MIC2128 Datasheet, PDF (23/32 Pages) Microchip Technology – 75V, Synchronous Buck Controller Featuring Adaptive On-Time Control with External Soft Start

EQUATION 5-23:
C_IN = ^I---^L-_-^O----^A_---^D--_f-_S--^-_W---^D--_----^-_----^_V--1--_I--_N-–---_{_}-^D-_C----^
Where:
I_LOAD
I_{L_PK}
V_INC
V_INESR
η
ESR_{C_IN} = ^-----^V-_I--_LI--^N-_{_}--_P-^_--_KE---^S--^R--
= Load Current
= Peak Inductor Current
= Input ripple due to capacitance
= Input ripple due to input capacitor ESR
= Power conversion efficiency
The input capacitor should be rated for ripple current
rating and voltage rating. The RMS value of input
capacitor current is determined at the maximum output
current. The RMS current rating of the input capacitor
should be greater than or equal to the input capacitor
RMS current calculated using the Equation 5-24.
EQUATION 5-24:
I_{C_IN(RMS)} = I_LOAD(MAX)  D  1 – D
The power dissipated in the input capacitor is
calculated using Equation 5-25.
EQUATION 5-25:
P_{DISS(C_IN)} = I_{C_IN(RMS)}²  ESR_{C_IN}
5.8 Ripple Injection
The minimum recommended ripple at the FB pin for
proper operation of the MIC2128 error amplifier and
comparator is 20 mV. However, the output voltage
ripple is generally designed as 1% to 2% of the output
voltage. For low output voltages, such as a 1V, the
output voltage ripple is only 10 mV to 20 mV, and the
feedback voltage ripple is less than 20 mV. If the
feedback voltage ripple is so small that the gm amplifier
and comparator cannot sense it, then the MIC2128
loses control and the output voltage is not regulated. In
order to have sufficient V_FB ripple, ripple injection
method should be applied for low output voltage ripple
applications.
The applications are divided into three situations
according to the amount of the feedback voltage ripple:
1. Enough ripple at the feedback due to the large
ESR of the output capacitor (Figure 5-5). The
converter is stable without any additional ripple
injection at the FB node. The feedback voltage
ripple is given by Equation 5-26.
 2016 Microchip Technology Inc.
MIC2128
EQUATION 5-26:
V_{FBPP} = _R----₂---^R-+---²--_R----₁-  ESR  I_{L_PP}
I_{L_PP} is the peak-to-peak value of the inductor current
ripple.
L
SW
MIC2128
FB
R₁
C_OUT
ESR
R₂
FIGURE 5-5:
Enough Ripple at FB.
2. Inadequate ripple at the feedback voltage due to
the small ESR of the output capacitor.
The output voltage ripple can be fed into the FB pin
through a feed forward capacitor, C_FF in this case, as
shown in Figure 5-6. The typical C_FF value is between
1 nF and 100 nF. With the feed forward capacitor, the
feedback voltage ripple is very close to the output volt-
age ripple which is shown in Equation 5-27.
EQUATION 5-27:
V_{FBPP} = ESR  I_{L_PP}
SW
MIC2128
FB
L
R₁
R₂
C_FF
C_OUT
ESR
FIGURE 5-6:
Inadequate Ripple at FB.
3. Virtually no ripple at the FB pin voltage due to
the very-low ESR of the output capacitors:
In this case, additional ripple can be injected into the
FB pin from the switching node SW via a resistor R_INJ
and a capacitor C_INJ, as shown in Figure 5-7.
DS20005620A-page 23