DC-DC Switch-Mode Converters
Applications:
• Regulated switch mode dc power supplies
• dc motor drives
dc-dc Converters:
• Step-down (buck) converter
• Step-up (boost) converter
• Step-down/step-up (buck-boost) converter
• Cuk converter
• Full-bridge converter
7-1
Functional Block Diagram of DC-DC Converter System
Controlled dc output at a desired
voltage level
Unregulated dc voltage obtained by
rectifying the line voltage, and therefore will
fluctuate with line voltage magnitude
7-2
Control of DC-DC Converters
In a dc-dc converter:
• Average output dc voltage must be controlled to equal a desired level.
• Utilizes one or more switches to transform dc from one level to another.
• The average output voltage is controlled by controlling the switch on and
off durations (ton and toff).
• Let’s consider the following switch-mode dc-dc converter:
• Average output dc voltage Vo depends on ton and toff.
• Switching is done at a constant frequency with switching time period Ts.
• This method is called pulse-width modulation (PWM) in which the duty ratio
D is varied to control Vo, where D=ton/Ts
7-3
Control of DC-DC Converters (cont’d)
• The switch control signal, which
controls the on and off states of the
switch, is generated by comparing a
signal level control voltage vcontrol with
a repetitive waveform.
• The switching frequency is the
frequency of the sawtooth waveform
with a constant peak.
• The duty ratio D can be expressed as
D
t on vcontrol
 ^
Ts
V st
7-4
Step-Down (Buck) Converter
•
•
•
•
•
•
converts dc from one level to another
the average output voltage is controlled by the
ON-OFF switch
pulse-width modulation (PWM) switching is
employed
lower average output voltage than the dc input
voltage Vd depending on the duty ratio, D
D=ton/Ts
Average output:
Ts

1 Ts
1  ton
V0   v0 t dt    Vd dt   0 dt 
Ts 0
Ts  0
t on


ton
Vd  DVd
Ts
•
•
Applications:
•
• regulated switch mode dc power supplies
•
• dc motor drives
•
low-pass filter: to reduce output voltage fluctuations
diode is reversed biased during ON period, input
provides energy to the load and to the inductor
energy is transferred to the load from the inductor
during switch OFF period
in the steady-state, average inductor voltage is zero
in the steady-state, average capacitor current is zero
7-5
Step-Down (Buck) Converter: Continuous current conduction mode
•
•
Inductor current iL flows continuously
Average inductor voltage over a time period
must be zero
Ts
t on
Ts
 v dt   v dt   v dt  0
L
0
L
0
L
t on
Area A and B m ustbe equal, therefore,
Vd  V0 ton  V0 Ts  ton 
or
V0 ton

D
Vd Ts
duty ratio
Assuming a lossless circuit
Vd I d  V0 I 0
and
I 0 Vd 1


I d V0 D
Buck converter is like a dc transformer where the turns ratio can be controlled
electronically in a range of 0-1 by controlling D of the switch
7-6
Example…..
For a buck converter, R=1 ohm, Vd=40 V, V0=5 V, fs=4 kHz. Find the duty ratio
and “on” time of the switch.
7-7
Solution….
D = V0 /Vd = 5/40 = 0.125 = 12.5%
Ts = 1/fs = 0.25 ms = 250 ms
Ton = DTs = 31.25 ms
Toff = Ts – ton = 218.75 ms
When the switch is “on”: VL = Vd - V0 = 35 V
When the switch is “off”: VL = -V0 = - 5 V
I0 = IL = V0 / R = 5 A
Id = D I0 = 0.625 A
7-8
Step-Up (Boost) Converter
• Output voltage always higher than the
input voltage
• When the switch is ON:
diode is reversed biased
output circuit is thus isolated
inductor is charged
• When the switch is OFF:
the output stage received energy from the
inductor as well as from the input
• Filter capacitor is very large to ensure
constant output voltage
Applications:
• regulated switch mode power supplies
• Regenerative braking of dc motors
7-9
Step-Up (Boost) Converter: Continuous current conduction mode
• Inductor current iL flows continuously
• Average inductor voltage over a time
period must be zero
Vd ton  Vd  V0 toff  0
Dividing both side by Ts
V0 Ts
1


