Transformer & Magnetic Design
 Transformer Core Materials & Geometries
 Core Losses
 Peak Flux Density Selection
 Maximum Transformer Core Output Power
 Flyback Transformer (Magnetics)
 Powdered Molypermalloy (MPP) Cores
 Transformer Copper Losses
1
Transformer & Magnetic Design
Why do we need a transformer?
 Isolation for off-line operation
 Obtain the output voltage for a given duty
cycle
 Multiple outputs
2
Selection of Topologies
Consideration of
 the voltage stress of the power switch at high
line
 the current stress of power switch at maximum
output
 the operating frequency and transformer core
size
3
Transformer Core Materials
Ferrites
 Mixture of iron, manganese or zinc oxides
 Ceramic ferromagnetic material (brittle!)
 High resistance, no eddy current loss
 Core loss is mainly due to hysteresis loss
 Manufacturers: Ferroxcube-Philips, Magnetics
Inc., Ceramic Magnetics Inc., Fairite, Ferrite
International, TDK, Thomson-CSF, etc.
4
Transformer Core Geometries
Pot cores (up to 125W)
 Almost entirely enclosed by
ferrite material therefore
excellent EMI performance
 Narrow notch for coil leads
 Restrict to low voltage and
current applications
5
Transformer Core Geometries
EE cores (5W to 10kW)
 Most widely used core
 No narrow notch restricting
coil leads
 Poor EMI performance
 Good thermal performance
due to unimpeded airflow
6
Transformer Core Geometries
EC & ETD cores
 Improved EE core
 Round centre leg
 Reduce the mean length of a
turn for a given core area by
11%
 Lower Copper loss
7
Transformer Core Geometries
RM or “Square” cores
 Compromise between a pot
and an EE core
 Good EMI performance
 No narrow notch
 Unimpeded airflow
8
Transformer Core Geometries
PQ cores
 Optimum ratio of volume to
radiating surface and coil
winding area
 Minimizing temperature rise
for a given power
 Minimizing volume for a
given power
9
Transformer Core Geometries
LP cores
 Designed for low profile
applications
 Minimizing leakage
inductance with long centre
legs
10
Transformer Core Geometries
UU and UI cores
 Mainly for high-voltage
or ultra-high power
applications
 Large window area
permits thick wire size
 Large leakage inductance
11
MKS Units
Flux Φ in weber = B × Area in m2
Flux Density B in tesla
Magnetic Field Strength H in A/m
H = NI/l
where magnetic path length l is in m
 And B = µ0H in free space
where µ0 is 4π ×10-7 H/m
12
CGS Units
Flux Φ in maxwell = B × Area in cm2
Flux Density B in gauss
Magnetic Field Strength H in oersted
H = (0.4 π NI)/l
where magnetic length l is in cm
 Why CGS? Because B = H numerically in free
space
13
Conversion Between Units
 1 weber = 108 maxwell
 1 tesla = 104 gauss
 1 A/m = 0.0126 oersted
Faraday’s Law of induction
V = N (dΦ/dt) in MKS
V = N (dΦ/dt) × 10-8 in CGS, i.e., if Φ is
calculated from gauss × cm2
14
Hysteresis Curve
At 100oC, complete
saturation occurs at
a flux density of
3200 G 1mT = 10G
At 100oC, residual
flux density is
about 900 G
3F3
15
Core Losses
Mainly due to hysteresis loss; expressed in mW/cm3
Peak
flux
density
3F3
16
Core Losses
Core loss ∝ (Bmax) 2.7
Core loss ∝ f 1.7
 Value of core losses are usually given for
bipolar magnetic circuits (first and thirdquadrant operation) by various manufacturers
 For unipolar circuits, e.g., forward, divide by 2
17
Table of Core Losses
Page A.1
18
Peak Flux Density Selection
 Although BH loop is still
linear up to 2000G, peak
flux density should be
chosen at 1600G such that
power switch will not be
destroyed due to saturation
which may occur with fast
load change if peak flux
density is too high
19
3F3
Peak Flux Density Selection
 How to detect the occurrence of saturation in
practice?
Saturation starts
Current Waveform
20
Maxi. Transformer Core Output Power
Forward Topology
Po = (0.5 Bmax f Ae Ab)/Dcma Watts
 Peak flux density Bmax in Gauss 1mT = 10G
 Switching frequency f in kHz
1A/m = 0.0126 Oersted
 Core area Ae in cm2
 Bobbin winding area Ab in cm2
 Dcma in circular mils per rms ampere (Inverse
of current density)
21
Maxi. Transformer Core Output Power
What is Dcma in circular mils per rms ampere?
