1. 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

2. 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

3. 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

4. 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

5. 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:
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

6. Step-Down (Buck) Converter: Continuous current conduction mode
Inductor current iL flows continuously
Average inductor voltage over a time period must be zero
Assuming a lossless circuit
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. 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.

8. Solution….
D = V0 /Vd = 5/40 = = 12.5%
Ts = 1/fs = 0.25 ms = 250 ms
Ton = DTs = ms
Toff = Ts – ton = 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 = A

9. 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

10. Step-Up (Boost) Converter: Continuous current conduction mode
Inductor current iL flows continuously
Average inductor voltage over a time period must be zero
Dividing both side by Ts
Assuming a lossless circuit

11. 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

12. 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 step-up 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
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

13. Buck-Boost Converter: Continuous current conduction mode
Inductor current iL flows continuously
Average inductor voltage over a time period must be zero
Assuming a lossless circuit
Depending on the duty ratio, the output voltage can be either higher or lower than the input

14. 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

15. 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

16. 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

17. Steady-state current and voltage equations…………..Cuk
Vc1 is constant and average voltages across L1 and L2 over a time period must be zero
Equating the above two equations,

18. 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 Vd
vo= Vo +
voi - id io Ia La ea
The output voltage, Vo, equals 200V.
Calculate the input voltage, Vd
Find the ripple in the armature current.
Calculate the maximum and the minimum value of the armature current
Sketch the armature current, ia(t), and the dc current, id(t).

19. 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.

20. 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 = 1 Ω
Switching frequency fs=10 kHz
(a) Duty ratio, switch on and off time.
(b) Plot inductor and diode voltages.

21. 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.

22. 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

23. 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:
where ton and toff are the ON and OFF intervals of TA+, respectively. Output voltage is independent of the direction of io

24. Similar arguments apply to the converter leg B.
VBN depends on Vd and the duty ratio of the switch TB+:
VBN is independent of the direction of io
Output voltage V0 (=VAN-VBN) can be controlled by controlling the switch duty ratios

25. (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

26. V0 varies linearly with the input control signal

27. 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

28. 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