Teoria completa per orale Elettronica di potenza

DC

THE HALF-BRIDGE PART 2

MODULATION

We have seen that the half bridge with a positive DC input can be used as a controllable voltage source.

The way we control the output voltage of the half bridge is by changing the state of the switches. S1 and S2

are ON when the corresponding GATE-EMITTER voltage is above the turn-on threshold.

= ∙

So at the moment we have a controllable voltage source that is not particularly controllable – it can take

only 2 discrete values [0, VDC], but we would like to be able to convert/transform VDC into a voltage that

can take any value in the range [0 - VDC]. What we want can be achieved with Pulse Width Modulation

(PWM)

PWM

PWM is a modulation technique that takes a low frequency signal – the modulation signal – and adds high

frequency harmonics so that the resulting modulated signal will be a switching waveform between 0 and 1

→ that we can use to drive our half-bridge! We have a low frequency voltage

waveform V we would like

BN

to generate with the half bridge.

Our half bridge doesn’t particularly

like to generate low frequencies,

since it can only flip its state

between 0 and V . The PWM can

DC

mix the waveform we want to

generate with an high frequency

carrier, resulting in something that

the bridge can generate. We recover the low frequency component we want at the bridge output by

demodulating V through a low pass filter.

BN We said that the PWM adds frequency components to the

modulation signal to turn it into a switched waveform like GB(t)

But if the trick works, we expect GB(t) to preserve the original

low frequency component – in this case DC (segnale continuo).

Looking at this example, it’s easy to understand that

2

̅̅̅̅ 1 0 0

= = 1 − () = 1 −

. , and in is equal to m(t), so

2

1 0

= =1−

we find out that

̅̅̅̅ (

= = )

This result in REMEMBER

̅̅̅̅̅̅

= ∙ = ∙ ≤

We can now write that . We now have what we wanted, because the

low frequency value of the output voltage of our half-bridge is fully controllable between 0 and V ! “m”

DC

(and “d”!) simply tells us the % of V that we want to generate at the output. “d” (and “m”!) is also the %

DC

of the switching period during which S1 is ON. 2

( )

() = − −

More general case (in which A and A different from 1 and 0): and

MAX MIN

−

̅̅̅̅

= =

so this result in −

EXTENSION TO “LOW FREQUENCY” MODULATION SIGNAL We are now able to generate an

output voltage of the half-bridge

with a DC component that we

control. Unfortunately, that is

not the only component we have

in the half-bridge output voltage!

To be able to generate it we have

also to accept the high frequency

components caused by switching

Fino ad ora abbiamo assunto che il segnale modulante fosse in continua (DC). Lo stesso discorso può essere

esteso per un generico segnale modulante di bassa frequenza (LF=Low Frequency), ma da cosa lo posso

(ℎ

≪ ).

capire? In generale, deve essere Perché può bastare questo?

Because if the condition applies, the modulation signal m(t) can be considered approximately constant in

each period TS, and we can therefore apply the same calculations we did for the DC case.

Let’s see a simple example – we keep T =1ms (switching frequency is f =1kHz) but now we define a

S S

() = 0.25 + 0.25 sin(25)

modulation signal which is DC + 5Hz: If m(t) can be assumed

constant in a single

carrier period, we can say

that:

̅̅̅̅̅

= () ∙ ≤

for a certain f , what is the maximum frequency that can be present in m(t)?

S We now understand that for a given

switching frequency there is a

maximum frequency of m(t) that we

can use.

From the last result you can see that

the maximum frequency that

~

m(t) can have is about .

3

However you must remember that

we don’t want the switching

harmonics, and we must filter them

out, and we can do that only if the LF

components are far enough from the

switching (HF) ones! As a rule of

thumb we can assume that the PWM

frequency must be at least 10 times

larger than the maximum frequency

we want in our m(t).

PWM SUMMARY Do we always need to use PWM?

• NO, there are applications where

PWM is not needed

• An example is the Dual Active

Bridge DC/DC converter that will be

discussed later

• Square Wave Modulation is an

alternative option

SQUARE WAVE MODULATION

Square Wave Modulation is a very simple modulation method:

The state of the half bridge is changed with fixed duty cycle, set at 50%.

