13
FN9040.2
October 4, 2005
The response time is the time interval required to slew the
inductor current from an initial current value to the load
current level. During this interval the difference between the
inductor current and the transient current level must be
supplied by the output capacitor(s). Minimizing the response
time can minimize the output capacitance required. Also, if
the load transient rise time is slower than the inductor
response time, as in a hard drive or CD drive, it reduces the
requirement on the output capacitor.
The maximum capacitor value required to provide the full,
rising step, transient load current during the response time of
the inductor is:
where, C
OUT
is the output capacitor(s) required, L
O
is the
output inductor, I
TRAN
is the transient load current step, V
IN
is the input voltage, V
O
is output voltage, and DV
OUT
is the
drop in output voltage allowed during the load transient.
High frequency capacitors initially supply the transient
current and slow the load rate-of-change seen by the bulk
capacitors. The bulk filter capacitor values are generally
determined by the ESR (Equivalent Series Resistance) and
voltage rating requirements as well as actual capacitance
requirements.
The output voltage ripple is due to the inductor ripple current
and the ESR of the output capacitors as defined by:
where, I
L
is calculated in the Inductor Selection section.
High frequency decoupling capacitors should be placed as
close to the power pins of the load as physically possible. Be
careful not to add inductance in the circuit board wiring that
could cancel the usefulness of these low inductance
components. Consult with the manufacturer of the load
circuitry for specific decoupling requirements.
Use only specialized low-ESR capacitors intended for
switching-regulator applications at 300kHz for the bulk
capacitors. In most cases, multiple small-case electrolytic
capacitors perform better than a single large-case capacitor.
The stability requirement on the selection of the output
capacitor is that the ‘ESR zero’, f
Z
, be between 1.2kHz and
30kHz. This range is set by an internal, single compensation
zero at 6kHz. The ESR zero can be a factor of five on either
side of the internal zero and still contribute to increased
phase margin of the control loop. Therefore,
In conclusion, the output capacitors must meet three criteria:
1. They must have sufficient bulk capacitance to sustain the
output voltage during a load transient while the output
inductor current is slewing to the value of the load
transient,
2. The ESR must be sufficiently low to meet the desired
output voltage ripple due to the output inductor current,
and
3. The ESR zero should be placed, in a rather large range,
to provide additional phase margin.
The recommended output capacitor value for the ISL6440 is
between 150µF to 680µF, to ensure stability when using the
components in the typical application schematic. Use of
aluminum electrolytic, POSCAP, or tantalum type capacitors
is recommended. Use of low ESR ceramic capacitors is
possible but would take more rigorous loop analysis to
ensure stability.
Output Inductor Selection
The PWM converters require output inductors. The output
inductor is selected to meet the output voltage ripple
requirements. The inductor value determines the converter’s
ripple current and the ripple voltage is a function of the ripple
current and output capacitor(s) ESR. The ripple voltage
expression is given in the capacitor selection section and the
ripple current is approximated by the following equation:
For the ISL6440, use Inductor values between 4.7µH to
10µH when using the component values in the Typical
Application Schematic for optimal compensation. Other
inductor values can be used but with a more rigorous design
for compensation.
Input Capacitor Selection
The important parameters for the bulk input capacitor(s) are
the voltage rating and the RMS current rating. For reliable
operation, select bulk input capacitors with voltage and
current ratings above the maximum input voltage and largest
RMS current required by the circuit. The capacitor voltage
rating should be at least 1.25 times greater than the
maximum input voltage and 1.5 times is a conservative
guideline. The AC RMS Input current varies with the load.
The total RMS current supplied by the input capacitance is:
where,
DC is duty cycle of the respective PWM.
Depending on the specifics of the input power and its
impedance, most (or all) of this current is supplied by the
input capacitor(s). Figure 17 shows the advantage of having
the PWM converters operating out of phase. If the
converters were operating in phase, the combined RMS
current would be the algebraic sum, which is a much larger
C
OUT
L
O
()I
TRAN
()
2
2V
IN
V
O
–()DV
OUT
()
---------------------------------------------------------- -=
V
RIPPLE
∆I
L
ESR()=
C
OUT
1
2Π ESR()f
Z
()
-------------------------------------=
∆I
L
V
IN
V
OUT
–()V
OUT
()
f
S
()L()V
IN
()
----------------------------------------------------------=
I
RMS
I
RMS1
2
I
RMS2
2
+=
I
RMSx
DC DC
2
–=
ISL6440
