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1 Challenge the future 1 Challenge the future

Electronic Power Conversion Switch Mode DC-DC Converters with Isolation

2 Isolated Power Supplies

Switch mode dc-dc converters

Drawbacks of linear power supplies •  50Hz transformer required •  transistor absorbs voltage è loss, heat

Frequent requirements: •  regulated output •  isolation (safety) • multiple outputs

Solutions: •  Linear power supplies •  Switch mode power supplies


Switch-mode power supplies

Major advantages: •  transistor operates as switch •  no 50Hz transformer needed è reduced weight and costs however: •  more complex •  measures to prevent (conducted) EMI needed •  resonant type dc power supplies are not considered here (Ch9)


Multiple outputs

•  one output is regulated by PWM •  if needed other output can be post-regulated by linear regulators


Transformer •  Ideal transformer

Faraday’s law

Ampere’s law

0l = Aµ

ℜ ≈

1,2i i

iN i φ

=

= ⋅ℜ∑ 1 1 2 2N i N i φ− = ⋅ℜ

1 1dv Ndtφ= ⋅ 2 2

dv Ndtφ= ⋅

v1N1

=v2N2

1 1 2 2i N i N=Core reluctance


Transformer •  Magnetising inductance

0l = Aµ

ℜ ≠

1 1 2 2N i N i φ− = ⋅ℜ

1 1dv Ndtφ= ⋅

1 21 1 2

1

( ) m mN Nd dv i i L i

dt N dt= ⋅ − = ⋅ℜ

21

mNL =ℜ2

1 21

mNi i iN

= −

Non-zero core reluctance


Transformer •  Leakage flux

111 1 1 1 1 1 1

ldd dv = R i N R i N

dt dt dtφφ φ⎛ ⎞+ = + +⎜ ⎟⎝ ⎠

222 2 2 2 2 2 2

ldd dv = R i N R i Ndt dt dt

φφ φ⎛ ⎞− − = − − −⎜ ⎟⎝ ⎠

1 1lφ φ φ= +

2 2lφ φ φ= − +

ϕl1,2 – leakage flux

R1,2 – ohmic resistances of the windings

8 Basic Electrical and Magnetic Circuit Concepts

11 1 1 1 1

22 2 2 2 2

l

l

div = R i L edtdiv = R i L edt

+ +

− − +

Equivalent Transformer Circuit

222 2 2 2 2 2 2

ldd dv = R i N R i Ndt dt dt

φφ φ⎛ ⎞− − = − − −⎜ ⎟⎝ ⎠

11 1 1 1

2 22 2 2 2

1

ml m

ml m

d di iv = R i L Ldt dt

Nd di iv = R i L Ldt N dt

+ +

− − +

/L = N iφ⋅

21 2

1m

Ni = i + iN

111 1 1 1 1 1 1

ldd dv = R i N R i N

dt dt dtφφ φ⎛ ⎞+ = + +⎜ ⎟⎝ ⎠


Transformer representation

•  Ll1 and Ll2 are often neglected because they are intentionally small and have a minor effect on the voltage transfer function (they are important for switch selection and snubber design) •  Lm is taken into account because it affects circuit operation

1 1 2 2/ /V N V N=

1 1 2 2N i N i=

and

slope

vdt∝ ∫

mi∝mL∝


• To understand operation of transformer-isolated converters: •  replace transformer by equivalent circuit model containing

magnetizing inductance •  analyze converter as usual, treating magnetizing inductance as

any other inductor •  apply volt-second balance to all converter inductors, including

magnetizing inductance


DC-DC converters with electrical isolation

Bidirectional core excitation •  full-bridge converter •  half-bridge converter •  push-pull converter

Unidirectional core excitation •  flyback converter •  forward converter


Flyback converter

Magnetic component: •  energy storage (coupled inductor) •  transformation •  isolation

Derived from buck-boost


I1

Here: N1 I1 + N2 I2 = 0

Flyback converter

,L avV = 0

10

2

( )d on s onNV t - V T - t = 0N

0 2

1d

V N D = V N 1 - D

Steady state:

so:


Approach in book: “ up-flux - down flux”

14

1

ˆ don

V(t) = (0) + tNφ φ 0

2

0

1 2

ˆ( ) ( )

( ) ( )

s s on

don s on

VT = - T - tN

V V = 0 + t - T - tN N

φ φ

φ

( ) (0) dm m

m

Vi t = i + tL

0 1 2( / )ˆ( ) ( )m m onm

V N Ni t = i - t - tL

ˆ (0) dT m on

m

VI = i + tL

gives same result. ‘Inductor’ current

Switch utilisation

è

Example: Vd=350; D=0.5 è VT,max=700V

DVV

NNVV d

odT −=+=1

ˆ2

1


• CCM •  Larger transformer •  Smaller peak currents

• DCM •  Smaller transformer •  Larger peak currents

• BCM (boundary condition mode) •  “Design of low power power supplies” course – Q3 (control,

