LTC3783
14
3783fb
OPERATION
Figure 6 illustrates these various quantities in relation to
one another.
Typically, in order to avoid visible flicker, f
PWM
should be
greater than 120Hz. Assuming inductor and capacitor
sizing which is close to discontinuous operation, 2 f
OSC
cycles are sufficient for proper PWM operation. Thus,
within the 1MHz rated maximum f
OSC
, a dimming ratio
of 1/D
PWM
= 3000 is possible.
the output current needs to be reflected back to the input
in order to dimension the power MOSFET properly. Based
on the fact that, ideally, the output power is equal to the
input power, the maximum average input current is:
I
IN(MAX)
=
I
OUT(MAX)
1–D
MAX
The peak input current is:
I
IN(PEAK)
= 1+
c
2
•
I
OUT(MAX)
1–D
MAX
The maximum duty cycle, D
MAX
, should be calculated at
minimum V
IN
.
Boost Converter: Ripple Current ∆I
L
and the ‘
c
’ Factor
The constant ‘
c
’ in the equation above represents the
percentage peak-to-peak ripple current in the inductor,
relative to its maximum value. For example, if 30% ripple
current is chosen, then
c
= 0.3, and the peak current is
15% greater than the average.
For a current mode boost regulator operating in CCM,
slope compensation must be added for duty cycles above
50% in order to avoid subharmonic oscillation. For the
LTC3783, this ramp compensation is internal. Having an
internally fixed ramp compensation waveform, however,
does place some constraints on the value of the inductor
and the operating frequency. If too large an inductor is
used, the resulting current ramp (∆I
L
) will be small relative
to the internal ramp compensation (at duty cycles above
50%), and the converter operation will approach voltage
mode (ramp compensation reduces the gain of the current
loop). If too small an inductor is used, but the converter is
still operating in CCM (near critical conduction mode), the
internal ramp compensation may be inadequate to prevent
subharmonic oscillation. To ensure good current mode
gain and to avoid subharmonic oscillation, it is recom-
mended that the ripple current in the inductor fall in the
range of 20% to 40% of the maximum average current.
For example, if the maximum average input current is 1A,
choose a ∆I
L
between 0.2A and 0.4A, and correspondingly
a value ‘
c
’ between 0.2 and 0.4.
Boost Converter: Duty Cycle Considerations
For a boost converter operating in a continuous conduction
mode (CCM), the duty cycle of the main switch is:
D=
OUT
D
IN
V
OUT
+ V
D
where V
D
is the forward voltage of the boost diode. For
converters where the input voltage is close to the output
voltage, the duty cycle is low, and for converters that
develop a high output voltage from a low input voltage,
the duty cycle is high. The maximum output voltage for a
boost converter operating in CCM is:
V
OUT(MAX)
=
V
IN(MIN)
1–D
MAX
– V
D
The maximum duty cycle capability of the LTC3783 is
typically 90%. This allows the user to obtain high output
voltages from low input supply voltages.
Boost Converter: The Peak and Average Input Currents
The control circuit in the LTC3783 is measuring the input
current (either by using the R
DS(ON)
of the power MOSFET
or by using a sense resistor in the MOSFET source), so
PWMIN
GATE
3783 F06
# = N
D
PWM
/f
PWM
1/f
PWM
1/f
OSC
Figure 6. PWM Dimming Parameters
