MIC2282 Datasheet, PDF (7/10 Pages) Micrel Semiconductor – Single-Cell Ultra Low EMI Boost LED Driver

Micrel, Inc.
They can also be very slow, especially those suited to
power rectification such as the 1N400x series, which
affects efficiency.
Inductor Behavior
The inductor is an energy storage and transfer device.
Its behavior (neglecting series resistance) is described
by the following equation:
I= ^V ×t
L
where:
V = inductor voltage (V)
L = inductor value (H)
t = time (s)
I = inductor current (A)
If a voltage is applied across an inductor (initial current is
zero) for a known time, the current flowing through the
inductor is a linear ramp starting at zero, reaching a
maximum value at the end of the period. When the
output switch is on, the voltage across the inductor is:
V₁ = V_IN – V_SAT
When the output switch turns off, the voltage across the
inductor changes sign and flies high in an attempt to
maintain a constant current. The inductor voltage will
eventually be clamped to a diode drop above V_OUT.
Therefore, when the output switch is off, the voltage
across the inductor is:
V₂ = V_OUT + V_DIODE – V_IN
For normal operation the inductor current is a triangular
waveform which returns to zero current (discontinuous
mode) at each cycle. At the threshold between
continuous and discontinuous operation we can use the
fact that I₁ = I₂ to get:
V₁ × t₁ = V₂ × t₂
V_{1 =} t ₂
V₂ t₁
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 t₁ is when V_IN is at its minimum value and the
worst case for t₂ is when V_IN is at its maximum value
(assuming that V_OUT, V_DIODE and V_SAT do not change
much).
MIC2282
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, one minimum input voltage.
Average I_IN(max)
=
V_OUT × I_OUT(max)
V_IN(min) × Efficency
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:
L
=
V
I
× t₁
L
=
V_IN(min)
2 × Average I_IN(max)
× t₁
where
t₁
=
duty cycle
f_OSC
=
0.67
20kHz
To illustrate the use of these equations a design
example will be given:
Assume:
V_OUT = 3.0V
I_OUT(max) =10mA
V_IN(min) = 1.0V
efficiency = 75%
Average I_IN(max)
=
5V × 5mA
1.0V × 0.75
=
33.3mA
L=
1.0V × 0.7
2 × 33.3mA × 20kHz
I_IN(max)
=
3.0 × 10mA
1.0 × .75
=
40mA
L = ^{1.0V × 0.7} = 438µH
2 × 40 × 20kHz
L = 438µH
Use the next lowest standard value of inductor and verify
that it does not saturate at a current below about 75mA
(< 2 ⋅ 33.3mA).
October 2009
7
M9999-102309