Design Section
(Continued)
Example: V
IN(MIN)
= 4.5V, V
OUT
= 2.5V, I
OUT(MAX)
= 3A
The hysteretic threshold is derived in a similar manner, the
only difference being that V
is compared V
(V
). Notice that V
does not vary with the duty cycle.
The hysteretic threshold is predetermined by the selection of
R
SN
above. The hysteretic threshold is:
Continuing with the example above,
If the
peak switch current
decreases below this threshold,
the LM3477/A will operate in hysteretic mode (see
OVER
VOLTAGE PROTECTION
section). In some designs, it will
be desired to use R
so that lower valued inductors can be
used (see
DEFAULT/ADJUSTABLE SLOPE COMPENSA-
TION
section and Inductor section). Using R
SL
will lower the
current limit and the hysteretic threshold. See
Figure 8
. R
effectively adds an additional slope to the existing slope of
the V
C
waveform.
When R
SL
is used, the following equations apply:
where MIN(V
50x10
-6
x R
x D
, 0) is the smaller of
the two values in the parenthesis and V
is 0.032V and
0.011V for the LM3477 and LM3477A, respectively. R
can
be used creatively to intentionally lower the hysteretic
threshold, allowing for better performance at lower loads.
However, when R
is used, there may be a minimum load
requirement (see
START-UP/SOFT-START
section).
Power Inductor Section
The LM3477/A operates at a high switching frequency of
500kHz, which allows the use of small inductors. This is
made apparent in the following set of equations used to
calculate the output voltage ripple.
V
OUT(Pk-Pk)
)
i
L(Pk-Pk)
x R
ESR
(V)
As the switching frequency fs increases, the inductance
required for a given output voltage ripple decreases. The
equations above for
V
OUT
and
i
L
provide criteria for
choosing the inductance. The maximum voltage ripple in
steady-state, PWM operation can be controlled by limiting
i
L
which in turn is set by the inductance value. Alternatively,
one can simply choose
i
L
as a percentage of the maximum
output current. Clearly, the size of the output capacitor ESR,
R
ESR
, will have an affect on which criteria is used to choose
the inductance. When the ESR is relatively low (less than
100m
), such as in ceramic, OSCON, and some low ESR
tantalum capacitors, it is convenient to choose the induc-
tance based on setting
i
to 30% of Iout(max). If the ESR is
high, then it may be necessary to restrict
i
to a lower value
so that the output voltage ripple is not too high. Generally
speaking, the former suggestion of setting
i
L
to 30% of
I
OUT(MAX)
is recommended.
The inductance also affects the stability of the converter. The
slopes S
and S
in
Figure 4
are functions of the inductance,
while the compensation ramp, S
, is fixed by default. There-
fore if the inductance is too small, the converter may expe-
rience sub-harmonic oscillations. The LM3477/A provides
sufficient internal slope compensation to allow for induc-
tances chosen according to the
i
= 0.3 x I
guideline in
most cases. Still, one should check to make sure the induc-
tance is not too low before continuing the design process. If
it is found that the selected inductance is too low, a patented
scheme to increase the compensation ramp, S
, is provided
in the LM3477/A (see
DEFAULT/ADJUSTABLE SLOPE
COMPENSATION
section). In the calculations that follow, if it
is found that the chosen inductance is too small, R
SL
can be
used to increase Se so that the inductance can be used.
In a current mode control architecture, there is an inherent
resonance
at
half
the
DEFAULT/ADJUSTABLE SLOPE COMPENSATION
sec-
switching
frequency
(see
200033K4
FIGURE 8. Current Limit and Hysteretic Threshold vs
Duty Cycle with R
SL
L
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