MIC2155_0911 Datasheet, PDF (23/35 Pages) Micrel Semiconductor – Two-Phase, Single-Output, PWM Synchronous Buck Control IC

Micrel, Inc.
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) x (1 + 0.0042 x
(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 1.9mΩs 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 C_OUT is
calculated below:
C_OUT
≥
I_PP
8 × ΔV_OPP × 2 × f_S
Where:
ΔV_OPP is the peak-to-peak output voltage ripple
I_PP is the peak-to-peak ripple current as see by the
capacitors
f_S is the per channel switching frequency
Notice the calculation is performed at 2x the switching
frequency since the capacitors see ripple current from
both phases.
MIC2155/2156
For this example, using ΔV_OPP = 10mV, the minimum
C_OUT is:
C_OUT
≥
2.3
8 ×10mV × 2 × 500kHz
=
29μF
A capacitance value this low is usually not used in high
current converters because of transient output current
requirements.
For this example, 500µF total capacitance is used. It is
split up into (4) 47µF ceramic capacitors and (2) 150µF
Aluminum Polymer capacitors
The total output ripple is a combination of the ESR and
the output capacitance. The total ripple is calculated
below:
[ ] ΔV_OUT =
⎡
⎢
⎣
8
×
I_PP
C_OUT ×
2
×
f_S
⎤²
⎥
⎦
+
I_PP
× R_ESR
2
To increase reliability, the recommended voltage rating
of capacitor should be twice the output voltage for a
tantalum and 20% greater for an aluminum electrolytic or
ceramic.
The output capacitor RMS current is calculated below:
I_COUT(RMS)
=
I_PP
12
=
2.3A
12
= 0.66A
The power dissipated in the output capacitors can be
calculated by the equation below:
( ) P_DISS(COUT) = I_COUT(RMS) ² × R_ESR
November 2009
23
M9999-111209-B