The voltage we generate now is not fully controllable! All the amplitudes of the frequency components are

fixed. The only control variable we have is the phase delay of the waveform (or equivalently, the time

delay). We can control the phase continuously. We will see that this control variable is essential for the

Dual Active Bridge

DIFFERENCES BEETWEEN PWM AND SWM:

• PWM modulation allows the generation of a fully controllable LF component of the output voltage

amplitude and phase can be defined defining m(t)

• In Square Wave Modulation, the amplitude of all the components of the output voltage is fixed.

The only variable left to control is the phase shift of the voltage waveform

THE HALF-BRIDGE PART 3

BASIC CONCEPTS OF VOLTAGE FILTERING

We must prevent the high frequency components from propagating to the rest of our converter. Why?

Because they would adversely affect Power Quality. This is why switching harmonics must be attenuated by

low pass filtering the generated voltage. The specific circuit used for filtering will depend on the converter

topology and will be discussed later. However, the choice of filter must respect few basic requirements:

• The transfer function from the input of the filter (the HF component of the half bridge voltage) to

the output current or voltage must be Low Pass

• The filter must be non dissipative

• The size of the filter must be the minimum needed to perform the required filtering action

The impedance of the

inductor increases with

frequency, thus

attenuating the HF

components of the bridge

=

output current

There are two important consequences

=

1. The output current IB must always have a path – remember the basics: . If IB is

interrupted, the voltage across L rises – we will see that the antiparallel diodes prevent this

2. Considering that IB can’t change quickly, we can assume that it remains constant during the

commutation of the switches

BASIC DYNAMIC MODELLING

For control design we are only interested in the LF components and we neglect the HF ones.

DEAD TIMES AND SIMPLIFIED LOSS ANALYSIS

Our semiconductors are not ideal. They present two basics non idealities:

1. Turn on and turn off delays

2. Voltage drops during conduction

→

DEAD TIMES If we implement the simple logic that uses a NOT gate to generate the complimentary gate

signals, we will ask to one of the switches to turn ON before the other one is OFF. DESTRUCTIVE

OPERATING MODE! The solution is intuitive: when we switch OFF one of the switches, we must wait

enough time before we can switch ON the other one – this time is called “Dead-Time”

What happens during the dead-times?

The sign of the output current

decides V ! During dead-times, the half-

BN

bridge loses temporary its voltage source

nature, since the voltage it generates

depends on the sign of the inductor current.

SIMPLIFIED LOSS ANALYSIS

Half bridges have two main sources of loss

– Conduction loss, related with the fact that when an IGBT or a DIODE are conducting, they have a

voltage drop ≠ 0

– Switching loss caused by the non zero current and voltage during each commutation These can be

divided in

• Turn on losses (MOSFETs)

• Turn off losses (MOSFETs)

• Reverse recovery losses (DIODEs)

CONDUCTION LOSSES • The voltage drops across

IGBT and DIODE depend on the

components we selected for

the converter

• i (t) depends on the

B

operating conditions of the

converter in

which the half bridge is used

• G (t) depends on the

1

operating conditions

The average (DC) component

of the instantaneous

powers give the average

conduction loss

SWITCHING LOSSES

The basic assumption here is that the filter inductor current i (t) does not change during commutation.

B

Let’s focus on one of the switches, S1, and look in detail at the different possible commutations:

→ →

1. S1 turns ON with i >0 HARD TURN ON LOSS

B → →

2. S1 turns OFF with i >0 HARD TURN OFF LOSS

B → →

3. S1 turns ON with i <0 SOFT TURN ON NO LOSS

B → →NO

4. S1 turns OFF with i <0 SOFT TURN OFF LOSS

B

→

NO LOSS This is always the case when the current flows the antiparallel diode at the time a switch is

turned OFF.

Let’s now see the other two cases, much more important: ∙ ∙

→ =

2

∙ ∙

→ =

2

REVERSE RECOVERY LOSSES

It happens every time the current flowing through a diode is “stolen” by an IGBT that turns ON.

The reverse recovery current has a double effect:

• Generates loss in the diode

• Increases the IGBT current and therefore increase turn on loss

DC/DC CONVERTERS (FOR CPUs)

It is usually referred to as “Synchronous Buck Converter”

Comparing two CPUs (Intel Pentium 1995 vs Intel Core i7 2008) we can see that:

• Clock frequency increased

• Power went up

• Supply voltages went down; but if power went up, current must be increased!

Remember that higher current always means more copper to keep the resistance

R low and avoid

1