DC-DC CONVERTERS

Classification

of DC- DC Converters

The converter

topologies are classified as:

Ø

Buck Converter: In Figure 1a a

buck converter is shown. The buck converter is step down converter

and produces a lower average output voltage than the dc input voltage.

Ø

Boost

converter: In Figure 1b a boost converter is shown. The output

voltage is always greater than the input voltage.

Ø

Buck-Boost converter: In Figure 1c a

buck-boost converter is shown. The output voltage can be either higher or lower

than the input voltage.

Figure 1a: General

Configuration Buck Converter Figure

1b: General Configuration Boost Converter

Figure 1c: General Configuration Buck-Boost Converter

Principle of Step Down Operation

The principle of step

down operation of DC-DC converter is explained using the circuit shown in Figure

2a. When the switch 1 S is closed for time

duration 1

T ,

the input voltage in V appears across the

load. For the time duration 2 T is switch 1

S remains

open and the voltage across the load is zero. The waveforms of the output

voltage across the load are shown in Figure 2b.

Figure 2a: Step down operation Figure 2b: Voltage across the

load resistance

The average output voltage is given by

The average load

current is given by

Where

T

is the chopping period

D = T1/ T2

F is the chopping frequency

The rms value of the output voltage is

given by

In case the

converter is assumed to be lossless, the input power to the converter will be

equal to the output power. Hence, the input power ( P) is given by

The effective resistance seen by the

source is

The duty cycle can be varied from 0 to 1

by varying T1 , T or f . Thus, the output voltage V0avg

can be varied from 0 to Vin by controlling D and eventually the

power flow can be controlled.

The Buck Converter with RLE Load

The buck converter is a voltage step

down and current step up converter. The two modes in steady state operations

are:

Mode 1 Operation

In this mode the switch S1 is

turned on and the diode D1 is reversed biased, the current flows

through the load. The time domain circuit is shown in Figure3. The load

current, in s-domain, for mode 1 can be found from

Where

I0 is the initial value of

the current and I0 =I1.

Figure

3: Time domain circuit of buck converter in mode 1

From equation 6, the current I1(s)

is given by

In time domain the solution of equation 7 is

given by

The mode1 is valid for the time

duration 0?t?T1 ? 0?t?DT. At the end of this mode, the load current

becomes

i1(t = T1 = DT) =

I2 (9)

Mode 2 Operation

Figure 4: Time domain circuit

of buck converter in mode 2

In this mode the switch 1 S is turned off

and the diode 1

D

is

forward biased. The time domain circuit is shown in Figure4. The load

current, in s

domain,

can be found from

Where

I02

is

the initial value of load current.

The current at the end of mode1 is

equal to the current at the beginning of mode 2.

Hence, from equation 9 I02 is

obtained as

I02 = I2 (11)

Hence, the load current is time domain is obtained

from equation 10 as

Determination of I1 and I2

At the end of mode 2 the

load current becomes

i2 = (t = T2 =

(1-D)T) = I3 (13)

At the end of mode 2, the

converter enters mode 1 again. Hence, the initial value of

current in mode 1 is

I01 = I3 = I1 (14)

From equation 8 and equation

12 the following relation between and is obtained as

Solving equation 15 and equation

16 for I1 and I2 gives 1

Where

Where f is the chopping frequency.

Current Ripple

The

peak to peak current ripple is given by

In case fL >>R , a?0

. Hence, for the limit a?0 equation 20 becomes

To determine the maximum current ripple

(?Imax ), the equation 20a is differentiated w.r.t. D. The

value of ?Imax is given by

For the condition , 4fL>> R

Hence, the maximum current ripple is

given by

If equation 20b is used to

determine the maximum current ripple, the same result is obtained.

Continuous and Discontinuous Conduction

Modes

In case of large off time, particularly

at low switching frequencies, the load current may be discontinuous, i.e. i2(t

= T2 = (1-D)T) will be zero.

The necessary condition to ensure continuous conduction is given by

The Buck Converter with R Load and

Filter

The output voltage and current of the

converter contain harmonics due to the switching action. In order to remove the

harmonics LC filters are used. The circuit diagram of the buck converter with

LC filter is shown in Figure 5. There are two modes of operation as

explained in the previous section.

The voltage drop across the inductor in mode

1 is

Where iL is the current through

the inductor Lf

isw is the current through

the switch

The switching frequency of the converter is very

high and hence, iL changes linearly.

Thus, equation 25 can be written

as

where

Ton is the duration for which the switch S remains on

T is the switching time

period

Figure 5: Buck converter with resistive load and

filter Figure 6: Voltage and

current waveform

Hence, the current ripple ?IL

is given by

When the switch S is turned

off, the current through the filter inductor decreases and the current through

the switch S is zero. The voltage equation is

Where iD is the

current through the diode D

Due to high switching

frequency, the equation 28 can be written as

Where Toff is the

duration in which switch S remains off the diode D conducts Neglecting the very

small current in the capacitor Cf, it can be seen that

i0 = iSW for

time duration in which switch conducts and

i0 = iD

for the time duration in which the diode D conducts

The current ripple obtained

from equation 29 is

The voltage and current

waveforms are shown in Figure 6.

From equation 27 and equation

30 the following relation is obtained for the current ripple

Hence, from equation 31 the

relation between input and output voltage is obtained as

If the converter is assumed

to be lossless, then

The switching period T can

be expressed as

From equation 34 the

current ripple is given by

Substituting the value of V0

from equation 32 into equation 35 gives

Using the Kirchhoff’s

current law, the inductor current iL is expressed as

If the ripple in load

current (i0 ) is assumed to be small and negligible, then

The incremental voltage ?VC

across the capacitor (Cf ) is associated with incremental charge ?Q

by the relation

The area of each of the

isoceles triangles representing ?Q in Figure 6 is given by

Combining equation 39 and

equation 40 gives

Substituting the value of ?IL

from equation 31 into equation 41 gives

MODELING AND DESIGN OF BASIC DC-DC CONVERTERS:

BUCK CONVERTER:

Figure7 circuit diagram of

buck converter

Figure8 input and output

waveforms of buck converter

Boost converter:

Figure9 circuit diagram of

boost converter

Figure10 input and output

waveforms of boost converter

Buck Boost converter:

Figure11 circuit diagram of

buck boost converter

Figure12 input and output

waveforms of buck boost converter