX =
The four groups of dependent parameters can now be calculated.
Average current IAVG is calculated from minimum DC input
voltage VMIN, output power PO, and efficiency η:
DC Input Voltage Parameters:
Minimum DC input voltage VMIN depends on the AC input
voltage, bridge rectifier, and energy storage capacitor.
Figure 7 shows how CIN charges to the peak of the AC input
voltage during a short conduction time tC. Because of full wave
rectification, CIN has a ripple voltage at twice line frequency.
CIN must supply the entire average primary current during the
discharge time between the peaks of the AC input voltage.
Minimum DC voltage VMIN can be found from the following
equation where PO is the power supply output power, η is an
estimate of efficiency, fL is line voltage frequency, VACMIN is the
minimum AC mains voltage, CIN is the value of the filter
capacitor, and tC is an estimate for conduction time. As an
example, for 60 Hz, 85 VAC input voltage, efficiency of 0.8,
15 Watt output power, 33 uF input filter capacitance, and
estimated conduction time of 3.2 mS, VMIN is 93 Volts DC.
VMIN = (2 × V
2
ACMIN
)−(
1
− tC )
2 × fL
)
η × CIN
2 × PO × (
1
2 × 15 × (
− 3.2 mS )
2
2
×
60
= (2 × 85 ) − (
) = 93V
0.8 × 33µF
Maximum DC input voltageVMAX is simply the peak value of
the highest AC input voltage (VACMAX ) expected in the
application. Operation from 265 VAC input results in a
maximum DC bus voltage VMAX of 375 Volts DC.
VMAX = VACMAX × 2 = 265 × 2 = 375V
Current Waveform Shape Parameters:
DMAX is the actual duty cycle occurring when the TOPSwitch
power supply delivers maximum output power from minimum
input voltage. DMAX has an upper limit equal to the minimum
value of the TOPSwitch Data Sheet parameter DCMAX (64%).
DMAX is calculated from reflected voltage VOR, minimum DC
input voltage VMIN, and TOPSwitch on-state Drain to Source
8
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VOR
VOR + (VMIN − VDS )
I AVG =
PO
η × VMIN
Peak primary current Ip is calculated from average current IAVG,
ripple to peak current ratio KRP, and maximum duty cycle DMAX:
IP = I AVG ×
2
(2 − K RP ) × DMAX
Ripple current IR is calculated from average current IAVG, peak
primary current IP, and maximum duty cycle DMAX:
I R = 2 × ( IP −
I AVG
)
DMAX
RMS current IRMS is calculated from maximum duty cycle DMAX,
peak primary current IP, and ripple to peak ratio KRP. I RMS can
also be calculated directly from DMAX, IP, and ripple current IR.
I RMS = IP × DMAX × (
2
K RP
− K RP + 1)
3
= DMAX × ( IP2 − ( IP × I R ) +
I R2
)
3
Transformer Design Parameters:
Primary inductance LP (in µH) is determined by the flyback
transformer energy equation defined below. The flyback
transformer stores energy proportional to the square of primary
current. When TOPSwitch is on, primary current linearly ramps
up over a current range, defined earlier as ripple current IR, and
increases the energy stored in the flyback transformer core.
When TOPSwitch turns off, the stored energy increment
associated with ripple current IR is delivered to the load and
secondary losses (rectifier and clamp). Inductance LP can now
by calculated from output power PO, efficiency η, loss allocation
factor Z, peak current IP, switching frequency fS, and ripple
current to peak current ratio KRP (which determines IR).
AN-17
( Z × (1 − η)) + η
PO × (
)
η
6
LP = 10 ×
K
fS × IP2 × K RP × (1 − RP )
2
Primary inductance LP (in µH) can also be determined from a
simple function of ripple current IR, effective primary voltage
(VMIN-VDS), maximum duty cycle DMAX, and switching frequency
fS as shown below but the resulting value for primary inductance
may be slightly different due to the selected value for loss
allocation factor Z and TOPSwitch on-state Drain to Source
voltage VDS. The energy equation given above is preferred for
selecting the value of inductance LP while the ripple current
equation given below is best for verifying the LP value using
in-circuit measurements.
