Chapter 4
SWITCH-MODE POWER SUPPLY
4-1 Introduction
As we discussed in the first chapter, the power electronics cares about change of the
power from one form to another form. The four forms of power conversion are:1. AC-DC conversion called rectification,
2. AC-AC conversion,
3. DC-AC conversion or inversion and
4. DC-DC conversion.
DC-DC converters sometimes called choppers in some textbooks and sometimes
called Switch Mode Power Supply SMPS. A switch mode power supply circuit is
versatile. It can be used to:
1. Step down an unregulated DC input voltage to produce a regulated DC
output voltage using a circuit known as Buck Converter or Step-Down
SMPS,
2. Step up an unregulated DC input voltage to produce a regulated DC
output voltage using a circuit known as Boost Converter or Step-Up
SMPS,
3. Step up or step down an unregulated DC input voltage to produce a
regulated DC output voltage ,
4. Invert the input DC voltage using usually a circuit such as the Cuk
converter, and
5. Produce multiple DC outputs using a circuit such as the fly-back
converter.
A switch mode power supply is a widely used circuit nowadays and it is used in a
system such as a computer, television receiver, battery charger etc. The switching
frequency is usually above 20 kHz, so that the noise produced by it is above the
audio range. It is also used to provide a variable DC voltage to armature of a DC
motor in a variable speed drive. It is used in a high-frequency unity-power factor
circuit.
This chapter describes the basics, operation and design of switched-mode power
supplies.
4-2 Step Down DC-DC Converter (Buck Converter)
A buck converter or step-down switch mode power supply can also be called a
switch mode regulator. Popularity of a switch mode regulator is due to its fairly
high efficiency and compact size and a switch mode regulator is used in place of a
linear voltage regulator at relatively high output, because linear voltage regulators
are inefficient. Since the power devices used in linear regulators have to dissipate a
fairly large amount of power, they have to be adequately cooled, by mounting them
on heatsinks and the heat is transferred from the heatsinks to the surrounding air
either by natural convection or by forced-air cooling. Heatsinks and provision for
cooling makes the regulator bulky and large. In applications where size and
efficiency are critical, linear voltage regulators cannot be used.
A switch mode regulator overcomes the drawbacks of linear regulators. Switched
power supplies are more efficient and they tend to have an efficiency of 80% or
more. They can be packaged in a fraction of the size of linear regulators. Unlike
linear regulators, switched power supplies can step up or step down the input
voltage.
A simplified diagram of a step down DC-DC converter is shown in Fig.4.1. The
output voltage is shown in Fig.4.2. This average output voltage depends on the duty
ratio, D where D 
t on
.
TS
2
Fig.4.1 Simplified circuit diagram of a step down DC-DC converter.
vo
Vd
Vo
ton
toff
Ts
Fig.4.2 The output voltage is shown in.
Fig.4.3 shows Buck converter, in this circuit we assume that the switch is ideal and
the output capacitor is assumed to be very large. When the switch S is turned on at
t=0, the diode will be reverse biased and the supply is connected to the load, vo=Vd
and it will supply the load and inductor with energy. When the switch S is turned
off, the diode will be forward bias and the inductor current will flow through the
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diode, transferring some of its stored energy to the load. The output voltage from
buck converter is shown in Fig.4.4.
Id
L
Vo
iL
Vd
R
Fig.4.3 circuit diagram of buck converter.
vL
Vd -Vo
A
-Vo
ton
B
t
toff
Ts
Fig.4.4 The output voltage from buck converter.
4-2-1 Continuous Conduction Mode
For the circuit in Fig.4.3, the output voltage equals the input voltage when the
switch is “ON” and it is zero when the switch is “OFF”. By varying the duration for
which the switch is ON and OFF, it can be seen that the average output voltage can
be varied, but the output voltage is not pure DC. The output voltage contains an
average voltage with a square-voltage superimposed on it, as shown in Fig.4.4.
Usually the desired outcome is a DC voltage without any noticeable ripple content.
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When the switch is on for a time duration ton, the switch conducts the inductor
current and the diode become reverse biased. This results in a positive voltage
vL=Vd-Vo across the inductor in Fig.4.3. This voltage causes a linear increase in the
inductor current iL. When the switch is turned OFF, because of inductive energy
storage, iL continues to flow. This current now flows through the diode, and vL=-Vo
in Fig.4.3. In steady state operation, the integral of the inductor voltage vL over one
time period must be zero. Then,
TS
ton
TS
 v L dt   v L dt   v L dt  0
o
o
(4.1)
ton
In Fig.4.4 the forgoing equation implies that the areas A and B must be equal.
Therefore;
(Vd  VO ) t on  VO (TS  t on )
(4.2)
VO t on

