台灣新竹‧交通大學808實驗室 (電力電子系統與晶片設計實驗室)
Flyback Converters
2008年2月15日
鄒 應嶼 教 授
國立交通學大學 電力電子系統與晶片設計實驗室
Flyback Converters
Power Electronics Systems & Chips Lab., NCTU, Taiwan
Flyback Converters
電力電子系統與晶片設計實驗室
Power Electronics Systems & Chips Lab.
交通大學 • 電機與控制工程研究所
1/57
Flyback Converters
„ Derivation of the Flyback Converter
„ Features of Flyback Converter
„ Why Choose the Flyback Converter?
„ Properties of Flyback Converters
„ Disadvantages of the Flyback Converters
„ Operating Principle of the Flyback Converter
„ Typical Waveforms of the Flyback Converter
„ Design Equations
„ Flyback Converter Transformer-Choke
„ Cross Regulation in Multiple Outputs Flyback Converters
2/57
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1
Flyback Converters
Invention of the Flyback Converter
How to design an isolated buck-boost converter
with minimum number of components?
?
vo
vg
3/57
Derivation of the Flyback Converter
–
–
Vi
Vo
L
+
Vi
L1
Vo
L2
+
+
(a)
(c)
+
–
Vi
L1
Vo
L2
Vi
L1
Vo
L2
_
+
+
(b)
(d)
4/57
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2
Flyback Converters
Features of Flyback Converter
Input Stage
DC-DC Converter
+
Vout
AC Line
Input
–
+
–
VSENS E
PWM
Isolati on
The isolated flyback converter is basically a buck-boost derived converter with
an isolation winding, so that the input circuit is isolated from the output circuit,
and the output voltage can be either positive or negative, depending on the
winding and diode connected polarities.
Application: Lowest cost, multiple output supplies in the 5-150W range. E.g.
mains input T.V. supplies, small computer supplies.
5/57
Why Choose the Flyback Converter?
„ 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 power levels higher than 100 Watts, topologies with lower voltage
and current stress levels (such as the forward converter) may be
more cost effective even with higher component counts.
6/57
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3
Flyback Converters
Properties of Flyback Converters
„ In design of a flyback power supplies, transformer design is usually
the biggest stumbling block.
„ Flyback transformers are not designed or used like normal
transformers.
„ Energy must be stored in the core, the core must be gapped, and the
transferred energy is stored in the air gap. The air gap inductance
represents most of the magnetization inductance. However, this
magnetization inductance is relative small.
n:1
+
Vin
D
Io
Co
R
Vo
−
Q
−
+
7/57
The “Flyback Transformer”
Transformer Model
n:1
+
Vin
−
Q
n:1
D
Io
Co
R
+
Vo
+
LM
Vin
D
Co
Io
R
Vo
−
−
−
+
Q
Ideal Transformer
LM
The air gap inductance represents most of the magnetization inductance.
8/57
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4
Flyback Converters
The “Flyback Transformer”
„ A two-winding inductor
Transformer Model
n:1
+
LM
Vin
D
Io
Co
R
„ Symbol is same as transformer,
but function differs significantly
from ideal transformer
+
Vo
„ Energy is stored in magnetizing
inductance
−
−
Q
„ Magnetizing inductance is
relatively small
„ Current does not simultaneously flow in primary and secondary windings
„ Instantaneous winding voltages follow turns ratio
„ Instantaneous (and rms) winding currents do not follow turns ratio
„ Model as (small) magnetizing inductance in parallel with ideal transformer
9/57
Current Flow in Flyback Converter
Q ON and D OFF
+
+
Vin
vgs
Io
n:1
LM
Co
R
Vo
2V in
Vin
Io
n:1
+
D
+
LM
on
Ip
Q OFF and D ON
−
VDS
off
−
−
Vin
on
Co
R
Vo
−
Is
Io
I out
δT
T
„ Current effectively flows in either the primary or secondary winding
but never in both windings at the same time.
