MIC2166_1009 Datasheet, PDF (19/28 Pages) Micrel Semiconductor – Adaptive On-Time DC-DC Controller Hyper Speed Control™ Family

Micrel, Inc.
The applications are divided into three situations
according to the amount of the V_FB ripple:
1. Enough ripple at V_OUT due to the large ESR of the
output capacitors.
As shown in Figure 7a, the converter is stable without
any ripple injection. The V_FB ripple is:
ΔV_FB(pp)
=
R2
R1+ R2
× ΔV_OUT
(34)
where ΔV_OUT = ESR_COUT ⋅ ΔI_L(PP) , ΔI_L(PP) is the peak-
to-peak value of the inductor current ripple.
2. Inadequate ripple at V_OUT due to the small ESR of
the output capacitors.
The output voltage ripple is fed into the FB pin through a
feedforward capacitor C_ff in this situation, as shown in
Figure 7b. The typical C_ff value is between 1nF and
100nF. With the feedforward capacitor, V_FB ripple is very
close to the output voltage ripple:
ΔV_FB(pp) ≈ ΔV_OUT
(35)
3. Virtually no ripple at V_OUT due to the very low ESR of
the output capacitors.
In this situation, the output voltage ripple is less than
20mV. Therefore, additional ripple is injected into the FB
pin from the switching node SW via a resistor R_inj and a
capacitor C_inj, as shown in Figure 7c. The injected ripple
is:
ΔV_FB(PP)
=
V_IN
× K _div
× D × (1- D) ×
1
f_SW × τ
(36)
K _div
=
R1//R2
R_inj + R1//R2
(37)
where:
V_IN = Power stage input voltage at VIN pin
D = Duty Cycle
f_SW = switching frequency
τ = (R1// R2 // R_inj ) ⋅ C_ff
MIC2166
In equations (36) and (37), it is assumed that the time
constant associated with C_ff must be much greater than
the switching period:
1 ₌ T _{<< 1}
f_SW × τ τ
If the voltage divider resistors R1 and R2 are in the kΩ
range, a C_ff of 1nF to 100nF can easily satisfy the large
time constant consumption. Also, a 100nF injection
capacitor C_inj is used in order to be considered as short
for a wide range of the frequencies.
Figure 7a.
R2
R1+ R2
× ΔV_OUT
>
20mV
Figure 7b.
R2
R1 + R2
×
ΔV_OUT
< 20mV
and
Δ V_OUT
> 20mV
Figure 7c. ΔV_OUT < 20mV
September 2010
19
M9999-092410-C