LTC3783 Datasheet, PDF (16/24 Pages) Linear Technology – PWM LED Driver and Boost, Flyback and SEPIC Controller

LTC3783
U
OPERATIO
During the switch on-time, the IMAX comparator limits the
absolute maximum voltage drop across the power
MOSFET to a nominal 150mV, regardless of duty cycle.
The peak inductor current is therefore limited to
150mV/R_DS(ON). The relationship between the maximum
load current, duty cycle, and the R_DS(ON) of the power
MOSFET is:
R_DS(ON)
<
150mV
•
⎛
⎝⎜
1+
χ
2
1– D_MAX
⎞
⎠⎟
• I_{OUT(MAX )}
•
ρ_T
The ρ_T term accounts for the temperature coefficient of the
R_DS(ON) of the MOSFET, which is typically 0.4%/°C. Fig-
ure 8 illustrates the variation of normalized R_DS(ON) over
temperature for a typical power MOSFET.
Another method of choosing which power MOSFET to use
is to check what the maximum output current is for a given
R_DS(ON), since MOSFET on-resistances are available in
discrete values.
I_O(MAX)
=
150mV
•
⎛
⎝⎜
1+
χ
2
1–
⎞
⎠⎟
•
D_MAX
R_DS(ON)
•
ρ_T
It is worth noting that the 1 - D_MAX relationship between
I_O(MAX) and R_DS(ON) can cause boost converters with a
wide input range to experience a dramatic range of maxi-
mum input and output currents. This should be taken into
consideration in applications where it is important to limit
2.0
1.5
1.0
0.5
0
– 50
0
50
100
150
JUNCTION TEMPERATURE (°C)
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Figure 8. Normalized R_DS(ON) vs Temperature
16
the maximum current drawn from the input supply, and
also to avoid triggering the 150mV IMAX comparator, as
this condition can result in excessive noise.
Calculating Power MOSFET Switching and Conduction
Losses and Junction Temperatures
In order to calculate the junction temperature of the power
MOSFET, the power dissipated by the device must be
known. This power dissipation is a function of the duty
cycle, the load current, and the junction temperature itself
(due to the positive temperature coefficient of its R_DS(ON)).
As a result, some iterative calculation is normally required
to determine a reasonably accurate value. Since the con-
troller is using the MOSFET as both a switching and a
sensing element, care should be taken to ensure that the
converter is capable of delivering the required load current
over all operating conditions (line voltage and tempera-
ture), and for the worst-case specifications for V_SENSE(MAX)
and the R_DS(ON) of the MOSFET listed in the manufacturer’s
data sheet.
The power dissipated by the MOSFET in a boost converter
is:
P_FET
=
⎛
⎝⎜
I_OUT(MAX)
1– D_MAX
⎞²
⎠⎟
•
R_DS(ON)
•
D_MAX
•
ρ_T
+
k
•
V_OUT1.85
•
⎛ I_OUT(MAX)
⎝⎜ 1– D_MAX
⎞
⎠⎟
•
C_RSS
•
f
The first term in the equation above represents the I²R
losses in the device, and the second term, the switching
losses. The constant k = 1.7 is an empirical factor inversely
related to the gate drive current and has the dimension of
1/current.
From a known power dissipated in the power MOSFET, its
junction temperature can be obtained using the following
formula:
T_J = T_A + P_FET • θ_JA
The θ_JA to be used in this equation normally includes the
θ_JC for the device plus the thermal resistance from the
case to the ambient temperature (θ_CA). This value of T_J can
then be compared to the original, assumed value used in
the iterative calculation process.
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