MIC2166_1009 Datasheet, PDF (16/28 Pages) Micrel Semiconductor – Adaptive On-Time DC-DC Controller Hyper Speed Control™ Family

Micrel, Inc.
MIC2166
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.
R_WINDING = R_{WINDING(20°C)} ×
(1+ 0.0042 × (T_H – T_20°C))
(17)
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 capacitors
are tantalum, low-ESR aluminum electrolytic, OS-CON,
POSCAPS, and ceramic. 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)
(18)
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 below:
( ) ΔV_OUT(PP) =
⎜⎜⎝⎛
ΔI_L(PP)
C_OUT × f_SW
×
8 ^{⎟⎟⎠⎞2}
+
ΔI_L(PP) × ESR_COUT
2
(19)
where:
C_OUT = output capacitance value
f_SW = switching frequency
As described in the “Theory of Operation” subsection in
“Functional Description”, MIC2166 requires at least
20mV peak-to-peak ripple at the FB pin to make the g_m
amplifier and the error comparator to behavior properly.
Also, the output voltage ripple should be in phase with
the inductor current. Therefore, the output voltage ripple
caused by the output capacitor C_OUT should be much
smaller than the ripple caused by the output capacitor
ESR. If low ESR capacitors, such as ceramic capacitors,
are selected as the output capacitors, a ripple injection
method should be applied to provide the enough FB
voltage ripples. Please refer to the “Ripple Injection”
subsection for more details.
The voltage rating of the capacitor should be twice the
output voltage for a tantalum and 20% greater for
aluminum electrolytic or OS-CON. The output capacitor
RMS current is calculated below:
I_{COUT (RMS)}
=
ΔI_L(PP)
12
(20)
The power dissipated in the output capacitor is:
P_{DISS(COUT )} = I_{COUT (RMS)2} × ESR _COUT (21)
Input Capacitor Selection
The input capacitor for the power stage input V_IN should
be selected for ripple current rating and voltage rating.
Tantalum input capacitors may fail when subjected to
high inrush currents, caused by turning on a “hot-
plugging”. A tantalum input capacitor’s voltage rating
should be at least two times the maximum input voltage
to maximize reliability. Aluminum electrolytic, OS-CON,
and multilayer polymer film capacitors can handle the
higher inrush currents without voltage de-rating. The
input voltage ripple will primarily depend upon the input
capacitor’s ESR. The peak input current is equal to the
peak inductor current, so:
ΔV_IN = I_L(PK) × ESR _CIN
(22)
The input capacitor must be rated for the input current
ripple. The RMS value of input capacitor current is
determined at the maximum output current. Assuming
the peak-to-peak inductor current ripple is low:
( ) I_CIN(RMS) ≈ I_OUT(max) × D × 1 − D
(23)
The power dissipated in the input capacitor is:
P_{DISS(CIN )}
=
I_CIN
2
(RMS)
× ESR _CIN
(24)
September 2010
16
M9999-092410-C