Vd toff 1  D
Assuming a lossless circuit
Vd I d  V0 I 0
and
I0
 1  D 
Id
7-10
Step-Up (Boost) Converter: Effect of parasitic elements
• Parasitic elements are due to the
losses associated with the inductor,
capacitor, switch and diode
• Figure shows the effect of the
parasitic elements on the voltage
transfer ratio
• Unlike ideal characteristics, in
practice, Vo /Vd declines as duty
ratio approaches unity
7-11
Step-Down/Step-Up (Buck-Boost) Converter
•
•
•
•
This converter can be obtained by the cascade connection
of two converters: the step-down converter and the stepup converter
The output voltage can be higher or lower than the input
voltage
Used in regulated dc power supplies where a negative
polarity output may be desired with respect to the
common terminal of the input voltage
The output to input voltage conversion ratio
V0
1
D
Vd
1 D
•
•
•
This allows V0 to be higher or lower than Vd
When the switch is ON:
diode is reversed biased
output circuit is thus isolated
inductor is charged
When the switch is OFF:
the output stage received energy from the inductor
7-12
Buck-Boost Converter: Continuous current conduction mode
•
•
Inductor current iL flows continuously
Average inductor voltage over a time
period must be zero
Vd D Ts   V0 1  D Ts  0

V0
D

Vd 1  D
Assuming a lossless circuit
Vd I d  V0 I 0
and
I 0 1  D 

Id
D
•
Depending on the duty ratio, the output
voltage can be either higher or lower than
the input
7-13
Buck-Boost Converter: Effect of parasitic elements
• Parasitic elements are due to the losses
associated with the inductor, capacitor,
switch and diode
• Parasitic elements have significant
impact on the voltage transfer ratio
7-14
Cuk DC-DC Converter
• Named after its inventor
• The output voltage can be higher or lower than the input voltage
• Provides a negative polarity output voltage with respect to the common
terminal of the input voltage
• C1 acts as the primary means of storing and transferring energy from the
input to the output
• In the steady-state, average inductor voltages, VL1 and VL2 are zero, therefore,
VC1 = Vd + V0
7-15
Cuk DC-DC Converter
•
•
When the switch is OFF:
- iL1 and iL2 flow through the diode
- C1 is charged through the diode by energy from
both the input and L1
- energy stored in L2 feeds the output
When the switch is ON:
- Vc1 reverse biases the diode
- iL1 and iL2 flow through the switch
- since Vc1>V0, C1 discharges through the switch,
transferring energy to the output and L2
- Therefore, iL2 increases
- Input feeds energy to L1 causing iL1 to increase
7-16
Steady-state current and voltage equations…………..Cuk
Vc1 is constant and average voltages across L1 and L2 over a time
period must be zero
L1 :
Vd D Ts  Vd  Vc1 1  D Ts  0

