MIC2159 Datasheet, PDF (10/17 Pages) Micrel Semiconductor – SYNCHRONOUS-itty™ Step-Down Converter IC

Micrel
inductance values are used with higher input voltages.
Larger peak-to-peak ripple currents will increase the
power dissipation in the inductor and MOSFETs. Larger
output ripple currents will also require more output
capacitance to smooth out the larger ripple current.
Smaller peak-to-peak ripple currents require a larger
inductance value and therefore a larger and more
expensive inductor. A good compromise between size,
loss and cost is to set the inductor ripple current to be
equal to 20% of the maximum output current. The
inductance value is calculated by the equation below.
( ) L = VOUT ⋅ VIN(max) − VOUT
V_IN(max) ⋅ F_S ⋅ 0.2 ⋅ I_{OUT (max)}
where:
F_S = switching frequency, 400 kHz
0.2 = ratio of AC ripple current to DC output
current
V_IN(max) = maximum input voltage
The peak-to-peak inductor current (AC ripple
current) is:
I_PP
= ^{VOUT .(VIN(max) − VOUT )}
V_{IN (max)}.F_S .L
The peak inductor current is equal to the average output
current plus one half of the peak-to-peak inductor ripple
current.
I_PK = I_OUT(max)+0.5 x I_PP
The RMS inductor current is used to calculate the I2R
losses in the inductor.
I_INDUCTOR = I_{OUT (max)} ⋅
1+
1
3
⋅
⎜⎛ ^IPK
⎜⎝ _{IOUT (max)}
⎟⎞²
⎟⎠
Maximizing efficiency requires the proper selection of
core material and minimizing the winding resistance. The
high frequency operation of the MIC2159 requires the
use of ferrite materials for all but the most cost sensitive
applications.
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 inductor. 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
MIC2159
calculated by the equation below:
P_INDUCTORCu = I_{INDUCTOR(rms)2}.R_WINDING
The resistance of the copper wire, RWINDING,
increases with temperature. The value of the winding
resistance used should be at the operating temperature.
( ( )) R_{WINDING(hot )} = R_WINDING(20o_C) ⋅ 1 + 0.0042 ⋅ T_HOT − T₂₀o_C
Where:
T_HOT = temperature of wire under full load
T_20oC = ambient temperature
R_WINDING(20o_C) = room temperature winding
resistance (usually specified by manufacturer)
Output Capacitor Selection
The output capacitor values are usually determined by
the capacitors ESR (equivalent series resistance).
Voltage and RMS current capability are two other
important factors for selecting the output capacitor.
Recommended capacitors are tantalum, low-ESR
aluminium electrolytic, and POSCAPS. The output
capacitor’s ESR is usually the main cause of output
ripple. The output capacitor ESR also affects the overall
voltage feedback loop from a stability point of view. See
“Feedback Loop Compensation” section for more
information. The maximum value of ESR is calculated:
R_ESR
≤
∆V_OUT
I_PP
Where:
V_OUT = peak-to-peak output voltage ripple
I_PP = peak-to-peak inductor ripple current
The total output ripple is a combination of the
ESR and output capacitance. The total ripple
is calculated below:
∆V_OUT =
⎜⎜⎝⎛
I_PP ⋅ (1 − D)
C_OUT ⋅ F_S
⎟⎟⎠⎞
2
+
(I_PP
⋅ R_ESR
)²
Where:
D = duty cycle
C_OUT = output capacitance value
f_S = switching frequency
The voltage rating of the capacitor should be
twice the voltage for a tantalum and 20%
greater for aluminium electrolytic. The output
capacitor RMS current is calculated below:
I_{COUT (rms )}
=
I _PP
12
The power dissipated in the output capacitor is:
P_{DISS (COUT}
)
=
I_COUT
(rms
2
)
⋅
R_{ESR (COUT}
)
October 2006
10
M9999-101206