MIC2166_1009 Datasheet, PDF (15/28 Pages) Micrel Semiconductor – Adaptive On-Time DC-DC Controller Hyper Speed Control™ Family

Micrel, Inc.
where:
R_DS(ON) = on-resistance of the MOSFET switch
D = Duty Cycle = V_OUT / V_IN
Making the assumption that the turn-on and turn-off
transition times are equal; the transition times can be
approximated by:
t_T
=
C_ISS
× V_DD + C_OSS × V_IN
I_G
(10)
where:
C_ISS and C_OSS are measured at V_DS = 0
I_G = gate-drive current
The total high-side MOSFET switching loss is:
P_AC = (V_IN + V_D )×I_PK × t _T × f_SW
(11)
where:
t_T = Switching transition time
V_D = Diode drop
f_SW = Switching Frequency
The high-side MOSFET switching losses increase with
the switching frequency and the input voltage V_IN. The
low-side MOSFET switching losses are negligible and
can be ignored for these calculations.
Inductor Selection
Values for inductance, peak, and RMS currents are
required to select the output inductor. The input and
output voltages and the inductance value determine the
peak-to-peak inductor ripple current. Generally, higher
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 equation 12:
L=
( ) V_OUT × V_{ΙΝ(max)} − V_OUT
V_{ΙΝ(max)} × f_SW × 20% × I_OUT(max)
(12)
MIC2166
where:
f_SW = switching frequency
20% = ratio of AC ripple current to DC output current
V_IN(max) = maximum power stage input voltage
The peak-to-peak inductor current ripple is:
ΔI_L(PP)
=
V_OUT × (V_IN(max) − V_OUT )
V_IN(max) × f_SW × L
(13)
The peak inductor current is equal to the average output
current plus one half of the peak-to-peak inductor current
ripple.
I_L(PK) = I_OUT(max) + 0.5 × ΔI_L(PP)
(14)
The RMS inductor current is used to calculate the I²R
losses in the inductor.
I_L(RMS) =
I_OUT(max)2
+
ΔI_L(PP)2
12
(15)
Maximizing efficiency requires the proper selection of
core material and minimizing the winding resistance. The
high-frequency operation of the MIC2166 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
calculated by the equation below:
P_INDUCTORCu=I_L(RMS)2 × R_WINDING
(16)
September 2010
15
M9999-092410-C