Datasheet
11
LT3433
3433f
R
L
= Inductor series resistance
∆
BST
= Boosted switch drive currents I
VBST
/I
SW
(in A/A)
∆
OUT
= Grounded switch drive currents I
VOUT
/I
SW
(in A/A)
V
F1
= Switch node catch diode forward voltage
V
F2
= Pass diode forward voltage
I
VIN
= V
IN
quiescent input current
I
IN
= V
IN
switched current
I
BIAS
= V
BIAS
quiescent input current
R
CESR
= Output capacitor ESR
Operational duty cycle is a function of voltage imposed
across the switched inductance and switch on/off times.
Using the relation for change in current in an inductor:
δI = V • δt/L
and putting the application variables into the above rela-
tion yields:
δI
ON(BRIDGED)
= (DC/f
O
• L)[V
IN
– I
SW
• (R
SWH
+ R
SWL
+ R
L
)]
δI
ON(BUCK)
= (DC/f
O
• L)[V
IN
– V
OUT
– V
F2
– I
SW
• (R
SWH
+ R
L
+ R
ESR
)]
δI
OFF
= [(1 – DC)/f
O
• L][V
OUT
+ V
F1
+ V
F2
– I
SW
• (R
L
+ R
ESR
)]
Current conservation in an inductor dictates δI
ON
= δI
OFF
,
so plugging in the above relations and solving for DC yields:
DC
(BRIDGED)
= [V
OUT
+ V
F1
+ V
F2
– I
SW
• (R
L
+ R
ESR
)]/
[V
IN
– I
SW
• (R
SWH
+ R
SWL
+ 2R
L
+ R
ESR
) + V
OUT
+
V
F1
+ V
F2
]
DC
(BUCK)
= [V
OUT
+ V
F1
+ V
F2
– I
SW
• (R
L
+ R
ESR
)]/
[V
IN
– I
SW
• (R
SWH
+ 2R
L
+ 2R
ESR
) + V
F1
]
In order to solve the above equations, inductor ripple
current (∆I) must be determined so I
SW
can be calculated.
∆I follows the relation:
∆I = (V
OUT
+ V
F1
+ V
F2
– I
SW
• R
L
)(1 – DC)/(L • f
O
)
As ∆I is a function of DC and vice-versa, the solution is
iterative. Seed ∆I and solve for DC. Using the resulting
value for DC, solve for ∆I. Use the resulting ∆I as the new
seed value and repeat. The calculated value for DC can be
used once the resulting ∆I is close (<1%) to the seed value.
Once DC is determined, maximum output current can be
determined using current conservation on the converter
output:
Bridged Operation: I
OUT(MAX)
= I
SW
• [1 – DC •
(1 + ∆
BST
+ ∆
OUT
)] – I
BIAS
Buck Operation: I
OUT(MAX)
= I
SW
• (1 – DC • ∆
BST
)
– I
BIAS
P
IN
= P
OUT
+ P
LOSS
, where P
LOSS
= P
SWON
+ P
SWOFF
+ P
IC
,
corresponding to the power loss in the converter. P
IC
is the
quiescent power dissipated by the LT3433. P
SWON
is the
loss associated with the power path during the switch on
interval, and P
SWOFF
is the PowerPath
TM
loss associated
with the switch off interval.
P
LOSS
equals the sum of the power loss terms:
P
VIN
= V
IN
• I
VIN
P
BIAS
= V
OUT
• I
BIAS
P
SWON(BRIDGED)
= DC • [I
SW
2
• (R
SWH
+ R
SWL
+ R
L
)
+ I
SW
• V
OUT
• (∆
BST
+ ∆
OUT
) + R
CESR
• I
OUT
2
]
P
SWON(BUCK)
= DC • [I
SW
2
• (R
SWH
+ R
L
) + I
SW
•
V
OUT
• ∆
BST
+ R
CESR
• (I
SW
• (1 – ∆
BST
) – I
BIAS
–
I
OUT
)
2
]
P
SWOFF
= (1 – DC) • [I
SW
• (V
F1
+ V
F2
) + I
SW
2
• R
L
+
R
CESR
• (I
SW
– I
BIAS
– I
OUT
)
2
]
Efficiency (E) is described as P
OUT
/P
IN
, so:
Efficiency = {1 + (P
VIN
+ P
BIAS
+ P
SWON
+ P
SWOFF
)/P
OUT
}
–1
Empirical determination of converter capabilities is ac-
complished by monitoring inductor currents with a cur-
rent probe under various input voltages and load currents.
Decreasing input voltage or increasing load current re-
sults in an inductor current increase. When peak inductor
currents reach the switch current limit value, maximum
output current is achieved. Limiting the inductor currents
to the LT3433 specified W/C current limit of 0.5V (cold)
will allow margin for operating limit variations. These
limitations should be evaluated at the operating tempera-
ture extremes required by the application to assure robust
performance.
APPLICATIO S I FOR ATIO
WUUU
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