 Area per unit ampere
 500 cma means that a wire with a diameter of
√ 500 mils (1 mil = 1/1000 of an inch) carries
1A rms
1A
√500 = 22.3 mil = 0.566 mm
22
Maxi. Transformer Core Output Power
How did we come up with this equation?
Po = (0.5 Bmax f Ae Ab)/Dcma Watts
Voltage
Current
Assume that
 Efficiency is 0.8
 Space factor SF is 0.4
 Duty cycle is 0.4
23
Maxi. Transformer Core Output Power
What is space factor ?
 The fraction of bobbin winding area occupied
by the winding of primary and secondaries
4mm
Why SF is 0.4?
4mm
24
Maxi. Transformer Core Output Power
We can increase the output power by
 Higher Efficiency (Mission Impossible!)
 Higher SF (Difficult!)
 Higher duty cycle (Yes, using different reset
arrangement, but higher voltage stress on
power switch)
 Higher switching frequency (Yes, but higher
switching and core losses)
25
Primary & Secondary Windings
Forward Topology
Np = (40000 Vdc )/( Ae ΔB f) Turns
 Core area Ae in cm2
 ΔB = Bmax ( Use 1600 Gauss)
 Switching frequency in kHz
 DC input voltage Vdc in volts
Assume that duty cycle is 0.4
26
Primary & Secondary Windings
Forward Topology
Vo ≅ 0.4 Vdc (Ns/Np)
500×(1/0.8)×(1/0.4)×√0.4
Ns can be easily found
 Wire size of primary winding is (988 Po)/Vdc
in circular mils
500×√0.4
 Wire size of secondary winding is 316 Io in
circular mils
Assume that duty cycle is 0.4 and efficiency is 0.8
27
Maxi. Transformer Core Output Power
Push-Pull Topology
Po = (Bmax f Ae Ab)/Dcma Watts
 Peak flux density Bmax in Gauss
 Switching frequency f in kHz
 Core area Ae in cm2
 Bobbin winding area Ab in cm2
 Dcma in circular mils per rms ampere (Inverse
of current density)
28
Maxi. Transformer Core Output Power
Push-Pull Topology
Po = (Bmax f Ae Ab)/Dcma Watts
 Output is two times compared to that of
Forward Topology
Why?
 Because the flux change is doubled
 Core is warmer due to double in core losses
29
Primary & Secondary Windings
Push-Pull Topology
Np = (40000 Vdc )/( Ae ΔB f) Turns
 Core area Ae in cm2
 ΔB = 2 Bmax ( Use 2 ×1600 Gauss)
 Switching frequency in kHz
 DC input voltage Vdc in volts
Assume that duty cycle is 0.4
30
Primary & Secondary Windings
Push-Pull Topology
Vo ≅ 0.8 Vdc (Ns/Np)
Ns can be easily found 1/2 × 500×(1/0.8)×(1/0.4)×√0.4
 Wire size of primary winding is (494 Po)/Vdc
in circular mils
500×√0.4
 Wire size of secondary winding is 316 Io in
circular mils
Assume that duty cycle is 0.4 and efficiency is 0.8
31
Maxi. Transformer Core Output Power
Half- or Full-Bridge Topologies
Po = (1.4 Bmax f Ae Ab)/Dcma Watts
 Peak flux density Bmax in Gauss 1mT = 10G
 Switching frequency f in kHz
 Core area Ae in cm2
 Bobbin winding area Ab in cm2
 Dcma in circular mils per rms ampere (Inverse
of current density)
32
Maxi. Transformer Core Output Power
Half- or Full-Bridge Topologies
 I thought a Full-Bridge delivers twice the
output power of a Half-Bridge!! (NOT TRUE
in transformer)
 If the same core size is used both for HalfBridge and Full-Bridge, no. of primary turns
must be doubled in Full-Bridge which leads to
a reduction in wire size, current, by half. (Equal
power)
33
Primary & Secondary Windings
Half-Bridge Topology
Np = (20000 Vdc )/( Ae ΔB f) Turns
 Core area Ae in cm2
 ΔB = 2 Bmax ( Use 2 ×1600 Gauss)
 Switching frequency in kHz
 DC input voltage Vdc in volts
Assume that duty cycle is 0.4
34
Primary & Secondary Windings
Half-Bridge Topology
Two current pulses per period
