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Typical Applications

(Continued)

d

V

T

i

L

From the relation V

L

I

j

e

L

L

d

L1

t

(V

V

) t

V

b

IN

o

ON

I

a

I

b

e

e

L

L

L1

Neglecting V

V

and settling

I

a

e

SAT

D

L

t

ON

V

j V

V

e

o

IN

IN

t

t

a

OFF

ON

where T

Total Period

e

The above shows the relation between V

IN

cycle

t

ON

I

I

e

IN(DC)

OUT(DC)

t

t

a

ON

OFF

as Q1 only conducts during t

ON

t

ON

P

I

V

(I

)

e

e

IN

IN(DC)

IN

o(DC)

t

t

a

ON

P

I

V

e

o

o

o

The efficiency

of the circuit is

P

I

V

o

o

o

MAX

e

e

P

(t

)

(V

t

IN

ON

SAT

ON

I

V

a

o

IN

T

V

o

for V

V

1V

e

e

e

SAT

D1

V

1

a

o

MAX will be further decreased due to switching losses in

Q1 For this reason Q1 should be selected to have the maxi-

mum possible f

which implies very fast rise and fall times

T

CALCULATING INDUCTOR L1

( I

a

)

L1

( I

b

c

L

L

t

t

j

e

ON

OFF

(V

V

)

V

b

IN

o

( I

a

)

L1

( I

b

c

L

L

t

t

T

a

e

e

a

ON

OFF

(V

V

)

V

b

IN

Q

0 4I

L1

0 4I

L1

o

o

e

a

(V

V

)

V

b

IN

o

o

Since I

a

I

b

0 4I

e

e

L

L

o

FIGURE 14

Solving the above for L1

t

L1

o

OFF

L1

I

b

L

where L1 is in Henrys

f is switching frequency in Hz

t

ON

Also see LM1578 data sheet for graphical methods of in-

T

ductor selection

CALCULATING OUTPUT FILTER CAPACITOR C

V

and duty

o

Figure 14 shows L1’s current with respect to Q1’s t

t

times This curent must flow to the load and C

OFF

current will then be the difference between I

From Figure 14 it can be seen that current will be flowing

into C

for the second half of t

o

V

IN

t

or a time t

OFF

ON

OFF

time is

I

4 The resulting

L

1

I

L

V

e

c

op-p

C

4

I

t

L

ON

V

t

)

a

e

D1

OFF

I

4C

o

T

V

(T

b

o

Since I

e

L

L1

T

V

o

V

e

op-p

4C L1

C

o

)

L1

c

where C is in farads T is

o

)

L1

c

V

is p-p output ripple

o

o

For best regulation the inductor’s current cannot be al-

lowed to fall to zero Some minimum load current I

thus inductor current is required as shown below

(V

IN

I

e

o(MIN)

TL H 8650– 18

11

2 5 V

(V

V

)

b

o

IN

o

e

I

V

f

o

IN

o

and

ON

C

’s

o

o

and I

L

o

Ic

I

I

e

b

o

L

o

through the first half of

ON

2

t

2 The current flowing for this

a

OFF

V

or

V

is described by

c

o

t

t

ON

OFF

a

c

2

2

t

a

OFF

2

t

)

V

T

ON

o

and t

e

ON

V

IN

V

T

o

b

2

V

T

(V

V

) V

T

b

IN

IN

o

o

or

e

2

8V

C

L1

IN

o

2

(V

V

) V

T

b

IN

o

o

e

8 V

V

L1

o

IN

1

switching frequency

and

o

V

) t

(V

V

) V

b

b

o

ON

IN

o

o

e

2L1

2fV

L1

IN

TL H 8650 – 19

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