LTC3784_15 Datasheet, PDF (17/38 Pages) Linear Technology – 60V PolyPhase Synchronous Boost Controller

LTC3784
Applications Information
Next, determine the DCR of the inductor. Where provided,
use the manufacturer’s maximum value, usually given at
20°C. Increase this value to account for the temperature
coefficient of resistance, which is approximately 0.4%/°C.
A conservative value for the maximum inductor temperature
(T_L(MAX)) is 100°C.
To scale the maximum inductor DCR to the desired sense
resistor value, use the divider ratio:
R_D
=
R_SENSE(EQUIV)
DCR_MAX at T_L(MAX)
C1 is usually selected to be in the range of 0.1μF to 0.47μF.
This forces R1|| R2 to around 2k, reducing error that might
have been caused by the SENSE^– pin’s ±1μA current.
The equivalent resistance R1|| R2 is scaled to the room
temperature inductance and maximum DCR:
R1||R2 =
(DCR
L
at 20°C)•C1
The sense resistor values are:
R1= ^R1||R2;
R_D
R2
=
R1•R_D
1− R_D
The maximum power loss in R1 is related to duty cycle,
and will occur in continuous mode at V_IN = 1/2V_OUT:
P_{LOSS _ R1}
=
(V_OUT − V_IN)• V_IN
R1
Ensure that R1 has a power rating higher than this value.
If high efficiency is necessary at light loads, consider this
power loss when deciding whether to use DCR sensing or
sense resistors. Light load power loss can be modestly
higher with a DCR network than with a sense resistor, due
to the extra switching losses incurred through R1. However,
DCR sensing eliminates a sense resistor, reduces conduc-
tion losses and provides higher efficiency at heavy loads.
Peak efficiency is about the same with either method.
Inductor Value Calculation
The operating frequency and inductor selection are in-
terrelated in that higher operating frequencies allow the
use of smaller inductor and capacitor values. Why would
anyone ever choose to operate at lower frequencies with
larger components? The answer is efficiency. A higher
frequency generally results in lower efficiency because
of MOSFET gate charge and switching losses. Also, at
higher frequency the duty cycle of body diode conduction
is higher, which results in lower efficiency. In addition to
this basic trade-off, the effect of inductor value on ripple
current and low current operation must also be considered.
The inductor value has a direct effect on ripple current.
The inductor ripple current ΔI_L decreases with higher
inductance or frequency and increases with higher V_IN:
ΔI_L
=
V_IN
f •L
⎛
⎝⎜
1−
V_IN
V_OUT
⎞
⎠⎟
Accepting larger values of ΔI_L allows the use of low
inductances, but results in higher output voltage ripple
and greater core losses. A reasonable starting point for
setting ripple current is ΔI_L = 0.3(I_MAX). The maximum
ΔI_L occurs at V_IN = 1/2V_OUT.
The inductor value also has secondary effects. The tran-
sition to Burst Mode operation begins when the average
inductor current required results in a peak current below
25% of the current limit determined by R_SENSE. Lower
inductor values (higher ΔI_L) will cause this to occur at
lower load currents, which can cause a dip in efficiency in
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