10/57
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5
Flyback Converters
Current Flow in Flyback Converter
vgs
on
VDS
off
on
2V in
Vin
Q OFF and D OFF
Ip
Io
n:1
+
D
+
LM
Vin
Co
Vo
R
−
Is
Io
−
I out
DT
T
11/57
Flyback Converter in Discontinuous Conduction Mode
D
n:1
+
+
Co
Vin
− vgs
Vo
Is
Ip
R
Io
vgs
on
VDS
off
on
2V in
Vin
−
Q
Ip
The Primary Current rising slope:
VDC − VCE ( sat )
dI
=
dt
Lp
Peak Primary Current:
Ip =
Is
Io
(VDC − VCE ( sat ) ) DT
Lp
I out
DT
T
12/57
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Flyback Converters
Flyback Converter in DCM
T1
V at
D1
C1
Nsl
Lp
Np
V dc
V om
D2
Q1
C0
Nsm
(a)
R1
R0
R2
DC voltage-controlled
v ariable width
pulse generator
EA
V ref
Ip
Is = I p
(b)
Np
Ns
Is
Ton
A1 = A2
(c)
Tr
Tdt
Vdc + (N m /N p )Vdc
A2
A1
Vdc
(d)
13/57
When the Primary Switch Is ON
Io
Ip
+
+
Lg
Vin
Co
R
Vo
−
Q
−
Lp
Primary Magnetizing Inductance
L1
Lg
L2
Ip
Ton
‹ The secondary diode is reverse biased
‹ The load power is supplied by the output capacitor
‹ The primary current store energy into the primary
magnetizing inductance!
Lp
Lp = L1//Lg //L2
≈ Lg
Q Lg >> L1//L2
14/57
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Flyback Converters
Energy Stored in The Magnetization Inductance
Io
Ip
+
+
Lg
Vin
Co
Vo
R
−
Q
−
Lp
Primary Magnetizing Inductance
The Gap Effect
Ip
Ton
E=
The Maximum Stored Energy is:
Lp (Ip ) 2
2
Most energy is stored in the air gap!
15/57
Release The Stored Energy to the Output Rectifier
When the Primary Switch Is OFF
Is
Ip
Io
D
+
+
Lg
Vin
Co
R
Vo
−
Q
−
Lp
Primary Magnetizing Inductance
Ip
Ton
Ip(max)
E=
Ls (Is ) 2
2
I s = Ip
The released energy is equal
to the stored energy when
operating in steady state.
Np
Ns
Toff
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16/57
8
Flyback Converters
Flyback Converter: Typical Waveforms
D
S
io
S
n:1
u ce
i1
i2
C RL
u ce
uO
u1
u1
s
+
ube
+
i1
-
u0=
i1
u ce
-
δ 1 u1
δ2 n
I2
i2
n
n
Ni
Ni
1
2
Ts
Ts
Ts
Ts
Ts
DCM
CCM
17/57
Typical Characteristics
n:1
IL
+
Suitable for Off-line SPS under 75 Watts
Vin
Co
R
+
Vo
−
−
Typical converter efficiency: η = 80%
Max. duty ratio: Dmax = 45%
Max. transistor voltage: Vds = 2Vin(max) + leakage spike
DC voltage gain (CCM):
D
Vo
= n⋅
Vin
1-D
DC voltage gain (DCM):
Vo
RL T
= nD ⋅
⋅
Vin
2 LP
Note: DCM buck-boost characteristic is linear.
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18/57
9
Flyback Converters
19/57
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10
Flyback Converters
Buck-Boost Converter: CCM and DCM Static Characteristics
CCM
M(D, K)
CCM
M(D, K)
t
os
Bo
Bu
1.0
o
-b
ck
os
t
1
K
1.0
Bu ck
0
0.2
0.4
0.6
0.8
0
1.0
0.2
0.4
D
0.6
0.8
1.0
D
DCM
CCM
21/57
Output Power and Voltage as a Function of PWM Duty
Io
Ip
+
+
Lg
Vin
Co
R
Vo
−
Q
−
The Maximum Stored Energy is:
Pavg =
T on
(Vin − Vsat )TON
Lp
Lp (Ip ) 2
2
The Average Power Pass Through The ChokeTransformer
Ip
Q Ip =
E=
Pavg =
Lp (Ip )2
2T
[Watts]
[(Vin - Vsat )TON )] 2
(V T ) 2
≈= in ON [Watts]
2TL p
2TL p
22/57
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11
Flyback Converters
Voltage Conversion Ratio in DCM Operation
Io
Ip
+
+
Lg
Vin
Co
R
Vo
−
Q
−
Pi
Po Output Power
Input Power
Average Input Power = Pi =
1
T
=
∫
t0 +T
t0
∫
vin (t)ip (t)dt
t +T
t
o
23/57
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12
Flyback Converters
Turn Ratio Î Maximum Switch Voltage
Transformer Model
n:1
+
LM
Vin
D
Io
Co
R
+
Vo
−
Q
−
Maximum OFF-Voltage Stress?