LP ( MEASURED) = 10 6 ×
(VMIN − VDS ) × DMAX
I R × fS
Number of primary turns NP depends on number of secondary
turns NS, output voltage VO, diode forward voltage drop VD,
effective primary voltage (VMIN-VDS), and maximum duty cycle
DMAX:
V − VDS
DMAX
N P = NS × MIN
×
VO + VD
1 − DMAX
The number of bias winding turns NB is calculated from the
output voltage VO, output diode voltage V D, secondary number
of turns NS, target bias voltage VB, and bias diode voltage VBD:
NB =
VB + VBD
× NS
VO + VD
ALG is the effective inductance for the gapped core in nH/T2.
Some core vendors offer standard gapped core sets with specified
ALG. The transformer manufacturer either procures the gapped
core for the given ALG value or grinds the gap to meet the
inductance specification in the finished transformer. ALG is
also used to simplify subsequent calculations. ALG is calculated
from primary inductance LP (in µH) and number of primary
turns NP. Note that ALG is specified in nH/(turn)2.
ALG
L
= 1000 × P2
NP
Maximum flux density BM is a dependent iteration variable to
be manipulated between the limits of 2000 and 3000 Gauss by
varying number of secondary turns NS which directly varies
number of primary turns NP as previously shown. BM is
calculated from peak current IP, number of primary turns NP,
effective gapped inductance ALG, and effective core cross
sectional area Ae. BM can also be calculated from effective
primary voltage (VMIN-VDS), output voltage VO , output diode
voltage VD , and maximum duty cycle DMAX:
BM =
N P × IP × ALG
10 × Ae
= NS ×
IP × ALG VMIN − VDS
DMAX
×
×
VO + VD
10 × Ae
1 − DMAX
BAC is the AC flux density component. The equation gives peak
AC flux density (rather than peak to peak) to use with core loss
curves provided by the core vendor. BAC can be calculated from
maximum flux density BM and ripple to peak current ratio KRP.
BAC can also be calculated from effective primary voltage
(VMIN-VDS), duty cycle, frequency, effective core cross sectional
area, and number of primary turns NP:
BAC =
BM × K RP (VMIN − VDS ) × DMAX × 108
=
2
2 × fS × Ae × N P
Relative permeability µr of the ungapped core must be calculated
to estimate the gap length Lg. µr is found from core parameters
Ae (cm2), Le (cm), and ungapped effective inductance AL:
µr =
AL × LE
0.4 × π × Ae × 10
Gap length Lg is the air gap ground into the center leg of the
transformer core. Grinding tolerances and ALG accuracy place
a minimum limit of 0.051 mm on Lg. L g (in mm) is calculated
from number of primary turns NP, core effective cross sectional
area Ae, primary inductance LP (in µH), core effective path
length Le, and relative permeability µr:
 0.4 × π × N P2 × Ae Le 
Lg = 
−  × 10
LP × 100
µr 

Effective bobbin width BWE takes into account physical bobbin
width BW, margins M, and number of layers L:
BWE = L × ( BW − (2 × M ))
C
6/96
9
AN-17
Primary insulated wire diameter OD in mm is found from
effective bobbin width BWE and number of primary turns NP:
OD =
BWE
NP
The bias winding is usually wound with the same wire diameter
as the primary to reduce the number of different wire gauges
necessary for production.
Actual magnet wire outside diameter OD is slightly larger than
the diameter DIA of the bare copper conductor. Insulation
thickness varies inversely with bare copper conductor American
Wire Gauge (AWG) size which means that smaller diameter
conductors have thinner insulation thickness. Data from several
different manufacturers were tabulated to generate an empirical
expression for total insulation thickness INS (in mm) as a
function of heavy insulated magnet wire outside diameter
(in mm).
INS = (0.0594 × LOG(OD)) + 0.0834
DIA = OD − INS
Another empirical equation determines the AWG for magnet
wire with a given bare conductor diameter DIA. Integer AWG
values are the standard sizes of available wire so the calculated
AWG value should always be rounded up to the next integer or
standard value (the next smaller standard conductor diameter)
before proceeding with the current capacity or CMA calculation.
