LTC1871EMS-7 Datasheet, PDF (26/36 Pages) Linear Technology – Wide Input Range, No RSENSE Current Mode Boost,

LTC1871
APPLICATIONS INFORMATION
During the MOSFET’s on-time, the control circuit limits
the maximum voltage drop across the power MOSFET to
about 150mV (at low 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)

V_SENSE(MAX)
I_O(MAX)
•


1+
1


2^
• _T
•



1
V_O + V_D
V_IN(MIN)


+1
The V_SENSE(MAX) term is typically 150mV at low duty cycle
and is reduced to about 100mV at a duty cycle of 92% due
to slope compensation, as shown in Figure 8. The constant
‘χ’ in the denominator represents the ripple current in the
inductors relative to their maximum current. For example,
if 30% ripple current is chosen, then χ = 0.30. The ρ_T term
accounts for the temperature coefficient of the R_DS(ON) of
the MOSFET, which is typically 0.4%/°C. Figure 9 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) 
V_SENSE(MAX)
R_DS(ON)
•


1+
1


2^
• _T
•



1
V_O + V_D
V_IN(MIN)


+1
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. As a result, some iterative calculation is normally
required to determine a reasonably accurate value. Since
the controller 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 (load, line and
temperature) 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.
26
The power dissipated by the MOSFET in a SEPIC converter
is:
P_FET
=


I_O(MAX)
•
D_MAX
1– D_MAX


2
•
R_DS(ON)
• D_MAX
•

_T
( ) ^{+ k •}
V_IN(MIN) + V_O
1.85
•
I_O(MAX)
•
D_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 •R_TH(JA)
The R_TH(JA) to be used in this equation normally includes
the R_TH(JC) for the device plus the thermal resistance from
the board to the ambient temperature in the enclosure.
This value of T_J can then be used to check the original
assumption for the junction temperature in the iterative
calculation process.
SEPIC Converter: Output Diode Selection
To maximize efficiency, a fast-switching diode with low
forward drop and low reverse leakage is desired. The output
diode in a SEPIC converter conducts current during the
switch off-time. The peak reverse voltage that the diode
must withstand is equal to V_IN(MAX) + V_O. The average
forward current in normal operation is equal to the output
current, and the peak current is equal to:
I_D(PEAK)
=


1+


2 
• I_O(MAX)
•


V_O + V_D
V_IN(MIN)

+ 1_
The power dissipated by the diode is:
P_D = I_O(MAX) • V_D
and the diode junction temperature is:
T_J = T_A + P_D • R_TH(JA)
The R_TH(JA) to be used in this equation normally includes
the R_TH(JC) for the device plus the thermal resistance from
the board to the ambient temperature in the enclosure.
1871fe