L2 :
Vc1 
1
Vd
1 D
Vc1  Vd D Ts   V0 1  D Ts  0

Vc1 
1
V0
D
Equating the above two equations,
V0 I d
D


Vd I 0 1  D
7-17
Example 1: Step-down (Buck) converter
The chopper below controls a dc machine with an armature inductance La = 0.2 mH. The
armature resistance can be neglected. The armature current is 5 A. fs = 30 kHz. D = 0.8
id
Ia
Vd
+
io
La
+
voi
-
vo= Vo
ea
-
The output voltage, Vo, equals 200V.
(a) Calculate the input voltage, Vd
(b) Find the ripple in the armature current.
(c) Calculate the maximum and the minimum value of the armature current
(d) Sketch the armature current, ia(t), and the dc current, id(t).
7-18
Example 2: Step-down (Buck) converter characteristics
A step-down dc-dc converter shown in the following figure is to be analyzed.
The input voltage
Vd = 48 V.
The output filter inductance L = 0.1 mH
Series resistor (with L)
R = 0.2 Ω
Assume in all calculations constant voltage over the series resistor R.
The output capacitor C is large; assume no ripple in the output voltage.
Rated output is 20 V and 25 A
(a) Calculate rated output power.
(b) Calculate equivalent load resistance.
(c) Calculate duty ratio D for rated output. The voltage across the series resistor R
must be taken into consideration.
7-19
Example 3: Step-up (Boost) converter characteristics
A step-up dc-dc converter shown in the following figure is to be analyzed.
The input voltage Vd = 14 V.
The output voltage V0 = 42 V.
Inductor
L = 10 mH
Output resistor
R = 1Ω
Switching frequency fs=10 kHz
(a) Duty ratio, switch on and off time.
(b) Plot inductor and diode voltages.
7-20
Example 7-3: Cuk Converter
• The above Cuk converter is operating at 50 Hz, L1=L2=1 mH and C1=5 mF
• The output capacitor is sufficiently large to yield constant voltage
• Vd=10 V and the output V0 is regulated to be constant at 5 V
• It is supplying 5 W to a load
-------------------------------------------------------------------------------------------------------• Calculate the percentage errors in assuming a constant voltage across C1 or in
assuming constant currents iL1 and iL2.
7-21
Full-Bridge dc-dc Converter
•
•
•
•
Four-quadrant operation: magnitude and direction of both v0 and i0 can be
controlled
This converter consists of two legs, A and B. Each leg consists of two switches
and their antiparallel diodes
A reversible flow of power is made possible by connecting diodes in antiparallel
with switches
Applications: dc motor drives and dc-to-ac conversion
7-22
•
•
•
•
•
•
One of the two switches in each leg is ON
The output current io will flow continuously
(TA+ , TB-) and (TA- , TB+) are treated as two
switch pairs: switches in each pair are
turned ON and OFF simultaneously
vAN=Vd
(if TA+ is ON and TA- is OFF) :: output current will flow through
TA+ if io is positive or it will flow through DA+ if io is negative
vAN=0
(if TA- is ON and TA+ is OFF) :: output current will flow through
TA- if io is negative or it will flow through DA- if io is positive
The average output voltage of the converter leg A:
VAN 
Vd ton  0  toff
Ts
 Vd  duty ratio of TA
where ton and toff are the ON and OFF intervals of TA+, respectively. Output voltage
is independent of the direction of io
7-23
•
•
Similar arguments apply to the converter leg B.
VBN depends on Vd and the duty ratio of the switch TB+:
VBN  Vd  duty ratio of TB
•
•
VBN is independent of the direction of io
Output voltage V0 (=VAN-VBN) can be controlled by controlling the switch duty ratios
7-24
•
•
•
•
(TA+ , TB-) and (TA- , TB+) are two switch
pairs: one of the two switch pairs is always
ON
Switching signal is generated by comparing
a switching-frequency triangular wave with
a control voltage
If vcontrol>vtri: TA+ and TB- are ON
If vcontrol<vtri: TA- and TB+ are ON
7-25

vtri  V tri
t
Ts
0t 
Ts
4
4
at t  t1
t1 
vcontrol Ts

4
V
tri
1
ton  2t1  Ts
2
ton 1  vcontrol 
Duty ratio of pair1 : D1 
 1 

Ts 2 
V tri 

Duty ratio of pair 2 : D1  1  D1 TB  , TA 
V0  VAN  VBN  D1Vd  D2Vd  2 D1  1Vd 
TA , TB  
Vd

vcontrol  kvcontrol
V tri
• V0 varies linearly with the input
control signal
7-26
Comparison of Converters
• Buck converter: step-down, has one switch, simple, high efficiency greater
than 90%, provides one polarity output voltage and unidirectional output
current
• Boost converter: step-down, has one switch, simple, high efficiency,
provides one polarity output voltage and unidirectional output current,
requires a larger filter capacitor and a larger inductor than those of a buck
converter
• Buck-boost converter: step-up/step-down, has one switch, simple, high
efficiency, provides output voltage polarity reversal
• Cuk converter: step-up/step-down, has one switch, simple, high efficiency,
provides output voltage polarity reversal, additional capacitor and inductor
needed
• Full-bridge converter: four-quadrant operation, has multiple switches, can
be used in regenerative braking
7-27
Conclusions
• In many industrial applications, it is required to convert fixed dc voltage
into variable dc voltage
• Various types of dc-to-dc converters
• Operation of dc-to-dc converters
• The step-down, step-up, buck-boost and Cuk converters are only capable
of transferring energy only in one direction
• A full-bridge converter is capable of a bidirectional power flow
• Like ac transformers, dc converters can be used to step-up or step-down a
dc voltage source
• Applications: electric automobiles, trolley cars, marine hoists, mine
haulers, etc.
• Also used in regenerative braking of dc motors to return energy back into
the supply –energy savings for transportation systems with frequent stops
7-28