MIC2570
at each cycle. At the threshold between continuous and
discontinuous operation we can use the fact that I
1
= I
2
to get:
L =
V
×
t
1
I
Micrel
V
1
×
t
1
= V
2
×
t
2
t
V
1
=
2
t
1
V
2
This relationship is useful for finding the desired oscillator
duty cycle based on input and output voltages. Since input
voltages typically vary widely over the life of the battery, care
must be taken to consider the worst case voltage for each
parameter. For example, the worst case for t
1
is when V
IN
is
at its minimum value and the worst case for t
2
is when V
IN
is
at its maximum value (assuming that V
OUT
, V
DIODE
and V
SAT
do not change much).
To select an inductor for a particular application, the worst
case input and output conditions must be determined. Based
on the worst case output current we can estimate efficiency
and therefore the required input current. Remember that this
is
power
conversion, so the worst case average input current
will occur at maximum output current and minimum input
voltage.
Average I
IN(max)
=
V
OUT
×
I
OUT(max)
V
IN(min)
×
Efficiency
L =
V
IN(min)
2
×
Average I
IN(max)
×
t
1
where t
1
=
duty cycle
f
OSC
To illustrate the use of these equations a design example will
be given:
Assume:
MIC2570-1 (fixed oscillator)
V
OUT
= 5V
I
OUT(max)
=50mA
V
IN(min)
= 1.8V
efficiency = 75%.
Average I
IN(max)
=
L =
5V
×
50mA
= 185.2mA
1.8V
×
0.75
1.8V
×
0.7
2
×
185.2mA
×
20kHz
L = 170µH
Use the next lowest standard value of inductor and verify that
it does not saturate at a current below about 400mA
(< 2
×
185.2mA).
4
Referring to Figure 1, it can be seen the peak input current will
be twice the average input current. Rearranging the inductor
equation to solve for L:
1997
4-69
MICREL [ MICREL SEMICONDUCTOR ]
