MIC2155 Datasheet, PDF (22/33 Pages) Micrel Semiconductor – 2-Phase, Single Output, PWM Synchronous Buck Control IC

Micrel, Inc.
I_OUT is output current of the each channel or ½ of
the total output current
η is the converters efficiency
For this example:
L = ^{1.8V × (0.88 ×12V − 1.8V)} = 1μH
0.88 ×12V × 500kHz × 0.2 ×15A
If another inductor value is used, the ripple current for
each channel is calculated from the formula below:
I_PP
=
V_OUT × (η × V_IN(MAX) − V_OUT )
η × V_IN(MAX) × f_S × L
I_PP
=
1.8V × (0.88 ×12V − 1.8V)
0.88 ×12V × 500kHz ×1μH
=
3A
The output capacitors see less ripple current than each
channel because they are out of phase.
The normalizing factor is
V_{OUT =}
1.8V
= 3.6
f_S × L_OUT 500kHz ×1μH
The output ripple current in the 2-phase configuration is
approximately:
0.65 × ^VOUT = 0.65 × ^1.8V
= 2.3A
f_S × L_OUT
500kHz ×1μH
For the input and output voltage in this application, going
to a 2-phase design decreased the total output ripple
current from 3A_PP to 2.3A_PP.
The peak inductor current in each channel is equal to the
average output current plus one half of the peak to peak
inductor ripple current.
I_PK = I_OUT + 0.5 × I_PP = 15A + 0.5 × 3A = 16.5A
The RMS inductor current is used to calculate the I² × R
losses in the inductor.
I_{INDUCTOR(RMS)} = I_OUT ×
1+
1
12
⎜⎜⎝⎛
I_PP
I_OUT
⎟⎟⎠⎞²
I_{INDUCTOR(RMS)} = 15A ×
1+ ¹ ⎜⎛ ^3A ⎟⎞² = 15.1A
12 _⎝ 15 _⎠
Maximizing efficiency requires the proper selection of
core material and minimizing the winding resistance. The
high frequency operation of the MIC2155 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 inductor 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,
MIC2155/2156
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.
For this example a Cooper HCF1305-1R0 inductor was
chosen. Core loss for this application was taken from
the data sheet and is 15mW. Winding resistance is
1.9mohms
Copper loss in the inductor is calculated by the equation
below:
P_{INDUCTOR(COPPER)} = (I_{INDUCTOR(RMS)} )² × R_WINDING
= 15.1² ×1.9mΩ = 0.43W
The resistance of the copper wire, R_WINDING, increases
with temperature. If so desired, a more accurate
calculation can be made if the maximum ambient
temperature and temperature rise of the inductor is
known. The value of the winding resistance at operating
temperature is calculated with the formula below.
R_WINDING(HOT) = R_WINDING(20) × (1+ 0.0042 × (Temp_HOT − T₂₀ )
Where:
Temp_HOT is the temperature of the wire under operating
load
T₂₀ is the ambient temperature
R_WINDING(20) is the resistance of the winding at room
temperature, usually specified by the manufacturer.
For this example, the approximate power dissipation is
0.43W. From the manufacturers data sheet this causes a
20°C rise in inductor temperature. Assuming ambient
temperature stayed at 20°C, the maximum winding
resistance would be increased from 1.9mohms to:
R_WINDING(HOT) = 1.9mΩ × (1+ 0.0042 × (40°C − 20°C) = 2.06mΩ
Output Capacitor Selection
In this example, the output capacitors are chosen to
keep the output voltage ripple below a specified value.
The output ripple voltage is determined by the capacitors
ESR (equivalent series resistance) and capacitance.
Voltage rating and RMS current capability are two other
important factors in selecting the output capacitor.
Ceramic output capacitors and most polymer capacitors
have very low ESR and are recommended for use with
the MIC2155/6. The output capacitance is usually the
primary cause of output ripple in Ceramic and very low
ESR capacitors. The minimum value of Cout is
calculated below:
C_OUT
≥
I_PP
8 × ΔV_OPP × 2 × f_S
Where:
May 2009
22
M9999-052709-A
[phone]