AWG = 9.97 × (1.8277 − (2 × LOG( DIA)))
Magnet wire for transformer winding usually has the cross
sectional area specified in circular mils. A circular mil is the
cross sectional area of a wire with a diameter of 1 mil (or
0.0254 mm). The effective cross sectional area in circular mils
(CM) of a standard AWG size bare conductor wire is found
from the following simple expression.
 50 − AWG 


3

CM = 2 
“Circular mils per Amp” or CMA is a convenient way to specify
winding current capacity. CMA, which is the inverse of current
density, is simply the ratio of cross sectional area in circular
mils to the RMS value of primary current. CMA should be
between 200 and 500 and is calculated from cross sectional
wire area in CM and RMS primary current IRMS.
10
C
6/96
CMA =
CM
I RMS
This completes all calculations necessary for the primary
winding. Secondary peak current, RMS current, average output
current, output capacitor ripple current, and secondary minimum
and maximum conductor diameter must also be calculated.
Peak secondary current ISP is a simple function of peak primary
current IP, primary turns NP, and secondary turns NS.
ISP = IP ×
NP
NS
Secondary RMS current ISRMS is found from maximum duty
cycle DMAX, secondary peak current ISP, and ripple to peak
current ratio KRP (KRP is identical for primary and secondary).
ISRMS
2
K RP
= ISP × (1 − DMAX ) × (
− K RP + 1)
3
Output current IO is simply the ratio of output power PO to output
Voltage VO:
IO =
PO
VO
Output capacitor ripple current IRIPPLE is not a true transformer
parameter but is needed for capacitor selection and easy to
calculate from other transformer parameters. IRIPPLE is found
from secondary RMS current ISRMS and output current I O.
2
I RIPPLE = ISRMS
− IO2
Minimum secondary bare conductor diameter DIAS (in mm)
based on previously calculated current capacity CMA and
secondary RMS current must be determined.
From the primary CMA and secondary RMS current ISRMS, the
minimum secondary bare conductor CMS is calculated.
CMS = CMA × ISRMS
Minimum secondary AWGS is then calculated from another
empirical equation. Secondary calculated wire gauge AWGS is
always rounded down to the next integer value which selects the
next larger standard wire size.
AN-17
AWGS = 9.97 × (5.017 − LOG(CMS ))
(Secondary conductors larger than 26 AWG should not be used
due to skin effects. Refer to AN-18 for suggestions on parallel
conductor techniques.)
Bare conductor diameter (in mm) is now determined.
DIAS =
 50 − AWGS 



4 × 2 3
1.27 × π
25.4
×
1000
The maximum wire outside diameter ODS (in mm) for a single
layer based on number of secondary turns and bobbin width
must also be calculated:
BW − (2 × M )
ODS =
NS
Secondary wire insulation thickness can now be calculated
from the bare conductor outside diameter (determined by
CMA) and the insulated wire outside diameter (determined by
number of turns and effective bobbin width). Note that secondary
insulation thickness INSS (in mm) is the insulation wall thickness
rather than the total insulation thickness used in the primary
winding calculation.
ODS − DIAS
INSS =
2
Obviously, if insulation thickness INSS is not a positive number,
another transformer design iteration is necessary with either
more secondary layers, a smaller number of secondary turns, or
a transformer core with a wider bobbin.
For insulated wire secondaries, INSS must be equal to or greater
than insulation thickness of the selected wire.
Parallel combinations of wire with half the diameter may be
easier to wind and terminate but the effective secondary CMA
will be half the value of the single winding.
Voltage Stress Parameters:
Maximum drain voltage is the sum of maximum DC input
voltage VMAX, an estimated drain clamp voltage term based on
VOR , and an estimated voltage term related to typical blocking
diode forward recovery. Refer to AN-16 for more detail.
Maximum peak inverse voltage PIVS for the output rectifier is
determined by transformer primary and secondary number of
turns NP and NS, maximum DC input voltage VMAX, and output
voltage VO .
