MIC2165 Datasheet, PDF (18/27 Pages) Micrel Semiconductor – Adaptive On-Time DC-DC Controller Featuring Hyper Light Load

Micrel, Inc.
Step 2: Add a capacitor, C_S, in parallel with the
synchronous MOSFET, Q2. The capacitor value should
be approximately 2 times the C_OSS of Q2. Measure the
frequency of the switch node ringing, f₂:
f₂ =
1
(31)
2π Lp × (Cs + Cp)
Define f’ as:
f ^' = ^f1
f₂
Combining the equations for f₁, f₂ and f’ to derive C_P, the
parasitic capacitance:
C_P
=
C_S
(f ^' )² −
1
(32)
L_P is solved by re-arranging the equation for f₁:
L_P
=
(2π)²
1
× C_P
× (f₁)²
(33)
Step 3: Calculate the damping resistor.
Critical damping occurs at Q = 1:
Q = R_S ×
C_{P = 1}
L_P
(34)
Solving for R_S
R_S =
L_P
C_p
(35)
Figure 8 shows the snubber in the circuit and the
damped switch node waveform. The snubber capacitor,
C_S, is charged and discharged each switching cycle. The
energy stored in C_S is dissipated by the snubber resistor,
R_S, two times per switching period. This power is
calculated in the equation below:
P_SNUBBER = f_SW × C_S × V_IN2
(36)
Ripple Injection
The V_FB ripple required for proper operation of the
MIC2165 g_m amplifier and error comparator is 20mV to
100mV. However, the output voltage ripple is generally
designed as 1% to 2% of the voltage. For a low output
voltage, such as a 1V output, the output voltage ripple is
only 10mV to 20mV, and the V_FB ripple is less than
20mV. If the V_FB ripple is so small that the g_m amplifier
and error comparator cannot sense it, the MIC2165 will
lose control and the output voltage is not regulated. In
order to have some amount of V_FB ripple, a ripple
injection method is applied for low output voltage ripple
applications.
The applications are divided into three situations
according to the amount of the V_FB ripple:
MIC2165
1) Enough ripple at V_OUT due to the large ESR of the
output capacitors.
As shown in Figure 9a, the converter is stable without
any ripple injection. The V_FB ripple is:
ΔV_FB(pp)
=
R2
R1+ R2
×
ΔV_OUT
(37)
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 9b. 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
(38)
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 9c. The injected ripple
is:
ΔV_FB(PP)
=
V_IN
× K _div
× D × (1- D) ×
1
f_SW × τ
(39)
K _div
=
R1//R2
R_inj + R1//R2
(40)
where:
V_IN = Power stage input voltage at VIN pin
D = Duty Cycle
f_SW = switching frequency
τ = (R1// R2 // R_inj ) ⋅ C_ff
In equations (39) and (40), 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.
June 2010
18
M9999-060810-D