EMI, magnetics design, loss calculation) • Flyback converter

•  Low part count (cheap) •  High transistor voltage stress


Other flyback converter topologies

1ˆ2 T d xV = V + V

Two-switch flyback converter •  T1 and T2 switch simultaneously •  switch voltage halved

Paralleling flyback converters •  phase shifted operation •  common output cap C filter •  double ripple current frequency at input cap and output cap è smaller passives


Forward converter

20

1L d

Nv = V - VN

0Lv = -V

(0 < t < ton)

( ton < t < Ts)

Demagnetisation winding function: remove energy stored in Lm

,L avv = 0 20 0

1

( )d on s onN V V t - V T - t = 0N

⎛ ⎞−⎜ ⎟

⎝ ⎠0 2

1d

V N = DV Nè è

,L avv = 00 ?d

VV

è

switch off, D2 on

switch on, D1 on


Mostly N1 = N3 so D<0.5

ˆ 2T dV = V

D

1

3T̂ d d

NV = V V N

+

11 3

3

NV = - VN

,Lm avv = 0 1

3on d m d

Nt V = t VN

switch off:

3

1

(1)m

s

t N = DT N

(1 ) (2)m st T D< −

3 1

1D 1 + N /N

<

with

From (1)&(2):

è

or:

Switch voltage:

or

1 1 3 3 2 2N i + N i = N i


Other forward converter topologies

Two-switch forward converter •  T1 and T2 switch simultaneously •  switch voltage halved •  no demagnetisation winding needed

Paralleling forward converters •  phase shifted operation •  single LC filter •  double ripple current frequency at input cap and LC filter è smaller passives


20

1L d

Nv = V - VN

0Lv = V−

,L avv = 0 0 2

1d

V N = 2 DV N

(0 < t < DTs)

(DTs < t < Ts/2)

è

0 ?d

VV

T̂ dV = V Switch voltage:

Full-bridge converter

Ts/2 Ts Ts/2+DTs DTs


Half-bridge converter

20

1 2d

LVNv = - V

N

0Lv = V−

,L avv = 0 0 2

1d

V N = DV N

(0 < t < ton)

( ton < t < Ts)

è

,L avv = 00 ?d

VV

Value of iT in full bridge is lower than in half bridge with same power rating:

( ) 2( )T HB T FBI = I


Push-pull converter

20

1L d

Nv = V - VN

0Lv = V

,L avv = 0 0 2

1d

V N = 2 DV N

(0 < t < ton)

( ton < t < Ts)

è

(0 < D < 0.5)

,L avv = 00 ?d

VV

ˆ 2T dV = V Switch voltage: •  risk of transformer saturation


DC-DC converters with electrical isolation

Bidirectional core excitation (ΔBp_p=2Bm)

•  push-pull converter •  half-bridge converter •  full-bridge converter

Unidirectional core excitation (ΔBp_p=Bm-Br) •  flyback converter •  forward converter


Transformer core selection

])B( [ f k =density loss Core bas maxΔ

max1

( )c s

VB = (at D = 0.5)4 N A f

Δ


PWM-control of dc-dc converters with isolation


3. A forward converter shown below is operating in a continuous conduction mode. The demagnetising winding is chosen to be N3=N1. All components can be assumed to be ideal, except for the presence of transformer magnetising inductance. The converter specifications are: • Vd=48V±10% • Vo=5V

• fs=100kHz • Pload=15-50W a) (10) Calculate the transformer turns ratio N2/N1 is this turns ratio is desired to be as small as possible.

b) (10) Calculate the minimum value of the filter inductance. c) (5) Calculate the voltage rating of the switch in terms of the input voltage Vd.


Design a flyback converter operating in the discontinuous conduction mode with the following specifications: • Input voltage 300V≤Vd≤400V (nominal value 400V) • Output power 0V≤Po≤50W (nominal value 50W) • Output voltage 20V≤Vo≤30W (nominal value 27V) • Switching frequency fs=50kHz • Peak –to-peak voltage ripple ΔV0p_p=20mV. a) (15) Select the transformer turn ratio N2/N1, the magnetising inductance Lm and the output capacitance C. You may assume that the maximum duty cycle value is 0.5. The voltage drop across the diode when it is in on-state is 1V. b) Sketch the waveforms and calculate RMS and DC values of the transistor and output diode current at the nominal operating point. c) Sketch the waveforms and calculate the maximum voltages across the transistor and output diode.


In the figure below two parallel forward converters are shown. Draw the input current id and iL waveforms if each converter is operating at a duty ratio of 0.3 in a continuous-conduction mode. Compare these two waveforms with those if a single forward converter (with twice the power rating but with the same value of the output filter inductance as in double forward) is used.


Image credits

• All uncredited diagrams are from the book “Power Electronics: Converters, Applications, and Design” by N. Mohan, T.M. Undeland and W.P. Robbins.

• All other uncredited images are from research done at the EWI faculty.

electronic power conversion - tu delft ocw · electronic power conversion switch mode dc-dc...

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