smps lecture 1

Switch Mode Power Supplies:From Circuit Theory to the Workbench

Michael Tse

Power Electronics Research Centre

Department of Electronic & Information Engineering

Hong Kong Polytechnic University

Michael Tse: Switch Mode Power Supplies 2

Prelude

How much can we trust the theory?

What can we do if the theory doesn’t match the outcome?

Can we live without heuristics?

Are complex models always better?

What makes the engineers lose faith in the theory?

Can theory really be used in practice?

How can we get the most of circuit theory forpractical design and analysis?


The theorists at fault!!

My EMI filter isn’t quite doing what it is supposed to do. Let

me change the order and a different filter configuration, andtry again.

I need to derive a more accurate model for my power

converter, preferrably up to 10 times the switchingfrequency.

Oh! I have found the answer from my algebra. A duty cycleof 1.2 for this theoretical power factor control!! How could I

achieve this?


The engineers at fault!!

The snubber gets pretty hot. Let me choose a smaller

resistance.

I would tend to think that the transformer has split

characters. The flyback transformer has never convinced methat it is related to the forward transformer.

Air gap stores more energy.

The output voltage of my constant-power-controlled circuit

isn’t high enough. Let me get a few more turns in thesecondary.


Objectives

To show how one can arrive at a practical circuit from

consideration of basic circuit theory.

To show how circuit theory can be used to explainphenomena observed in practical circuits.

To show how a switch mode power supply can be

systematically cons-tructed, starting from the simplestconverter topology.


Contents

Basic topologies and practical requirements

How theory solves problems:

First problem: practical transformer

Second problem: real device switching

Third problem: closed-loop control

Fourth problem: isolation

Fifth problem: input filter

Conclusion


Genesis of converters Aim: To convert controllable power

from a voltage source to a load,with NO LOSS.

Source Load

?

Lossless

Controllable

Simple

Kirchhoff’s laws restrict terminalconditions.

Source Load

?

Lossless

Controllable

Simple


An old solution

Lossy linear regulator

Source Load


Elements wanted

Lossless requirements

current sinking for input

current sourcing foroutput

Ideas

An inductor switchingbetween source and load

Relative sourcing andsinking durations wouldcontrol the energy flow

Bear in mind what

Kirchhoff’s laws say:

Inductors must not be leftopen.

-> An inductor switchingbetween source and load.

-> At least one current pathmust be available at alltimes.

-> At least two switches areneeded to divert theinductor current

-> THREE POSSIBILITIES


The buck converter

Switch S is turned on and off very quickly, at a rate much

greater than the output filter natural frequency

Control parameter is duty cycle

iLLS

D

ON

OFF

+

–

E

+

–

U

dS t

T

Duration when is on

Period

on= =


Steady-state operation

Suppose we fix the duty cycle and wait until a steady state is

reached.

Inductor current goes up during the ON time, and goes down duringthe OFF time.

Periodic operation forces

Increment during ON = Decrement during OFF

⇒−

=−

⇒ = ×

( ) ( )E U DT

L

U D T

L

U D E

1


Putting it to practice

We need transformer isolation

closed-loop control

drivers for MOSFETs

self start-up

snubbers as switching aids

protection

input EMI filter

Proper component selection

mechanical design: heat sink, layout, packaging, etc

Direct

Mandatory

Requirements

Indirect

Mandatory

Requirements

Regulatory

Requirements


Practical circuit requirement

Forward converter—

transformer isolatedbuck converter

?

Does it work?

?

driver

EMI filter needed

ControlIC andcircuits

?

isolation?

?

start-up

fromaux

output

? ?

EMI

protection (over I / V)


First problem: practical transformer

The previous forward converter worked only if the

transformer were ideal.

However, practical transformers have magnetisinginductance.

L m

Ideal transformer

1:n

v nv

in

i

2 =

=

1

2 1

1


What the theory says?

If we have to use a transformer for the forward

converter, the transformer should be idea.

That means INDEFINITELY LARGE magnetizinginductance.

⇓

Either an infinitely permeable core

OR an infinite number of turns

THAT’S IMPOSSIBLE!!


