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LT3433IFE#TRPBF

P1-P3P4-P6P7-P9P10-P12P13-P15P16-P16
10
LT3433
3433f
APPLICATIO S I FOR ATIO
WUUU
The requirement for avoiding current mode instability is
that the rising slope of sensed inductor ripple current (S1)
is greater than the falling slope (S2). At duty cycles greater
than 50% this is not true. To avoid the instability condition,
a false signal is added to the sensed current with a slope
(S
X
) that is sufficient to prevent current mode instability,
or S1 + S
X
≥ S2. This leads to the following relations:
S
X
≥ S2(2DC – 1)/DC
If the forward voltages of a converter’s catch and pass
diodes are defined as V
F1
and V
F2
, then:
S2 = (V
OUT
+ V
F1
+ V
F2
)/L
Solving for L yields a relation for the minimum inductance
that will satisfy slope compensation requirements:
L
MIN
= (V
OUT
+ V
F1
+ V
F2
)(2DC – 1)/(DC • S
X
)
The LT3433 maximizes available dynamic range using a
slope compensation generator that generates a continu-
ously increasing slope as duty cycle increases. The slope
compensation waveform is calibrated at 80% duty cycle to
generate an equivalent slope of at least 0.05A/µs. The
equation for minimum inductance then reduces to:
L
MIN
= (V
OUT
+ V
F1
+ V
F2
)(15e-6)
For example, with V
OUT
= 5V and using V
F1
+ V
F2
= 1.1V
(cold):
L
MIN
= (5 + 1.1)(15e-6) = 91.5µH
Converter Capabilities
The output current capability of an LT3433 converter is
affected by a myriad of variables. The current in the
switches is limited by the LT3433. Switch current is
measured coming from the V
IN
supply, and does not
directly translate to a limitation in load current. This is
especially true during bridged mode operation when the
converter output current is discontinuous.
During bridged mode operation, the converter output
current is discontinuous, or only flowing to the output
while the switches are off (not to be confused with discon-
tinuous switcher operation). As a result, the maximum
output current capability of the converter is reduced from
that during buck mode operation by a factor of roughly
1 – DC, not including additional losses. Most converter
losses are also a function of DC, so operational duty cycle
must be accurately determined to predict converter load
capabilities.
V
OUT
(V)
4
50
L
MIN
(µH)
100
150
200
250
812
16
20
3433 AI01
300
350
610
14
18
Slope Compensation Requirements
Typical Minimum Inductor Values vs V
OUT
SW_H
LT3433
V
IN
V
OUT
3433 AI02
SW_L
L
D1
D2
Application variables:
V
IN
= Converter input supply voltage
V
OUT
= Converter programmed output voltage
V
BST
= Boosted supply voltage (V
BST
– V
SWH
)
DC = Operational duty cycle
f
O
= Switching frequency
I
MAX
= Peak switch current limit
∆I
L
= Inductor ripple current
I
SW
= Average switch current or peak switch current
less half the ripple current (I
MAX
– ∆I
L
/2)
R
SWH
= Boosted switch “on” resistance
R
SWL
= Grounded switch “on” resistance
L = Inductor value
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
PowerPath is a trademark of Linear Technology Corporation
12
LT3433
3433f
Design Example
4V-60V to 5V DC/DC converter (the application on the
front page of this data sheet), load capability for T
A
= 85°C.
Application Specific
Constants: LT3433 W/C Constants:
V
IN
= 4V I
MAX
= 0.55A
V
OUT
= 5V R
SWH
= 1.2Ω
L = 100µHR
SWL
= 1Ω
R
L
= 0.28Ω f
O
= 190kHz
V
F1
= 0.45V ∆
BST
= 0.05
V
F2
= 0.4V ∆
OUT
= 0.05
R
CESR
= 0.01Ω I
VIN
= 600µA
I
BIAS
= 800µA
The LT3433 operates in bridged mode with V
IN
= 4V, so the
relations used are:
DC = [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
]
∆I = (V
OUT
+ V
F1
+ V
F2
- I
SW
• R
L
) • (1 – DC)/(L • f
O
)
I
OUT(MAX)
= I
SW
• [1 – DC • (1 + ∆
BST
+ ∆
OUT
)] – I
BIAS
Iteration procedure for DC:
(1) Set initial seed value for ∆I (this example will set
∆I = 0).
(2) Using seed value for ∆I, determine I
SW
(I
SW
= 0.55 –
0 = 0.55).
(3) Use calculated I
SW
and above design constants to
solve the DC relation (DC = 0.683).
(4) Use calculated DC to solve the ∆I relation (yields ∆I =
0.0949).
(5) If calculated ∆I is equal to the seed value, stop.
Otherwise, use calculated ∆I as new seed value and
repeat (2) through (4).
CALCULATED VALUES
ITERATION # SEED ∆II
SW
DC ∆I
1 0 0.55 0.683 0.095
2 0.095 0.503 0.674 0.098
3 0.098 0.501 0.674 0.098
After iteration, DC = 0.674 and ∆I = 0.098.
Use iteration result for DC and above design constants to
solve the I
OUT(MAX)
relation:
I
OUT(MAX)
= 0.501 • [1 – 0.674 • (1 + 0.05 + 0.05)] –
800µA
I
OUT(MAX)
= 129mA
Increased Output Voltages
The LT3433 can be used in converter applications with
output voltages from 3.3V through 20V, but as converter
output voltages increase, output current and duty cycle
limitations prevent operation with V
IN
at the extreme low
end of the LT3433 operational range. When a converter
operates as a buck/boost, the output current becomes
discontinuous, which reduces output current capability by
roughly a factor of 1 – DC, where DC = duty cycle. As such,
the output current requirement dictates a minimum input
voltage where output regulation can be maintained.
APPLICATIO S I FOR ATIO
WUUU
V
OUT
(V)
4
V
IN(MIN)
(V)
12
16
200mA
125mA
175mA
20
3433 AI03
8
4
8
12
16
24
20
150mA
Typical Minimum Input Voltage as a Function of
Output Voltage and Required Load Current
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LT3433IFE#TRPBF

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Buy LT3433IFE#TRPBF
Manufacturer:
Analog Devices / Linear Technology
Description:
Switching Voltage Regulators 200kHz, 500mA, High Voltage Buck-Boost Converter
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New from this manufacturer.
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