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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 (K
), 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 N
, ripple to peak current ratio K
,
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
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 B
, gap length L
, 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 (C
) 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