Probing further into the theory

First, consider the ON time.

Ideal transformer

1:n

Practical transformer

What happens when the FET is off?

Secondary of T/F hasno current.

↓ Primary has no current

either.

↓ Current in magnetising

inductance can gonowhere!!


Deriving solution: core reset

A path must exist during OFF time to bring the

magnetizing current back to zero

Circuit theory works and explains everything!

Ideal transformer

1:n

Practical transformer

+

–Vz

0A0A

+

– –

+


Waveforms (with core reset)Secondary current of ideal t/f

same asabove;scaled by factor n

0

0

Primary current of practical t/f

Primary current of ideal t/f

Magntizing current

slopecontrolledby outputinductance


Requirements for core reset

Negative voltage polarity applied to the winding

during OFF time.

This voltage must be large enough to bring themagnetising current back to zero.

If d = 0.5, then .

If d = 0.8, then .

Technique: clamping the voltage during OFF time.

V Vz in≥

V Vz in≥ 4


Some core reset possibilities

1:n

Vz

1:n

1:n

1:n

nt

Tertiary winding as voltage clamp

n controls clamped voltage for re-sett

Advantage:

Two-wheeler forward converter

Duty cycle restricted below 0.5

Advantage: simple transformer

Disadvantage:

Disadvantage: bulky transformer


Recapitulation

Although we cannot make an ideal transformer, we

solve the problem with a reset circuit.

We now care much less how large Lm is, since wehave a way to get around it.

QUESTION: Can the magnetizing inductance be usedto advantage?

YES, in a flyback converter!


Flyback converter

In this case, we don’t needan ideal transformer. That’sgood. We don’t have itanyway.

The magnetizing inductancebecomes crucial as part ofthe circuit element.

Requirement:

Linear inductor!

Air-gap to augment BHcurve (then more turns toobtain inductance)

1:n

0A0A

1:n

During ON-time, magnetizing inductance charges up.

+

–

reverse polarity, current can't go!

ideal t/f primary current = 0

During OFF-time, magnetizing current forces its way outthrough the ideal t/f primary.

+

–

di/dt negative,hence reversepolarity

+

–

+

–


Second problem: real switching

Consider turning theswitch in a buckconverter.

The result of this realdevice switching is

POWER LOSS(switching loss)

+

–

E

+

–

U

0

5

idsvds+ –

turn-off

ids

vds

diode won't conduct unless forward biased

ON OFF

diode turns on

ids can't go downunless diode turns on

i.e., vds reaches the input voltage


Deriving solution: snubber

Give the switch current achance to go down before thediode turns on.

⇓ Set up a PARALLEL CURRENT

PATH right after the turn-offinstant.

⇓ Place a capacitor across the

switch at turn-off to supplycurrent for the output inductor.

+

–

E

+

–

U

0

5

ids

turn-off

idsvds

ON OFF

ids goes down immediately


Completing the solution

What happens when the switch is turned on again in the next cycle?

The current will rush through the switch!!

⇓ We must protect the switch from such huge in-rush.

The complete snubber is:

Energy loss per cycle

=

+

–

E

+

during turn-on

during turn-off

Snubber

1

2

2C vssnubber


Other examples (same principle)

+

–

E


Third problem: closed-loop control

Why?

Because the system is dynamic.

What is a dynamical system?

A simplified definition: a system that does not assume an operating point instantlywhen an input parameter is changed.

0.2

0.4

4.8V

9.6Voutput voltage

duty cycle

Consider a buck converter with input 24V.

Suppose d is forced to step up from 0.2 to 0.4.

Suppose d stays constant, but the load

resistance steps up.

4.8Voutput voltage

load resistance


The need for control

Obviously we need to controlthe duty cycle if we want thesystem to have a dynamicbehaviour different from thenatural behaviour.

2 common approaches Voltage mode control

Current mode control

+

–

voltage-mode fb

current-mode fb


Voltage mode control

A general feedback circuit representation is:

Z f

Vref

–+

Vout

–+

Vm

vcon R1

R2

vR R

Z R Rv

R

R R

Z

Z R Rvcon

fref

f

fout

1 2

1 2

2

1 2 1 2

||

( || ) ( || )+

= −

+ +


Small-signal analysis

We can separate the AC from theDC component.

