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SNVS570L – JANUARY 2009 – REVISED MAY 2013
DETERMINING DUTY-CYCLE (D)
Duty cycle (D) approximately equals:
DESIGN GUIDE
V LED
V BUCK
=D= t ON + t OFF
t ON
= t ON x f SW
(4)
With efficiency considered:
1 u V LED = D
K V BUCK
(5)
For simplicity, choose efficiency between 75% and 85%.
CALCULATING OFF-TIME
The “Off-Time” of the LM3445 is set by the user and remains fairly constant as long as the voltage of the LED
stack remains constant. Calculating the off-time is the first step in determining the switching frequency of the
converter, which is integral in determining some external component values.
PNP transistor Q3, resistor R4, and the LED string voltage define a charging current into capacitor C11. A
constant current into a capacitor creates a linear charging characteristic.
i = C dv
dt
(6)
Resistor R4, capacitor C11 and the current through resistor R4 (i COLL ), which is approximately equal to V LED /R4,
are all fixed. Therefore, dv is fixed and linear, and dt (t OFF ) can now be calculated.
t OFF = C11 x 1.276V x
R4
V LED
(7)
Common equations for determining duty cycle and switching frequency in any buck converter:
f SW =
1
t OFF + t ON
D= t
= V LED
'? = t
Therefore:
t ON
ON + t OFF
t OFF
ON + t OFF
V
BUCK
(8)
D t -
f SW = t ON , and f SW = 1 OFF D
With efficiency of the buck converter in mind:
V LED
V BUCK = K u D
Substitute equations and rearrange:
(9)
(10)
V LED ·
K u V BUCK ?1
f SW =
§
¨ 1
?
1
t OFF
(11)
Off-time, and switching frequency can now be calculated using the equations above.
SETTING THE SWITCHING FREQUENCY
Selecting the switching frequency for nominal operating conditions is based on tradeoffs between efficiency
(better at low frequency) and solution size/cost (smaller at high frequency).
20
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