Chapter 5: Power Electronics: Devices and Circuits potx

Chapter 5
Power Electronics: Devices and
Circuits
5.1 Introduction
Power electronics is an enabling technology for all electrical and electronic apparatus
requiring electric power to drive. Over the past twenty years, the power electronics
industry has grown tremendously. Its growth is a result from increasing demand of re-
liable, efficient, compact and cost effective power supplies for telecommunication, com-
puter, and motor drive industries as well as for medical equipments and military use.
This growth is facilitated by the significant improvement in semiconductor technology
in which smaller packaging and higher power handling devices have been marketed. In
response to the advancement in semiconductor and magnetics technology, power elec-
tronics researchers and engineers h ave strived to thoroughly employ these technologies
through new circuit design and topologies, optimized control and packaging techniques,
in order to meet the industry demands.
Power electronics is all about using electronic devices and circuits with storage el-
ement to control the level of voltage and current, either in the form of AC or DC. Power
electronics circuits are switching converters with periodic switching actions to process
the electrical energy to meet the design s pecification. Apart from semiconductors, in-
ductor and transform er are the critical magnetic components in the power switching
converter. Th eir functions such as storage element, power splitting, and safety isolation
83
5. Power Electronics: Devices and Circuits 84
will be explained in detail in Chapter 6. In order to control power, some form of control
techniques are needed and will be discussed in Chapter 7.
This ch apter we will begin with the semiconductor devices used for power con-
verters. We th en analyze the basic DC/DC converters at the steady state. That is,
the output voltage and current are at stable cond ition. Finally, the operation of gate
driver, w hich drives the transistor, is presented.
5.2 Electrical Energy Conversion by Switching
The characteristics of power conversion by power electronics converters are summarized

as follows:
1. Electrical energy can be generated, transmitted and converted to a form that is
suitable for the load we are interested in.
2. Power Electronics concerns conversion and processing of electrical energy by
power semiconductor devices and storage elements.
3. Power Electronics technologies enable great efficiency enhancement, tremendous
size and weight reduction of electrical equipment.
4. Power Electronics technologies are based on switching on and off the power source
by power semiconductors. The electrical energy conversion process can be pre-
cisely controlled in a manner far much better than electromech an ical devices.
5. Power Electronics applications include power supplies for computers, communi-
cation equipment, machine dr ives, lighting, automobile and m any applications.
6. Electrical energy conversion can be classified into the following four categories :
AC to AC, AC to DC, DC to DC, and DC to AC.
5. Power Electronics: Devices and Circuits 85
Figure 5.1: Four categories of electrical energy conversion.
Figure 5.2: Diode: (a) Symbol, (b) I-V characteristic, (c) idealized characteristics.
Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 86
Figure 5.3: Diode switching characteristics. Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 87
5.3 Power Semiconductor Devices as Switches
5.3.1 Diodes
A diode performs as a switch. It is driven by the voltage applied across its two terminals:
anode and catho de. Fig 5.2(a) shows the symbol of a diode. A is the anode, the positive
terminal. K is the cathode, the negative terminal. When a diode is forward biased, v
d
is positive (i.e. potential at A is higher than K), th e arrow shows the direction of the
diode current i
D

. When the diode conducts, a small forward voltage drop denoted as
V
F
is established and the magnitude is usually around 1V. When the diode is reverse
biased, it is blocked and the diode current becomes slightly negative. This is du e to the
contribution of reverse saturation current. For example, 1N4004 has a reverse current
of 50µA. And this reverse current is of temperature-dependent; when temperature is
higher the reverse current is increased and vice versa. The reverse voltage applied on
a diode has a limit. Beyond the limit the diode will breakdown and becomes a short
circuit. This limit is usually called the peak inverse (or reverse) voltage.
Another interesting fact of semiconductor is that it can handle repetitive pulse
current which has a magnitude much higher than the continuous diode current. For
example, 1N4004 has a maximum forward current at 1A but its allowable repetitive
pulse current is at 10A. This property is of particular interest to power electronics
circuit because of its switching nature.
Owing to the intrinsic resistance, inductance and capacitance of a diode, it expe-
riences voltage overshoot (especially in power diode) and reverse recovery transition.
When the diode is forward biased, large amount of excess carriers are driven across the
junction and the depletion region is reduced. This behaves like charging a capacitor
plus the ohmic resistance and in ductance that cause the voltage overshoot. When the
charging action is finished the forward current I
F
becomes steady and the effect of
di/dt on inductance becomes zero, and thus the drop after the overshoot. When the
diode is reversed biased, it will turn off and the current decreases. If it was an ideal
diode, cur rent would have dropped to zero and remained zero afterwards. In practice,
I
F
becomes negative for a while before it settles to zero. This period is known as
reverse recovery period. The reverse recovery period is due to charge storage in the

