Datasheet

( )
( )
( )
Omin IN max Omin DS(on)min D O min L D
V = 0.096 × V I × R + V I × R V- - -
( )
( )
( )
Omax IN min O max DS(on) max D O max L D
V = 0.91 × V I × R + V I × R V- - -
TPS54231
www.ti.com SLUS851C –OCTOBER 2008–REVISED JULY 2012
OUTPUT VOLTAGE LIMITATIONS
Due to the internal design of the TPS54231, there are both upper and lower output voltage limits for any given
input voltage. The upper limit of the output voltage set point is constrained by the maximum duty cycle of 91%
and is given by Equation 31:
(31)
Where:
V
IN min
= Minimum input voltage
I
O max
= Maximum load current
V
D
= Catch diode forward voltage
R
L
= Output inductor series resistance
The equation assumes maximum on resistance for the internal high-side FET.
The lower limit is constrained by the minimum controllable on time which may be as high as 130 ns at 25°C
junction temperature. The approximate minimum output voltage for a given input voltage and minimum load
current is given by Equation 32:
(32)
Where:
V
IN max
= Maximum input voltage
I
O min
= Minimum load current
V
D
= Catch diode forward voltage
R
L
= Output inductor series resistance
This equation assumes nominal on-resistance for the high-side FET and accounts for worst case variation of
operating frequency set point. Any design operating near the operational limits of the device should be carefully
checked to assure proper functionality.
POWER DISSIPATION ESTIMATE
The following formulas show how to estimate the device power dissipation under continuous conduction mode
operations. They should not be used if the device is working in the discontinuous conduction mode (DCM) or
pulse skipping Eco-mode
TM
.
The device power dissipation includes:
1) Conduction loss: Pcon = Iout
2
x R
DS(on)
x V
OUT
/VIN
2) Switching loss: Psw = 0.5 x 10
-9
x VIN
2
x I
OUT
x Fsw
3) Gate charge loss: Pgc = 22.8 x 10
-9
x Fsw
4) Quiescent current loss: Pq = 0.075 x 10
-3
x VIN
Where:
I
OUT
is the output current (A).
R
DS(on)
is the on-resistance of the high-side MOSFET (Ω).
V
OUT
is the output voltage (V).
VIN is the input voltage (V).
Fsw is the switching frequency (Hz).
So
Ptot = Pcon + Psw + Pgc + Pq
For given T
A
, T
J
= T
A
+ Rth x Ptot.
For given T
JMAX
= 150°C, T
AMAX
= T
JMAX
– Rth x Ptot.
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