Let’s not worry about the steady-state operating point.

The small-signal AC equation is:

Taking into account the PWM, wehave

vR R

Z R Rv

R

R R

Z

Z R Rvcon

fref

f

fout

1 2

1 2

2

1 2 1 2

||

( || ) ( || )+

= −

+ +

∆ ∆vZ

Rvcon

fout= −

1

∆ ∆dV

Z

Rv

m

= −1

1

fout

If we know the duty-cycle-to-output small-signal transferfunction, then we can find theloop gain and hence be able todesign the required compensatorto give sufficient bandwidth andstability.

HERE, we need small-signalmodels from circuit theory.


Design criteria

Fast response — high gain and wide bandwidth of loop gain

Stability — phase shift must be well below 180deg at 0dBcrossover.

The converter is a second-order system which can becomeunstable under closed-loop condition, especially when the gain ishigh causing the phase shift of the loop gain to get close to180deg at 0dB crossover.

We must limit the bandwidth somehow if we allow a high DCgain.


Workbench construction

The concept of POLE — frequency location where the gain beginsto roll off.

E.g., if the circuit has a capacitor to ground forming an RC networkwith the rest of the equivalent resistance, then a pole exists at1/2 CR Hz.

A simple educated trial-and-error:

Select an RC combination (in the compensation circuit associated withthe control IC) for a deep lag compensation — narrow band first.

Then, relax the time constant (widen the band) until the circuit beginsto oscillate!

Finally, reduce the capacitor value down 10 times to restore stability.


Current mode control

Essential concept — The systemreduces to first order, more orless!

The system is therefore faster,with less chance for instability.

IDEA:

Make the inductor currentdependent on the output voltageby forcing the current peak tofollow the output voltage analog.

Disqualify the inductor current asa state variable.

The converter becomes firstorder.

Z f

Vref

–+

Vout

–+

v con

R1

R2

currentsensor

R

SQ

driver


Fourth problem: isolation

Need for isolating the load fromthe mains.

But the control circuit connectsthe two!

Put control in the primary-side

Mainsrectifier

driver

control IC

Vout

+V

aux. supply

bootstrapstart-up

Mainsrectifier

driver

control IC

Vout

+V

aux. supply

Put control in the secondary-side


Fifth problem: filter

An input filter is always needed toprevent differential-mode andcommon-mode noise from getting intothe mains.

L

N

E

~ differential

commoncommon

SMPS

Basic requirement:

Let 50Hz gets in, butprevent high

frequencies fromgetting out!


Basic filter theory

Voltage filter (low-passleft-to-right)

Current filter (low-passright-to-left)

Voltage filter (low-passright-to-left)

noise currentat switchingfrequencyand above

50Hz SMPS load

x

noise voltageat switchingfrequencyand above

x+–

Rs

Rs

Rs


Conceptual placement

Voltage filter (low-passleft-to-right)

Current filter (low-passright-to-left)

Voltage filter (low-passright-to-left)

SMPS

L

N

E

SMPS

L

N

E

Differential-mode filter

Common-mode filter


Practical placement

NOTE:

The EMI filter often

fails to do what itis supposed to do.

Does the theory

fall short ofanything?

Or have we missed

out someimportant things?!

SMPS

L

N

E

common-modeand differential-mode

capacitor

common-mode chokedifferential-mode choke(may be provided by leakageof common-mode choke)

differential-modecapacitor

differential-modecapacitor

Lc

Ld

Cc1 Cc2Cm1

Cc1

Cm

2+

Cm2,

1 Cc2

Cm

2+ 2

2LdLc+

Ld

2

2Cm1

2Cm2


Conclusion

The curses to the theory:

A capacitor may not behave as a capacitor.

An inductor may not behave as an inductor.

Parasitics and nonlinearity strike in.

Signals get around the filter, instead of being filtered.

The theory does not fail. The engineers fail to identify the

right ingredients for constructing theories that are viable.


There is nothing more practical than a good theory.

— James C. Maxwell

smps lecture 1

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