diode when it is forward biased. When the diode turns off the charge storage has to b e
5. Power Electronics: Devices and Circuits 88
Figure 5.4: N-Channel MOSFET: (a) Symbol, (b) I-V characteristic, (c) idealized
characteristics. Sources: Mohan 1995 [2].
removed before the junction can become reverse biased again.
The effects of reverse recovery of diode are not only increasing the power dissi-
pation of diode itself but also increaseing the losses of other devices connected. For
power electronics circuits switching at high frequency in the range of hu ndred kHz to
few MHz, fast recovery time diodes are preferred.
There are at least three different types of diode:
• Line frequency diode or general purpose diode - on-state or forward voltage of
theses diodes is made as low as possible but higher t
rr
, which is acceptable for
line frequency applications (50 Hz or 60 Hz).
• Fast recovery diode - small reverse recovery time, t
rr
less than a few microseconds,
for high frequency switching circuits.
• Schottky diode - these diodes have low forward voltage drop(typically 0.3V) and
the dio de dissipation is reduced. However Schottky diodes are limited in their
voltage blocking capabilities, typically less than 250V.
5.3.2 MOSFET
The MOSFET has three terminals: Gate (G), Drain (D) and Source (S). It is a voltage-
controlled device which needs a voltage across gate-to-source (V
GS
) be greater than a
threshold voltage V
th
to drive the transistor on. When the transistor is on, the drain-to-

source becomes a channel for electric current to pass through at both directions. This
5. Power Electronics: Devices and Circuits 89
channel has an internal resistance called on-state r esistance R
ON
which is voltage-
and temperature-dependent. In general, the higher the voltage and temperature, the
higher the on-state resistance. R
ON
is at the range from a few milli-ohms to a few
ohms. Besides, due to the formation structure of MOSFET, there is a body diode
across the source-to-drain term inals.
The MOSFET has intrinsic capacitances across all its terminals. Of particular
concern is the capacitances across G-S and G-D. These capacitances will cause delay in
the turning on or off the MOSFET. T his leads to switching losses. In order to minimize
the losses, the gate driver circuit (i.e. to provide V
GS
) has to be of high current and
fast switching response. We will discuss that in more detail in the last Section of this
chapter.
The gate-to-source voltage needs to stay above the threshold voltage to maintain
the transistor on. One important point to stress is that, for a practical MOSFET, V
GS
and drain current I
D
are inter-related. For example, in Fig. 5.5, the drain current I
D
only reaches 6.5A maximum when V
GS
is at 4.5V. I
D

increases when V
GS
increases.
When the V
GS
decreases to zero, the transistor is off and I
D
decreases to zero. Current
MOSFET can sustain a reverse voltage up to 1kV.
5.4 Basic Power Converter Topologies
5.4.1 Buck
The buck converter with MOSFET is shown in Fig. 5.6. The buck converter performs
voltage step-down function. That is, V
o
is less than V
S
. By the switching actions of
MOSFET, the buck converter can be described by two basic operation stages as s hown
in Fig. 5.7. The switching waveforms of the buck converter is shown in Fig. 5.8. In
this operation mode, the inductor current d oes not reach zero. Th is mode is called
continuous (inductor) conduction mode (CCM).
Stage 1
Prior to this stage, the switch Q1 is turned off. But there is current flowing in the
inductor L. When Q1 is turned on at the beginning of this stage (t = 0), the voltage
5. Power Electronics: Devices and Circuits 90
Figure 5.5: N-Channel MOSFET IRF540N I-V characteristic. Sources: International
Rectifier.
❄
Q1
v

P ulse1
L
C
R
L
V
S
i
D1
✻
+ −V
L
(t)
+
−
V
C
(t)
❄
I
c
(t)
I
a
V
o
(t), V
a
D
f w

✲ ✲ ✲
i
s
(t) i
L
(t)
I
o
+
−
Figure 5.6: Circuit diagram of a buck converter.
5. Power Electronics: Devices and Circuits 91
L
C
R
L
V
S
i
D1
✻
+ −V
L
(t)
+
−
V
C
(t)
❄

I
c
(t)
I
a
V
o
(t), V
a
D
fw
✲ ✲ ✲
i
s
(t) i
L
(t) I
o
+
−
(a) Stage 1 (0 − DT )
Q1
L
C
R
L
V
S
i
D1