Vo ≅ 0.4 Vdc (Ns/Np)
Ns can be easily found 2 × 500×(1/0.8)×(1/0.8)×√0.8
 Wire size of primary winding is (1397 Po)/Vdc
in circular mils
500×√0.4
 Wire size of secondary winding is 316 Io in
circular mils
Assume that duty cycle is 0.4 and efficiency is 0.8
35
Primary & Secondary Windings
Full-Bridge Topology
Np = (40000 Vdc )/( Ae ΔB f) Turns
 Core area Ae in cm2
 ΔB = 2 Bmax ( Use 2 ×1600 Gauss)
 Switching frequency in kHz
 DC input voltage Vdc in volts
Assume that duty cycle is 0.4
36
Primary & Secondary Windings
Full-Bridge Topology
Two current pulses per period
Vo ≅ 0.8 Vdc (Ns/Np)
500×(1/0.8)×(1/0.8)×√0.8
Ns can be easily found
 Wire size of primary winding is (699 Po)/Vdc
in circular mils
500×√0.4
 Wire size of secondary winding is 316 Io in
circular mils
Assume that duty cycle is 0.4 and efficiency is 0.8
37
Table of Maxi. Output Power
Page A2-5
38
Transformers (Forward-Type Converters)
 In Forward-type
converters, when the
power switch is ON,
primary current flows into
a dot and secondary
current flows out of a dot
 Primary and secondary
mmfs in transformer are
balanced.
39
Transformers (Forward-Type Converters)
 Mmfs are balanced
except magnetization
inductance in the primary
winding of a Forward
converter and that’s why
we need a reset winding
 No core saturation if the
peak flux density is
chosen properly
40
Flyback Transformer (Magnetics)
 However in
Flyback, no mmf
balance during
ON time therefore
cores can reach
saturation easily
if they are
ungapped
41
Flyback Transformer (Magnetics)
 Recall Buck-Boost topology, the unisolated
version of Flyback. There is a coil for storing
energy
 Flyback transformer is actually a set of
magnetic coupled coils
 Energy is stored in primary winding during the
ON time, believe or not, most of the energy is
stored in the air gap!
42
Flyback Transformer (Magnetics)
Turn ratio (Np/Ns)
 voltage stress on power switch
Vstress = 1.3 Vdcmax + (Np/Ns)(Vo + 1)
Voltage spike due to leakage inductance
Choose Vstress with 30% margin
Vstress = 0.7 Vbreakdown
43
Flyback Transformer (Magnetics)
Find TONmax from
Vdc/L
(Np/Ns)(Vo+ 1)/L
0.2T
For DCM, dead time of 0.2T
TON TOFF
 TONmax= (Np/Ns)(Vo+ 1)(0.8 T)/(Vdc+(Np/Ns)(Vo+ 1))
For CCM,
 TONmax= (Np/Ns)(Vo+ 1)T/ Vdc
44
Flyback Transformer (Magnetics)
Peak current
DCM
 Ip = Vdc TONmax/ Lp
CCM
 Ip = 1.25 Pomax /(Vdc (TONmax/ T)) is half of that
of DCM
Assume that efficiency is 0.8
45
Flyback Transformer (Magnetics)
Primary inductance
2)/T
P
=
(0.8
×
0.5L
I
omax
p p
DCM
 Lp = (Vdc TONmax)2/(2.5 T Pomax)
CCM
 Lp = (Vdc TONmax)2/(2.5 T Pomin)
Inductance at mode boundary
Assume that efficiency is 0.8
46
Primary & Secondary Windings
Flyback Topology
DCM
 Wire size of primary winding is
289 Ip √ TONmax/ T in circular mils
 Wire size of secondary winding is
289 (Np/Ns)( Ip √ (T-TONmax)/ T ) in circular mils
500/√3
47
Primary & Secondary Windings
Flyback Topology
CCM
 Wire size of primary winding is
500 Ip √ TONmax/ T in circular mils
 Wire size of secondary winding is
500 (Np/Ns)( Ip √ (T-TONmax)/ T ) in circular mils
48
Primary & Secondary Windings
Flyback Topology
Np = 1000 √Lp/ Alg Turns
 Alg, the inductance per 1000 turns with air gap
Avoiding saturation,
 Np Ip must be less than N Isat given by the
manufacturer at the chosen air gap
Bigger airgap; smaller Alg; higher N Isat
49
Primary & Secondary Windings
What if Alg is not given?