VQ(max) = Vdc(max) +
Np
Ns
(Vo + Vdiode(on) ) + Vspike(leak age)
Worst Case Condition:
Max. transistor voltage: Vds = 2Vin(max) + leakage spike
25/57
Ensure Core Does Not Saturate Î Remains in DCM Mode
Is
Ip
Ip
Ton
Lg
Co
R
Vo
−
TR
A= B
+
+
Vin
Reset Time
Toff
Io
D
Ip(max)
Q
−
To guarantee the core does not saturate, the
stored energy must be completely released!
Tdt
A
B
Dead Time
(Vin(min) − VQ(on) )Ton(max) = (Vo + Vdiode(on) )
Np
Ns
TR
A 20%T dead time margin will
limit the maximum output voltage
with a specified turn ratio!
26/57
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13
Flyback Converters
Why Flyback Converters Are Usually Designed in DCM Mode?
„ To Ensure Core Does Not Saturate
1
Ip TON
1
Pi = Vin 2
= VinIpD
T
2
Saturated!
Not Saturated!
‹ To get larger input power , we need higher input
current!
‹ To ensure the inductor does not saturate, we need
to reduce the inductance!
Ip
‹ This also implies a lower volt-second product. For a
same DC input, it means a lower duty ratio!
27/57
Why Flyback Converters Are Usually Designed in DCM Mode?
„ To Avoid Sub-Harmonic Oscillations Due to Duty Divergence
‹ For peak current mode control, when the current
falling slope is greater than the rising slope, i.e.
|m2|>|m1|, this occurs when the converter reach
into the CCM region, the current will diverge under
a constant current reference. To avoid this
phenomena, we can restrict the converter operating
in DCM mode.
‹ If the converter needs to be operated in CCM mode,
then a negative slope compensation is needed to
stabilize this sub-harmonic oscillations.
I. Zafrany and S. Ben-Yaakov, “A chaos model of subharmonic oscillations in current
mode PWM boost converters,” IEEE PESC Conf. Rec., pp. 1111-1117, 1995.
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28/57
14
Flyback Converters
Determination of Turn Ratio
How to determine turn ratio?
Transformer Model
Np : Ns
+
LM
Vin
D
Io
+
Co
R
Vo
−
Q
−
Ton(max) + TR + Tdt = T
If a 20% dead time is specified as the safe margin, then Ton(max) + TR = 0.8T
(Vin(min) − VQ(on) )Ton(max) = (Vo + Vdiode(on) )
Ton(max) =
Np
Ns
TR
(Vo + Vdiode(on) )(Np /Ns )0.8T
(Vin(min) − VQ(on) ) + (Vo + Vdiode(on) )(Np/Ns )
29/57
Determination of Turn Ratio ..
Define
Ton(max) =
Define
n=
Np
V2 = Vo + Vdiode(on)
V1 = Vin(min) − VQ(on)
Ns
(Vo + Vdiode(on) )(Np /Ns )0.8T
(Vin(min) − VQ(on) ) + (Vo + Vdiode(on) )(Np/Ns )
λ=
Ton(max) + TR
T
n=
Ton(max) =
V2n0.8T
V1 + V2n
Vin(min) − VQ(on) Dmax
Vo + Vdiode(on) λ - Dmax
For the DCM flyback transformer design
The proper turn ratio must be determine to ensure the DCM operation under
a minimum input voltage, maximum specified duty, and a safety dead time
ratio.