✻
+ −V
L
(t)
+
−
V
C
(t)
❄
I
c
(t)
I
a
V
o
(t), V
a
D
fw
✲ ✲ ✲
i
s
(t) i
L
(t)
I
o
+

−
(b) Stage 2 (DT − T )
Figure 5.7: Equivalent circuits for the buck converter of the two operation stages.
5. Power Electronics: Devices and Circuits 92
✲
✲
✲
✲
✲
✲
t
I
a
V
a
I
c
(t)
V
DW
(t)
i
L
(t)
i
S
(t)
v
C
(t) = V

o
(t)
I
o
(t)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D T T
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D T T
V
S
I
1
I
2
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I
L
= I
a
I
1
I
2
❄
✻
∆V
C
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
❄
✻
∆I
L
Figure 5.8: Key switching waveforms of a buck converter.
5. Power Electronics: Devices and Circuits 93
applied across the inductor is
V
L
(t) = V
S
− V
o
(t) (5.1)
Since the resultant voltage is positive on V
L
, inductor L is charged up linearly with a
rate equals
di
L
dt
=
V
L
(t)
L
=
V
S

− V
a
L
(5.2)
where we assume V
o
t is constant and at a value equals V
a
. As the inductor current rises
from I
1
to I
2
, we may substitute ∆I = I
2
− I
1
into (5.2) to give
V
S
− V
a
= L
∆I
L
DT
(5.3)
And by re-arranging of terms we have the duration of Stage 1
t
on

= DT = L
∆I
L
V
S
− V
a
(5.4)
Stage 2
This stage begins when switch Q1 is turned off. The drain-to-source terminal becomes
an open circuit. I nput current is ceased to flow. However, the current in the inductor
cannot change abruptly. Without a path to continue I
L
, the energy stored in the
inductor will be released sudd en ly that appears as a destructive voltage spike on the
MOSFET and eventually would burn it out. Fortunately, a free wheeling diode D
fw
is
presented in the buck converter. I
L
is diverted to flow through th is diode. Neglecting
the forward voltage drop of diode V
D f w
, the voltage applied across L has reversed
polarity and its magnitude is described as
V
L
(t) = −V
o
(t) = −V

a
(5.5)
The rate of change of inductor current is given by
di
L
dt
=
V
L
(t)
L
=
−V
a
L
(5.6)
And we may fin d the duration of Stage 2 is
t
off
= (1 − D)T = L
I
2
− I
1
−V
a
(5.7)
One important property of magnetic component is the change of inductor current
is proportional to the change of magnetic flux of the indu ctor or tr an s former core. If
5. Power Electronics: Devices and Circuits 94

we can maintain a contant change of inductor current, then we are able to prevent the
core from walking towards saturation. This property leads to the following equality
∆I
L
(t
on
) = ∆I
L
(t
off
)
V
S
−V
a
L
DT =
−V
a
L
(1 − D)T
(5.8)
From (5.8) we arrive the following conclusion:
V
a
= V
s
D (5.9)
which is the voltage conversion ratio of buck converter at operating at CCM. Since D
is always less than 1, it im plies that V

a
is always less than V
s
.
Critical Inductance
From Fig. 5.8, we know that I
a
= (I
2
− I
1
)/2. In order to maintain inductor current
at CCM, we must ensure the following inequality
I
2
− I
1
2
≤ I
a
(5.10)
Substitute (5.2) into (5.10),
V
S
− V
a
2L
DT ≤ I
a
=

V
a
R
L
(5.11)
Substitute (5.9) into (5.11) and rearrange of terms, we get
L ≥
(1 − D)T R
L
2
=
(1 − D)R
L
2f
s
= L
crit
(5.12)
where f
s
is the switchin g frequency.
Input and Output Ripples
The average charging or discharing current of the output capacitor C is equal to the
trangular area I
C
(t) covered. Take the capacitor charging part as an example. I t can
be written as
I
C
=

∆I
L
2
×
T
2
2T
=
∆I
L
8
(5.13)
The capacitor ripple voltage ∆v
C
of each period is
∆v
C
=
1
C