D
Vd TS
(4.3)
Neglecting power losses associated with all the circuit elements, the input power Pd
equals the output power PO:
Pd  PO
(4.4)
Vd I d  VO I O
(4.5)
I O Vd 1


I d VO D
(4.6)
Output Voltage Ripple
In the previous analysis, the output capacitor is assumed to be so large as to
yield vO (t )  VO . However, the ripple in the output voltage with a practical value of
capacitor can be calculating by considering the waveform shown in Fig.4.7 in
continuous conduction mode of operation and Fig.4.8 in discontinuous conduction
mode of operation.
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I LB  I OB
vL
Vd -Vo
-Vo
ton
toff
Ts
iL,peak
iL
Q
I LB  I OB
Ts / 2
VO
VO
Fig.4.7
In case continuous conduction mode, assume that all of the ripple component in iL
flows through the capacitor and its average component flows through the load
resistor, the shaded area in Fig.4.7 represents an additional charge to the capacitor,
the peak to peak voltage ripple VO can be written as:
VO 
Q 1 1 I L TS

C
C2 2 2
(4.27)
From Fig.4.7 during tOFF
I L 
VO
(1  D)TS
L
(4.28)
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Therefore, substituting from equation (4.27) into the previous equation gives:
VO 
TS VO
(1  D )TS
8C L
f 
VO 1 TS2 (1  D)  2


(1  D) C 
VO
8
LC
2
 fS 
(4.29)
2
(4.30)
Where switching frequency f S  1 TS and f C 
1
2 LC
Step Up (Boost) Converter
Fig. shows a step up converter. Its main application is in regulated DC power
supplies and the regenerative braking of DC motors. As the name implies, the
output voltage is always greater than the input voltage. When the switch is ON, the
diode is reverse biased, thus isolating the output stage. The input supplies energy to
the inductor. When the switch is OFF, the output stage recives energy from the
inductor as well as from the input. In steady state analysis presented here, the output
filter capacitor is assumed to be very large to ensure a constant output voltage
vo (t )  VO .
Continuous Conduction Mode
Fig. shows the steady state waveform for this mode of condition where the
inductor current flows continuously[iL(t)>0].
Since in steady state the time integral of the inductor voltage over one time period
must be zero,
Vd t on  (Vd  VO ) t off  0
Dividing both sides by TS and rearranging terms yield
VO
T
1
 S 
Vd Toff 1  D
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Assuming a lossless circuit, Pd=PO,
Vd I d  VO I O
and
IO
 (1  D)
Id
Output Voltage Ripple For Continuous Conduction Mode
The peak to peak ripple in the output voltage can be calculated by considering the
waveform shown in Fig. for a continuous mode of operation. Assuming that all
the ripple current component of the diode current iD flows through the capacitor
and its average value flows through the load resistor, the shaded area in Fig.
represents charge Q. Therefore, the peak-to-peak voltage ripple is given by:
VO 
Q I O DTS VO DTS


C
C
RC
VO DTS
T

 D S (Where  =RC time constant)
VO
RC

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