30/57
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15
Flyback Converters
Determination of Primary Inductance
Transformer Model
Np : Ns
+
LM
Vin
D
Io
+
Co
R
Vo
Ip
Ip(max)
Reset Time
Ton
TR
−
Q
−
Lp
Tdt
T
Primary Magnetizing Inductance
To ensure the flyback converter operating in DCM mode:
1
(L I2 )
1
1 Vo2 2 p p
=
Pi = Po =
η
η Ro
T
Lp =
ηRo ⎛ Vin(min)Ton(max) ⎞
⎜
2T ⎜⎝
2
⎟⎟
⎠
Vo
31/57
Design Equations: Maximum Switch Current (DCM)
n:1
+
Vin
Co
IL
+
R
Vo
Max. transistor
current:
Ip(max) =
−
Vdc(min) Ton(max)
Lp
−
Emax
Ip(max)
T on(max)
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32/57
16
Flyback Converters
Primary RMS Current and Wire Size
Ip(max) =
Vdc(min) Ton(max)
Lp
T on(max)
T
Ip(rms) =
Ip(max)
3
Ton(max)
T
At 500 circular mils per rms ampere, the required number of circular mils is:
Circular mils required (primarty) = 500I p(rms)
=
Ip(max)
3
Ton(max)
T
33/57
Definition of Circular mils
AWG
Diam.
(mils)
Circular
mils
Ohms/100
0ft
Current
Carrying
Feet per
Pound
12
80.8
6529
1.619
9.33
50.59
13
72.0
5184
2.042
7.40
63.80
14
64.1
4109
2.575
5.87
80.44
15
57.1
3260
3.247
4.65
101.4
16
50.8
2581
4.094
3.69
127.9
17
45.3
2052
5.163
2.93
161.3
18
40.3
1624
6.510
2.32
203.4
19
35.9
1289
8.210
1.84
256.5
20
32.0
1024
10.35
1.46
323.4
21
28.5
812
13.05
1.16
407.8
22
25.3
640
16.46
.918
514.12
23
22.6
511
20.76
.728
648.4
24
20.1
404
26.17
.577
817.7
mils = thousandths-of-an-inch
1 circular mil = define the Area of a circular wire with a diameter of 1 mil
1 square mil = define the Area of a square wire with width of a mil
Curre nt Notes:
The current shown per wire size listed above is based on 1 amp/700 Circular mils, other tables provide
different current per wire size, and different current for open air ~ check your local electrical code for the
correct current capacity [Ampacity]. The 1 amp/ 700 Circular mils seems to be the most conservative,
other sites provide/allow for 1 amp per 200 or 300 Circular mil. For shot wire lengths use 1A/200 Circular
mil, for longer wire runs use 300 Circular mil, and for very long wire runs use the table above, 1 amp / 700
Circular mil.
34/57
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17
Flyback Converters
RMS Values of Typical Waveforms
F ( sqr ) AVG = A
F (sin) AVG =
F (tri ) AVG =
2
π
F ( sqr )RMS = A
A
A
A
2
F (sin)RMS =
A
= 0.707 A
2
F (tri ) RMS =
A
= 0. 577 A
3
Crest Factor
Form Factor
Square wave
1
1
SIN wave
1.414
1.11
Triangular wave
1.732
1.15
A period sinusoidal waveform with amplitude of A, its half period
average value is 2A/π (0.636A) and RMS value is A / 2 .
35/57
RMS Values of Typical Waveforms ..
i(t)
I RMS = I
i(t)
I
ΔI
0
I RMS =
ΔI
3
t
t
i(t)
i(t)
I pk
I pk
I RMS = I pk
− I pk
0
2
I
ΔI
D1 + D2
3
0
t
Ts
i(t)
I RMS = I pk
1 ⎛ ΔI ⎞
I RMS = I 1 + ⎜ ⎟
3⎝ I ⎠
D1 Ts
D2 Ts
Ts t
i(t)
I pk
I RMS = I pk
D
3
0
Ts t
0
DTs
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Ts t
36/57
18
Flyback Converters
Primary RMS Current and Wire Size
Ip(max) =
Ip
Vdc(min) Ton(max)
Lp
Reset Time
Ton
Is(max) = Ip(max)
Np
Ns
Tdt
TR
T
Is(rms) =
Ip(max) (Np/N s )
3
Tr
T
At 500 circular mils per rms ampere, the required number of circular mils is:
Circular mils required (secondary ) = 500I s(rms)
37/57
Flyback Transformer
Is
Ip
Io
D
+
+
Lg
Vin
Co
R
Vo
−
−
Q
„ The ideal flyback transformer operating as an ideal transformer parallel with a
magnetization inductance. This magnetization inductance is the value required for
a buck-boost converter. Therefore, the flyback transformer performs the function
of an inductor as well as a transformer.
„ To let the flyback transformer carry large primary current without saturating, the
core is selected as
‹ Gapped Ferrite Core
‹ MPP (Molybdenum Permalloy Powder) Core
„ In practical realization of the flyback transformer, it is difficult to keep the leakage
inductance small, especially when the rated power is increased.