 Well, Al , the inductance per 1000 turns of
ungapped core is always given
Alg can be estimated as Al(l/µ)/(lair + l/µ)
 l is the magnetic path length
 lair is the air gap length
 µ is the effective core permeability
50
Primary & Secondary Windings
What if N Isat is not given?
 First find the Bsat in Gauss for the chosen
material
NIsat can be estimated as (Bsat (lair + l/µ))/(0.4 π)
 l is the magnetic path length in cm
 lair is the air gap length in cm
 µ is the effective core permeability
51
Primary & Secondary Windings
Alg = Al(l/µ)/(lair + l/µ)
NIsat = (Bsat (lair + l/µ))/(0.4 π)
52
Powdered Molypermalloy (MPP) Cores
 Powder is Square
Permalloy 80, an alloy
of nickel, iron, and
molybdenum
 Powdered particles are
mixed with plastic
resin and cast in the
shape of toroids
53
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Powdered Molypermalloy (MPP) Cores
 Each particle is encapsulated in a resin
envelope that provides the core with
distributed air gap
 Behaves like gapped core with less EMI
 For building inductors in power supplies,
cores of permeability greater than 125 is
rarely chosen because of the saturation
caused by DC bias current
54
Powdered Molypermalloy (MPP) Cores
10% drop in
inductance
55
Powdered Molypermalloy (MPP) Cores
 At 10% drop in inductance, the values of H
in Oersteds for materials having µ of 14, 26,
60, 125 are 170, 85, 36, and 19
Maximum ampere-turn can be calculated as
NI = H lm/(0.4 π)
 lm is the length of magnetic path in cm
Nmax and Lmax are tabulated in given tables
56
Powdered Molypermalloy (MPP) Cores
NI = H lm/(0.4 π)
Page A6-8
Nmax
57
Lmax
Transformer Copper Losses
At low frequency
 Copper loss = (Irms)2 Rdc
 Rdc is length of wire times resistive per unit
length
At high frequency, there are losses due to
 Skin effect
 Proximity effect
58
Transformer Copper Losses
 Both skin and proximity effects arise from
eddy currents which are induced by varying,
high-frequency, magnetic field.
 Skin effect -- the magnetic field is generated
from the current carried by the wire itself
 Proximity effect -- the magnetic field is
generated from the current in adjacent wires
59
Skin Effect
 Skin effect causes current in a wire flow only
on the surface of the wire
 Reduction in the effective cross-sectional area
 Increase the resistance at high frequency
At high frequency
 Copper loss = (Irms)2 Rac
 Rac can be found from the ratio of Rac/ Rdc
60
Skin Depth
 The thickness at which the current density is
decreased to 36% of the value at surface
 Skin depth d = √1/(πfµσ) in m
1A/mm2
 f is frequency in Hz
 µ is permeability in H/m
0.36A/mm2
 σ is the conductivity in S/m
 For copper, d = 2.1mm at 1kHz and 0.067 mm
at 1MHz
61
Skin Depth
 Iron has a conductivity that is only about 6
times less than that of copper, not too bad
indeed!
 Why not use cheap iron for transmission of
power?
 Because iron has high µ value, the skin depth
is very small even at low frequency, 0.7 mm at
50Hz
62
Table of Rac/ Rdc (Sine-Wave Currents)
63
Table of Rac/ Rdc (Square-Wave Currents)
64
Skin Effect
 Skin effect is more profound when wire
diameter is large but thick wire still yields less
loss! Getting worse when frequency is high
 Use a number of small-diameter wires instead
of a single large-diameter wire because the
total area in annular skin of the small-diameter
wires is bigger
 Litz wire; take good care in soldering
65
Skin Effect
 Skin effect is more profound for square-wave
currents because they have a lot of highfrequency harmonics
66
Proximity Effect
 Proximity effect is caused by high-frequency
magnetic fields arising from currents in
adjacent wires or winding layers
Effective area for current flow
67
Proximity Effect
 Proximity effect is more profound when the
no. of winding layers is large
A 3-layer
secondary
winding in a
EE core
0A
–1A –2A
1A
2A
3A
68
Proximity Effect
 Primary/secondary without interweaving
Sec-- Layer 2
Sec-- Layer 1
Higher Rac/ Rdc
Pri-- Layer 2
Pri-- Layer 1
mmf
Core centre leg
69
Proximity Effect
 Primary/secondary with interweaving
Sec-- Layer 2
Pri-- Layer 2
Lower Rac/ Rdc
Sec-- Layer 1
Pri-- Layer 1
mmf
Core centre leg
70