LTC3704_15 Datasheet, PDF (16/28 Pages) Linear Technology – Wide Input Range, No RSENSE Positive-to-Negative DC/DC Controller

LTC3704
APPLICATIO S I FOR ATIO
200
2.0
150
1.5
100
1.0
50
0.5
0
0
0.2 0.4 0.5 0.8 1.0
DUTY CYCLE
3704 F11
Figure 11. Maximum SENSE Threshold Voltage vs Duty Cycle
Another method of choosing which power MOSFET to use
is to check the maximum output current for a given
R_DS(ON), since MOSFET on-resistances are generally
available in discrete values.
I_O(MAX)
=
–V_SENSE(MAX)
•
⎛
⎝⎜¹⁺
1– D_MAX
χ⎞
2 ⎠⎟
• R_DS(ON)
• ρ_Τ
For the case where a conventional sense resistor is used,
R_SENSE
=
V_SENSE(MAX)
•
D_MAX – 1
⎛
⎝⎜¹⁺
χ⎞
2 ⎠⎟
• I_O(MAX)
Sense resistors are generally low TC and are available with
different ranges of tolerance depending on price. The
power dissipated in the sense resistor is:
2
P_SENSE = I_SW(PEAK) •R_SENSE •D_MAX
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)).
16
0
– 50
0
50
100
150
JUNCTION TEMPERATURE (°C)
3704 F12
Figure 12. Normalized R_DS(ON) vs Temperature
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 (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 positive-to-
negative converter is:
P_FET
=
⎛ _{–IO(MAX)} ⎞ ²
⎝⎜ ^{1– D}MAX ⎠⎟
• R_DS(ON)
• D_MAX
• ρ_T
+
k
•
(V_IN
–
V_O )^1.85
•
I_O(MAX)
1– D_MAX
•
C _RSS
•
f
where I_O(MAX) and V_O are negative numbers.
The first term in the equation above represents the
I²R losses in the device, and the second term, the switch-
ing 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)
3704fb