38/57
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19
Flyback Converters
Energy Stored in an Inductor
N: number of turns
Mean path length l
Cross-sectional
area A
The energy stored in the core:
t
E L = ∫ Pdt =
0
t
1
∫ Li ' di ' = 2 LI
2
0
The energy density (energy/volume) is:
I
1 1 ⎛ μ N 2 A ⎞⎛ B 2 l 2 ⎞
LI 2
⎜
⎟⎜
⎟
=
Al
Al 2 ⎜⎝ l ⎟⎠⎜⎝ μ 2 N 2 ⎟⎠
B2
=
2μ
ηB =
Permeability μ
L = N 2μ
A
l
1
2
The energy stored in the core:
EL =
1 2
LI = ηBVcore
2
Vcore =
μc LI 2 μ0μr LI 2
=
B2
B2
Vcore: volume of the core
39/57
Flyback Converter Transformer-Choke
Since the transformer-choke of the flyback converter is driven in one
direction of the B-H characteristic curve, it has to be designed so that
it will not saturate.
The effective transformer-choke volume is:
Volume =
2
μ 0 μrLsIo(max)
2
Bmax
μ0 = permeability of vacuum space
μr = relative permeability of the chosen core material
Io(max) = maximum load current
L
= output (secondary) inductance
Bmax = maximum flux density of the core
40/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
20
Flyback Converters
Effect of the Leakage Inductance
Leakage Inductance
+
Vin
−
D
Co
Llk −
LM
vlk
Vo
Co
Np : Ns
+
D1
Vinn
Vi
Transformer Model
Io
R
n:1
+
Vo
TR1
−
Q
Primary
current
I p = Vin.ton / Lp
(discontinuous)
Ip
ISW
t
0
ISec =Idiode
The induced leakage spike voltage is:
Sec
current
IS
ID
0
vlk(max) = Llk
Ip(max)
leakage
inductance
spike
V
Switchingorce
voltage
V ds
TQ(off)
0
V in +V o
ton
n1
n2
t
V in
t
toff
T
discontinuous
TQ(off) is the primary switch turn-off time.
41/57
Clamp Circuits for Flyback Transformer
C
R
Dz
D
D
Drain
Drain
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交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
21
Flyback Converters
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交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
22
Flyback Converters
Transient Oscillation Due to Mode Transition
D
Ip2
Ip1
Ip discontinuous
B
A
C E
H
(a)
F
K
Ip2
Ip1
Ip discontinuous
GJ
I
(b)
L
Tdt
O R
N
Ip continuous
M
(c)
P S
U Y
Is continuous
Z
V
T X
(d)
W
45/57
46/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
23
Flyback Converters
Design Considerations for Flyback Converters
„ Poor Dynamics: In flyback converters, the gapped transformer
inductance results a zero in the right-half-plane (RHP), which makes
the closed-loop compensation in CCM (continuous conduction mode)
very difficult. Typically, the closed-loop bandwidth in CCM is very
narrow and the transient response is slow.
„ Larger Output Capacitor: In flyback converters, a large output
capacitor is required due to the lack of a second-order low-pass
inductor/capacitor filter at the output.
„ Difficulties in Flyback Transformer Design: Processing power
is limited by the flyback transformer. It is hard to reduce the leakage
inductance for when the processing power is increased.
„ High Blocking Voltage: Main power transistor blocking voltage
must sustain 2Vin plus leakage voltage spike.
47/57
Multiple Outputs of Isolated Flyback Converter
+
Vout,1
Vout,2
Vin
An advantage of the flyback converter
is it is easy to provide multiple outputs.
This is because the isolation element
acts as a common choke to all outputs,
thus only a diode and a capacitor are
needed for an extra output voltage.
Q
−
48/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
24
Flyback Converters
Cross Regulation in Multiple Outputs Flyback Converters
„ The cross regulation of a multi-output flyback converter can be
significantly improved by lowering the clamp voltage, especially to
slightly above the reflected output voltage. However, it causes more
loss in a traditional RC clamp. Some solutions for improving the
cross regulation with low loss are provided and discussed in future
publications.
„ Larger leakage inductance in the secondary windings leads to better
cross regulation of that output when it is lightly loaded.
