MIC2103 Datasheet, PDF (24/36 Pages) Micrel Semiconductor – 75V, Synchronous Buck Controllers featuring Adaptive On-Time Control

Micrel, Inc.
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:
I_L(pp)

V_OUT  (V_IN(max)  V_OUT )
V_IN(max)  f_sw  L
(Eq. 14)
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)
(Eq. 15)
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
(Eq. 16)
Maximizing efficiency requires the proper selection of
core material and minimizing the winding resistance. The
high frequency operation of the MIC2103/04 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 magnetic vendor.
Copper loss in the inductor is calculated by Equation 17:
P_INDUCTOR(Cu) = I_L(RMS)2  R_WINDING
(Eq. 17)
The resistance of the copper wire, R_WINDING, increases
with the temperature. The value of the winding
resistance used should be at the operating temperature.
MIC2103/04
P_WINDING(Ht) = R_{WINDING(20°C)}  (1 + 0.0042 × (T_H – T_20°C)) (Eq. 18)
where:
T_H = temperature of wire under full load
T_20°C = ambient temperature
R_{WINDING(20°C)} = room temperature winding resistance
(usually specified by the manufacturer)
Output Capacitor Selection
The type of the output capacitor is usually determined by
its ESR (equivalent series resistance). Voltage and RMS
current capability are two other important factors for
selecting the output capacitor. Recommended capacitor
types are tantalum, low-ESR aluminum electrolytic, OS-
CON and POSCAP. The output capacitor’s ESR is
usually the main cause of the output ripple. The output
capacitor ESR also affects the control loop from a
stability point of view. The maximum value of ESR is
calculated:
ESR _COUT

ΔV_OUT(pp)
ΔI_L(PP)
(Eq. 19)
where:
ΔVOUT(pp) = peak-to-peak output voltage ripple
ΔI_L(PP) = peak-to-peak inductor current ripple
The total output ripple is a combination of the ESR and
output capacitance. The total ripple is calculated in
Equation 20:
ΔV_OUT(pp) 
  _{}
C
ΔI_L(PP)
OUT ^{ f}SW
 8 ^{2}

ΔI_L(PP)  ESR _COUT
2
(Eq. 20)
where:
D = duty cycle
C_OUT = output capacitance value
f_sw = switching frequency
As described in the “Theory of Operation” subsection in
Functional Description, the MIC2103/04 requires at least
20mV peak-to-peak ripple at the FB pin to make the g_m
amplifier and the error comparator behave properly.
Also, the output voltage ripple should be in phase with
the inductor current. Therefore, the output voltage ripple
caused by the output capacitors value should be much
August 2012
24
M9999-080712-A