AN11041_15 Datasheet, PDF (12/23 Pages) NXP Semiconductors – buck

NXP Semiconductors
AN11041
Non-dimmable buck converter in low ripple configuration
However, to reach the same LED current, the peak value must be adjusted and this in turn
alters the converter frequency. The average current I_LED at the output can be calculated
with Equation 10, Equation 11, Equation 12 and Equation 13:
I_LED
=
-^I---^p--^e---^a--^k----^---^--^t--¹----⁺-----^t-²----⁺-----^t--³---^-
2  t₁ + t₂ + t₃ + t₄
(20)
 = ------^V----^o------
(21)
V_i – V_o
t₃
=
I_{---p--e---a--k----}_---L_---2_--
V_o
(22)
t₁
=
I_{---p--e---a--k----}_---L_---2_--
V_i – V_o
(23)
Combining Equation 20, Equation 21, Equation 22 and Equation 23 results in
Equation 24:
I_{---p--e---a--k--}²_--_---L_---2_{--   + 1}
2

I_LED
=
--------------^V----^o-------------------------------------
-^I--^p--^e---^a--^k----^---^L---²--
V_o



+
1

+
t
4
(24)
When written out, it results in:
0
=
L2


+
1

I_p
ea
2
k
–
2

I_LED


+
1

L2

I_peak
–
2

I_LED

t₄

V_o
(25)
This 2^nd order function can be solved using the ABC formula:
a = L2   + 1
(26)
b = –2  L2   + 1  I_LED
(27)
c = –2  t₄  V_o  I_LED
(28)
I_peak
=
-^–----^b----^---------^b----²---^–-----⁴----^---^a-----^---^c-
2a
(29)
For example:  = 1, a = 0.714  10^3, b = 1  10^3, c = 83.1  10^6, I_peak = 1.48 A,
t₁ = 5.28 s, t₃ = 5.28 s, t₄ = 0.594 s, f = 89.6 kHz.
When switching from primary to secondary stage (i.e. when the MOSFET is switched off),
a high voltage is induced on the DRAIN pin which becomes equal to V_i (excluding the
freewheel diode drop). This fast rising of the DRAIN pin is controlled by the SSL21081,
the SSL21083, or the SSL2109 to about 4 V/ns.
AN11041
Application note
All information provided in this document is subject to legal disclaimers.
Rev. 1.3 — 23 October 2012
© NXP B.V. 2012. All rights reserved.
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