„ Larger leakage inductance in primary side will be beneficial to
improve the cross regulation of multiple output flyback converters.
However, it results more loss in a traditional RC clamp.
„ Reducing core gap to achieve larger magnetizing inductance in
flyback converter design will improve cross regulation.
49/57
Interleaved Flyback
Converter
50/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
25
Flyback Converters
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交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
26
Flyback Converters
Control of a Flyback Converter
V in
Is
Lp
Ls
V ac
n:1
V cc
L6590
L6590D
L6590A
S
Clock
1
+
OCP
–
PWM
E/A
Isolated
Feedback
Q
2.5V
–
Ip
Driv er
R
+
Drain
Max. Duty cycle
OSCILLATOR
VFB
V out
LEB
Clock
1/100
Rsense
0.5V
GND
COMP
Frequency
Compensation
53/57
1.3 W, 24 Vin, 3.3 Vout Flyback DC-DC Converter
24V
D2
Si9121DY
GND
C1
33μ F
16T
LX
V CC
C2
0.1μ F
7T
10MQ100N
D1
D3
C6 BAS21
23T
1μ F
10MQ100N
7T
C9
3V3 400 mA
220μF
C7
1μ F
Feedback
BYPASS
C3
0.1μ F
V NEG
V OUT
CS
COMP
C5
0.1μ F
R1
0.25Ω
GEN
C4
180pF
R2
27kΩ
54/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
27
Flyback Converters
A 5W Flyback Converter with 170 Vin and Multiple Outputs
55/57
50 Watt, 48Vin, 5Vout, Isolated Flyback Converter
Using a Primary Side PWM Control UCC3809 and the UC3965 Precision Reference and Error Amplifier
56/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
28
Flyback Converters
100V IN to 300VIN, 5VOUT at 1A Isolated Flyback Power Supply
Isolated Flyback Converter Regulates Without an Optocoupler
57/57
交換式電源供應器基礎：教育訓練課程講義, Sept. 2006.
交通大學 808-PowerLab 電力電子系統與晶片設計實驗室
29
台灣新竹‧交通大學808實驗室 (電力電子系統與晶片設計實驗室)
台灣新竹交通大學808實驗室 (電力電子系統與晶片設計實驗室)
Flyback Converters
n:1
IL
+
Vin
Co
R
+
Vo
−
−
台灣新竹交通大學808實驗室 (電力電子系統與晶片設計實驗室)
Flyback Converter: Selected Reading
[1] G. Chryssis, High-Frequency Switching Power Supplies: Theory and
Design, Chap. 3: Types of Power Converters, McGraw-Hill Book Company, 1984.
[2] Christophe Basso, Average simulations of FLYBACK converters with SPICE3,
Technical Report, May 1996.
[3] Sanjaya Maniktala, Chap. 6: Isolated topologies for off-line applications of
Switching Power Supply Design & Optimization, 2004.
[4] Bob Bell, On Semiconductor, "Two-switch topology benefits forward and flyback
power converters," EDN pp. 107-111, September 1, 2000.
[5] Design Guidelines for Off-line Flyback Converters Using Fairchild Power Switch
(FPS), Application Note AN4137, Fairchild.
[6] Ravindra Ambatipudi, Design of Isolated Converters Using Simple Switchers
Using the LM2587, National Semiconductor.
[7] MathCAD Design Example: Switching Power Supply Design: Discontinuous
Flyback Converter, Michele Sclocchi, Application Engineer, National
Semiconductor.
[8] MathCAD Design Example: Switching Power Supply Design: Continuous
Flyback Converter, Michele Sclocchi, Application Engineer, National
Semiconductor.
[9] Lisa Dinwoodie, Design Review: Isolated 50 Watt Flyback Converter Using the
UCC3809 Primary Side Controller and the UC3965 Precision Reference and Error
Amplifier, TI Application Note U-165, 1999.
[10] Sanjaya Maniktala, Chap. 10: Flyback Transformer Design of Switching
Power Supply Design & Optimization, 2004.
[11] Technical Bulletin CG-03, For Flyback Transformers . . .Selecting a Distributed
Air-Gap Powder Core, Magnetics.
[12] S.-K. Chung, "Transient characteristics of high-voltage flyback transformer
operating in discontinuous conduction mode," IEE Proc.-Electr. Power Appl., vol.
151, no. 5, pp. 628-634, Sept. 2004.