T
0
∆I
L
8
dt =
T ∆I
L
8C

(5.14)
5. Power Electronics: Devices and Circuits 95
Substitute (5.3) and (5.9) into (5.14), the capacitor ripple voltage is expressed as
∆v
C
=
V
S
D(1 − D)
8f
2
s
LC
(5.15)
In fact, the capacitor ripple voltage ∆v
C
is the output ripple voltage ∆v
o
because the
capacitor is directly connected to the load. It can be seen that to decrease the ripple
voltage, one can in crease one or both of the following parameters: switching frequency,
output capacitance and inductance.
As the input current of buck converter is pulsating, it may affect the equipment
or power s ou rces connected to the input of the buck converter. A common practice is
to insert an LC filter between the source V
S
and the switch Q1. The filter also reduces
the magnitude of electromagnetic interference (EMI).
Example: The buck converter shown in Fig. 5.6 has an input voltage of 12V.
The switching frequency is 50kHz. The load requires an average voltage of 5V with a

maximum ripple voltage of 20mV. The maximum ripple current of the output inductor
is 0.2A. Determine: (a) the duty cycle, (b) the output inductance, (c) the output
capacitance, and (d) the output inductance if the switching frequency is increased to
100kHz.
Solution: (a) From (5.9),
D =
V
a
V
S
=
5
12
= 0.417.
(b) From (5.4)
L = DT
(V
S
− V
a
)
∆I
=
0.417
50000
×
12 − 5
0.2
= 0.29mH.
(c) From (5.15)

C =
V
S
D(1 − D)
8f
2
s
L∆v
C
=
12 · 0.417 · (1 − 0.417)
8 · 50000
2
· 0.29mH · 0.02
= 25µF
(d) The duty cycle remains unchanged. But the frequency has increased that
caused the inductor to decrease, as indicated from (5.4)
L = DT
(V
S
− V
a
)
∆I
=
0.417
100000
×
12 − 5
0.2

= 0.146mH.
We can see that by doubling the switching frequency, the inductance is reduced by half.
5. Power Electronics: Devices and Circuits 96
Q1
L
C
R
L
V
S
i
D1
✻
+ −V
L
(t)
+
−
V
C
(t)
❄
I
c
(t)
I
a
V
o
(t), V

a
D
f w
✲ ✲ ✲
i
s
(t) i
L
(t)
I
o
+
−
Figure 5.9: Stage 3 of the buck converter at DCM.
✲
✲
V
DW
(t)
i
L
(t)
.
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.

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D T
D
1
T
T
I
LP
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I
L
✲
.
.
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.

.
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.
.
.
.
.
.
.
v
L
(t)
0
0
V
S
− V
a
−V
a
✛ ✲
Figure 5.10: Key s witching waveforms of a bu ck converter at DCM.

5. Power Electronics: Devices and Circuits 97
Discontinuous Condution Mode (DCM)
In discontinuous conduction mode (DCM), there is an additional stage after Stage 2 in
which the inductor current has already reached zero, as shown in Figs. 5.9 and 5.10.
The output voltage is sustained by the output capacitor C.
Since the average voltage across the inductor is zero, we can write the following:
(V
S
− V
a
)DT − V
a
D
1
T = 0 (5.16)
Rearranging of terms we have the duration of inductor cur rent discharging
D
1
T =
(V
S
− V
a
)DT
V
a
(5.17)
Now if we assume the buck converter is lossless, then the input power equals output
power, which is given by
V

S
×
I
LP
· DT
2T
=
V
2
a
R
L
(5.18)
As the peak of indu ctor current is given by
I
LP
=
V
S
− V
a
L
DT (5.19)
Substitute (5.19) into (5.18), we get an quadratic equation
2L
D
2
T R
L
V

2
a
+ V
S
V
a
− V
2
S
= 0 (5.20)
Solving the equation, we finally have the voltage conversion ratio of buck converter in
DCM
V
a
V
S
=
D
2
T R
L
4L
(

1 +
8L
D
2
T R
L

− 1) (5.21)
5.5 Driving the Transistor
5.5.1 Losses
Fig. 5.11(a) shows a circuit modeling a general switching converter switching an in-
ductive load. As it is common in power electronics circuits that they process energy to
be s tored and transferred from inductive element such as inductor and transformer. It
is in this circuit modeled as I
o
. V
d
is the power source, v
T
and i
T
are the voltage and
current through the transistor respectively.
5. Power Electronics: Devices and Circuits 98
Figure 5.11: Cause of switching losses in transistor. Sources: Mohan 1995 [2].
5. Power Electronics: Devices and Circuits 99
Switching Loss
When the switch control signal is at On state, after certain delay t
d(on)
the trans istor
is closed. The current of the transistor increases while the voltage across it decreases.
The duration takes t
c(on)
= t
ri
+ t
fv

for i
T
to reach I
o
and v
T
to reach V
on
. V
on
is
non-zero in practical transistor as it has internal resistance.
From 5.11(c), it shows the energy losses to switching on and off of the transistor
(shaded area), which can be approximately written as
W
c(on)
=
1
2
V
d
I
o
t
c(on)
(5.22)
W
c(off )
=
1

