April 2005

9

M9999-062205

MIC2168A

Micrel, Inc.

I

V

(V m

V

)

V m

f

L

PP

OUT

V

(

V

(

IN

V m

V m

OUT

V

)

V

)

IN

V m

V m

S

f

L

f

L

=

×

−

V

(

V

(V m

V m

V m

V m

V m

V m

× ×

f

L

f

L

f

L

f

L

f

L

f

L

(

)

V m

V max

ax

(

)

V m

V max

ax

×

−

×

−

V m

V m

V m

V max

ax

ax

ax

(

)

V m

V max

ax

Thepeakinductorcurrentisequaltotheaverageoutputcurrent

plus one half of the peak-to-peak inductor ripple current.

I

I

0.5 I

PK

I

I

I

I

OUT

PP

=

+

I

I

I

I

OUT

OUT

×

(

)

max

max

=

+

=

+

max

max

max

max

losses in the inductor.

I

I

x

1

x

1

1

3

I

I

m

INDUCTOR(rms)

I

I

I

I

OUT

P

OUT

I

m

I

m

2

x

1

x

1

=

×

I

I

I

I

OUT

OUT

+









(

)

ma

max

1

x

1

(

)

ma

max

1

x

1

=

×

=

×

ma

ma

ma

max

1

x

1

x

1

x

1

(

)

I

m

I

max

ax

Maximizing efficiency requires the proper selection of core

material and minimizing the winding resistance. The high

frequency operation of the MIC2168A requires the use of

ferrite materials for all but the most cost sensitive applica-

tions. Lower cost iron powder cores may be used but the

increase in core loss will reduce the efficiency of the power

supply. This is especially noticeable at low output power. The

winding resistance decreases efficiency at the higher output

current levels. The winding resistance must be minimized

although this usually comes at the expense of a larger induc-

tor. The power dissipated in the inductor is equal to the sum

of the core and copper losses. At higher output loads, the

core losses are usually insignificant and can be ignored. At

lower output currents, the core losses can be a significant

contributor. Core loss information is usually available from the

magnetics vendor. Copper loss in the inductor is calculated

by the equation below:

P

I

R

INDUCTOR

P

I

P

I

Cu

P

I

P

I

INDUCTOR(rms)

WINDING

2

=

×

P

I

P

I

INDUCTOR(rms)

temperature.The value of the winding resistance used should

be at the operating temperature.

R

R

WINDING(hot)

R

R

R

=

×

R

R

R

WINDING(20 C)

C)

(

)

1 0

1 0.0042

.0042

(T

(T

T

)

T

)

HOT

HOT

20

20

T

)

T

)

T

)

T

)

C

C

T

)

T

)

T

)

T

)

+

×

+

×

1 0

1 0

1 0

1 0.0042

.0042

.0042

.0042

−−

°

°

C)

C)

=

×

=

×

C)

C)

C)

C)

(

)

(

)

1 0

1 0

1 0

1 0.0042

.0042

.0042

.0042

(T

(T

(T

(T

T

)

T

)

T

)

T

)

HOT

HOT

HOT

HOT

T

)

T

)

T

)

T

)

T

)

T

)

T

)

+

×

+

×

+

×

+

×

1 0

1 0

1 0

1 0

1 0

1 0

1 0.0042

.0042

.0042

.0042

.0042

.0042

.0042

where:

ally specified by the manufacturer)

WINDING(20°C)

WINDING(20°C)

Output Capacitor Selection

The output capacitor values are usually determined capaci-

tors ESR (equivalent series resistance). Voltage and RMS

current capability are two other important factors selecting

the output capacitor. Recommended capacitors tantalum,

low-ESR aluminum electrolytics, and POSCAPS. The output

capacitor’s ESR is usually the main cause of output ripple.

The output capacitor ESR also affects the overall voltage

feedbackloopfromstabilitypointofview.See“FeedbackLoop

Compensation” section for more information. The maximum

value of ESR is calculated:

R

V

I

ESR

OUT

PP

≤

∆

where:

The total output ripple is a combination of the ESR output

capacitance. The total ripple is calculated below:

∆V

I

(1 D)

C

f

OUT

PP

I

(

I

(

OUT

C

f

C

C

f

C

f

2

2

=

× −

I

(

I

(1 D

1 D

C

f

C

f

















+

×

(

)

I

R

I

R

PP

PP

ESR

ESR

+

×

+

×

I

R

I

R

I

R

I

R

I

R

I

R

I

R

I

R

I

R

I

R

I

R

where:

D = duty cycle

The voltage rating of capacitor should be twice the voltage for

a tantalum and 20% greater for an aluminum electrolytic.

The output capacitor RMS current is calculated below:

I

I

12

C

PP

OUT(rms)

=

The power dissipated in the output capacitor is:

P

I

R

DISS(C

P

I

P

ESR(C

)

OUT

OUT(rms) 2

OUT

)

P

I

P

I

=

×

P

I

P

Input Capacitor Selection

The input capacitor should be selected for ripple current rating

and voltage rating. Tantalum input capacitors may fail when

subjected to high inrush currents, caused by turning the input

supply on. Tantalum input capacitor voltage rating should

be at least 2 times the maximum input voltage to maximize

reliability. Aluminum electrolytic, OS-CON, and multilayer

polymer film capacitors can handle the higher inrush currents

without voltage derating.The input voltage ripple will primarily

depend on the input capacitor’s ESR. The peak input current

is equal to the peak inductor current, so:

∆V

I

R

IN

V

I

V

ESR(C

)

IN

=

×

V

I

V

INDUCTOR(peak)

The input capacitor must be rated for the input current ripple.

The RMS value of input capacitor current is determined at

the maximum output current. Assuming the peak-to-peak

inductor ripple current is low: