Datasheet

tpeak =
'I
OUT(MAX)
x L
V
OUT
-D
MIN
V
IN
- C
OUT
R
ESR
'V
q
=
C
OUT
'I
OUT(MAX)
t -
2 X L X C
OUT
t
2
(V)
V
OUT -
D
MIN
V
IN
R
ESR(MAX)
=
V
OS(MAX)
'I
OUT(MAX)
:
'V
r
= R
ESR
('I
OUT(MAX)
-
L
V
OUT -
D
MIN
V
IN
t)
(V)
'V
c2
Time
Voltage
Upper Voltage
Limit
V
OS (MAX)
'V
c1
0
ESR too large
capacitance too small
LM3477
SNVS141K –OCTOBER 2000–REVISED MARCH 2013 www.ti.com
Figure 29. Output Voltage Overshoot Violation
The ESR and the capacitance of the output capacitor must be carefully chosen so that the output voltage
overshoot is within the design's specification V
OS(MAX)
. If the total combined ESR of the output capacitors is not
low enough, the initial output voltage excursion will violate the specification, see ΔV
C1
. If the ESR is low enough,
but there is not enough output capacitance, the output voltage will travel outside the specification window due to
the extra charge being dumped into the capacitor, see ΔV
C2
. The LM3477/A has output over voltage protection
(OVP) which could trigger if the transient overshoot is high enough. If this happens, the controller will operate in
hysteretic mode (see OVER VOLTAGE PROTECTION) for a few cycles before the output voltage settles to its
steady state. If this behavior is not desired, substitute V
OVP
(referred to the output) for V
OS(MAX)
(V
OVP
is found in
the Electrical Characteristics) to find the minimum capacitance and maximum ESR of the output capacitor.
CALCULATIONS FOR THE OUTPUT CAPACITOR
During a loading transient, the delta output voltage ΔV
c
has two changing components. One is the voltage
difference across the ESR (ΔV
r
), the other is the voltage difference caused by the gained charge (ΔV
q
). This
gives:
ΔV
c
= ΔV
r
+ ΔV
q
(24)
The design objective is to keep ΔV
c
lower than some maximum overshoot (V
OS(MAX)
). V
OS(MAX)
is chosen based
on the output load requirements.
Both voltages ΔV
r
and ΔV
q
will change with time. For ΔV
r
the equation is:
(25)
where,
R
ESR
= the output capacitor ESR
ΔI
OUT
= the difference between the load current change I
OUT(MAX)
− I
OUT(MIN)
D
MIN
= Minimum duty cycle of device (0.165 typical)
Evaluating this equation at t = 0 gives ΔV
r(max)
. Substituting V
OS(MAX)
for ΔV
r(MAX)
and solving for R
ESR
gives:
(26)
The expression for ΔV
q
is:
(27)
From Figure 30 it can be told that ΔV
C
will reach its peak value at some point in time and then decrease. The
larger the output capacitance is, the earlier the peak will occur. To find the peak position, let the derivative of ΔV
C
go to zero, and the result is:
(28)
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