2
V
d
I
o
t
c(off )
(5.23)
And the power dissipation of the transistor due to sw itching losses can be written as
P
s
=
1
2
V
d
I
o
(t
c(on)
+ t
c(off )
)f
s
(5.24)
It can be seen th at the switching loss increases with the switching frequency. This
becomes the trade-off when we want to reduce the component size such as magnetic
components and capacitor by increasing the switching frequency, th e switching loss
increases as well. Converters with this type with conventional switching of transistor
are often called “hard-switching” converters. In order to have a breakthrough, we may

need to consider soft-switching technique which is able to minimize or even eliminate
the cross conduction of voltage and current through the transistor. This is however
beyond the scop e of this unit of study. Students who want to have further studies in
soft-switching technique can go to Chapter 3 of Ang’s book [1].
Conduction Loss
The conduction loss of the transistor is defined as the energy dissipation in the transistor
during this on-state interval. It can be approximated as
W
on
= V
on
I
o
t
on
(5.25)
The power dissipation of conduction loss is then approximated as
P
on
= V
on
I
o
t
on
T
(5.26)
5. Power Electronics: Devices and Circuits 100
s
✰

✛
v
GS
Totem-pole
V
DD
0
+
−
V
BE
v
P W M
+
V
BE
−
+
−
I
D
❄
Q3
+
−
Q1
Q2
x
R
i

❄
i
B1
i
B2
✲
✛
i
c
β
β
✲
i
G
Figure 5.12: Totem-pole gate driver for MOSFET.
5.5.2 Totem-pole Gate Drive
Another way to reduce the switching loss is to have a fast switching gate driver to speed
up the rate of turn-on and turn-off of transistor. As we have mentioned in Section 5.3.2
t=hat the MOSFET has intrinsic input capacitance across its gate and source. In usual
cases the switch control signal v
P W M
is of low current capability. We may use a so-
called totem-pole circuit to amplify the current of the signal. It consists of one NPN
transistor and one PNP trans istor connected in series, as shown in Fig. 5.12.
The operation is briefed as follows: To proper switch on the transistor Q3, the
control signal v
P W M
should be greater than the transistor forward biase voltage of Q1
plus the gate-to-source threshold voltage of Q3.
v

P W M
> V
BE
+ V
th
(5.27)
The base current of Q1 can be written as
i
B
=
v
P W M
− V
BE
− V
th
R
i
(5.28)
As the current gain ratio of Q1 is given by β, then the current to the gate of MOSFET
becomes
i
G
=
v
P W M
− V
BE
− V
th

R
i
β (5.29)
5. Power Electronics: Devices and Circuits 101
Figure 5.13: Floating gate drive IR2111. Sources: International Rectifier.
Figure 5.14: Floating gate drive IR2111 functional block diagram. Sources: Interna-
tional Rectifier.
The base-to-emitter voltage of Q2 is reverse biased and it is in off-state.
To switch off Q3, we need to turn off Q1 and switch on Q2. It is achieved by
decreasing v
P W M
to zero. Now Q2 is forward biased and the charge of gate-to-source
of Q3 will be taken away as current through emitter then collector of Q3 to ground.
This is a quick discharge of the intrinsic capacitor and th e transistor is turned off
quickly.
5.5.3 Floating Gate Drive
The totem-pole gate driver is only able to drive the transistor with reference to ground.
If we need to drive a MOSFET with its source node not connecting to ground, for
example the MOSFET of bu ck converter, we need to have a floating gate drive to
provide voltage across gate-to-source of the MOSFET. For example, the half-bridge
5. Power Electronics: Devices and Circuits 102
driver m odel IR2111 from International Rectifier in Fig. 5.13. The functional block
diagram is sh own in Fig. 5.14.
The whole idea of this driver is to provide voltage to charge up the upper MOSFET
v
GS
. This voltage is from the small capacitor across V
B
and V
S

in Fig. 5.13. How to
charge up this capacitor? It is when the lower transistor is turned on. It provides a
current path from V
cc
, diode across V
cc
and V
B
, capacitor, lower transistor then the
return path to charge up this capacitor. When the upper switch control signal is On,
the capacitor will transfer its charge through the internal circuit of the chip to the
intrinsic input capacitor of upper MOSFET.
Bibliography
[1] S. Ang, and A. Oliva, Power-switching converters, CRC Press, 2
nd
Ed., 2005.
[2] N. Mohan, T. M. Undeland, and W. P. Robbins, Power electronics: converters,
applications and devices, John Wiley & Sons, Inc., 2
nd
Ed., 1995.
[3] International Rectifier, IR2111 half-bridge driver. [Online]
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