PIVS = VO + (VMAX ×
NS
)
NP
Maximum peak inverse voltage PIVB for the bias rectifier is
determined from a similar equation using number of bias turns
NB.
PIVB = VB + (VMAX ×
NB
)
NP
Additional or auxiliary output winding number of turns NX and
rectifier diode peak inverse voltage PIVX can be determined
from the desired value for auxiliary output voltage VX, auxiliary
rectifier diode forward voltage drop VDX, output voltage VO,
output rectifier diode forward voltage drop VD, and number of
secondary turns NS.
NX =
VX + VDX
× NS
VO + VD
PIVX = VX + (VMAX ×
NX
)
NP
Iteration can now be used to reach a final and acceptable
solution for the flyback transformer design.
Iterate number of secondary turns NS or primary ripple to peak
current ratio KRP until maximum flux density BM is between
indicated limits and check that gap length Lg is higher than
indicated minimum value. BM will decrease and L g will increase
as NS or KRP is increased.
Examine primary current capacity in Circular Mils per Amp
(CMA). If CMA is below the specified lower limit of 200,
consider increasing number of primary layers from one to two
or use the next larger core size and perform new iteration. If
CMA is greater than 500, consider using the next smaller core
size. (CMA greater than 500 simply means that the wire
diameter is oversized for the expected RMS current).
The transformer design is now complete. The transformer
VDRAIN = VMAX + (1.4 × 1.5 × VOR ) + 20V
C
6/96
11
AN-17
References
manufacturer needs the following information:
Core part number and gapped effective inductance ALG
Bobbin part number
Wire gauge and insulation style on all windings
Safety or Electric strength and Creepage distance
specifications
Primary Inductance LP
Number of turns (NP, NS, NB, etc.) for each winding
Bobbin pin connections
Winding layer placement and winding instructions
Temperature class of operation (class A is 105 °C, class B
is 130 °C, etc.)
Spreadsheet Improvements
The order of the spreadsheet has been changed to simplify the iteration
process. Reflected voltage VOR and ripple to peak current ratio KRP are
now independent variables which make peak current Ip and duty cycle
DMAX dependent variables. Loss allocation factor Z is introduced to
distinguish between power losses occurring before energy is stored in
the transformer (primary losses) and power losses occurring after
energy is released from the transformer (secondary losses). Primary
inductance LP is now calculated from output power PO, KRP, efficiency
η, and loss allocation factor Z. The spreadsheet now takes into account
primary magnet wire insulation thickness as well as the discrete steps
of standard AWG wire sizes. Metric dimensions are used throughout
(with the exception of Circular mils for wire cross sectional area).
Drain Voltage VDRAIN now includes an estimate for the effect of leakage
inductance induced voltage spikes on typical primary clamp circuits.
Bisci, J., Part IV: Magnet Wire: Selection Determines
Performance, PCIM, October 1994, pp. 37.
Leman, B., Finding the Keys to Flyback Power Supplies
Produces Efficient Design, EDN, April 13, 1995, pp. 101-113.
McLyman, C., Transformer and Inductor Design Handbook,
Marcel Dekker, Inc. 1978
Insulated Wire Sources
Rubudue Wire Company
5150 E. LaPalma Ave, Suite 108
Anaheim Hills, CA 92807 USA
(714) 693-5512
(714) 693-5515 FAX
Furukawa Electric America, Inc.
200 Westpark Dr., Suite 190
Peachtree City, GA 30269 USA
(770) 487-1234
(770) 487-9910 FAX
The Furukawa Electric Co., Ltd.
6-1, Marunouchi 2-chome,
Chiyoda-ku, Tokyo 100, Japan
81-3-3286-3226
81-3-3286-3747 FAX
Power Integrations reserves the right to make changes to its products at any time to improve reliability or manufacturability.
Power Integrations does not assume any liability arising from the use of any device or circuit described herein, nor does it
convey any license under its patent rights or the rights of others.
PI Logo and TOPSwitch are registered trademarks of Power Integrations, Inc.
©Copyright 1994, Power Integrations, Inc. 477 N. Mathilda Avenue, Sunnyvale, CA 94086
WORLD HEADQUARTERS
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