A4450 Datasheet, PDF (30/34 Pages) Allegro MicroSystems – Buck-Boost Controller with Integrated Buck MOSFET

A4450
Buck-Boost Controller
with Integrated Buck MOSFET
POWER DISSIPATION AND THERMAL CALCULATIONS
The power dissipated in the A4450 is the sum of the power dis-
sipated from the V_IN supply current (P_IN), the switching power
dissipation of the integrated buck switch (P_SW1), the conduction
power dissipation of the integrated Buck switch (P_COND1), and
the power dissipated by both gate drivers (P_DRIVER).
The power dissipated from the V_IN supply current can be calcu-
lated using equation 23,
P_IN = V_IN × I_Q + (V_IN – V_GS1) × Q_G1 × f_SW + P_IN2 (23)
where
{^{PIN2 =}
(V_IN – V_GS2 ) × Q_G2 × f_SW, in Buck-Boost mode
0,
in Buck mode
V_IN is the input voltage,
I_Q is the input quiesent current drawn by the A4450 (see
Electrical Characteristics table),
V_GS1 is the MOSFET gate drive voltage of high-side buck
switch (typically 5 V),
Q_G1 is the internal high-side buck switch gate charges
(approximately 5.7 nC),
Q_G2 is the external boost switch gate charges, and
f_SW is the PWM switching frequency.
The switching power dissipation of the high-side buck switch can
be calculated using equation 24,
P_SW1 =
1
2
× V_IN ×
I_OUT
1 – D_Boost
× (t_r + t_f ) × f_SW
(24)
where
V_IN is the input voltage,
I_OUT is the regulator output current,
D_Boost is the duty cycle of the boost switch,
f_SW is the PWM switching frequency, and
t_r and t_f are the rise and fall times measured at the SW node.
The exact rise and fall times at the LX node will depend on the
external components and PCB layout, so each design should be
measured at full load. Approximate values for both t_r and t_f range
from 5 to 20 ns.
The power dissipated by the high-side Buck switch while it is
conducting can be calculated using equation 25,
P = I × R = _COND1
2
RMS(FET)
DS(ON)HS
(25)
( ) ( ) DBuck
(1 – D_Boost )²
×
I2
OUT
+
ΔI_L2
12
× R _DS(ON)HS
where
I_OUT is the regulator output current,
ΔI_L is the peak-to-peak inductor ripple current,
D_Boost is the duty cycle of the boost switch,
D_Buck is the duty cycle of the buck switch, and
R_DS(ON)HS is the on-resistance of the high-side buck switch
MOSFET.
The R_DS(ON)HS of the high-side buck switch has some initial
tolerance plus an increase from self-heating and elevated ambi-
ent temperatures. A conservative design should accomodate
an R_DS(ON) with at least a 15% initial tolerance plus 0.39%/°C
increase due to temperature.
The sum of the power dissipated by both gate drivers of the inte-
grated buck switch and the external boost switch is,

P_DRIVER = P_G1 + P_G2
(26)
where
P_G1 = Q_G1 × V_GS1 × f_SW
{^{PG2 =}
Q_G2 × V_GS2 × f_SW, in Buck-Boost mode
0,
in Buck mode
Finally, the total power dissipated by the A4450 (P_TOTAL) is the
sum of the previous equations,
P_TOTAL = P_IN + P_SW1 + P_COND1 + P_DRIVER
(27)
The average junction temperature can be calculated with the
equation 28,

T_J = P_TOTAL × R_θJA + T_A
(28)
Allegro MicroSystems, LLC
30
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Worcester, Massachusetts 01615-0036 U.S.A.
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