LM3429_14 Datasheet, PDF (26/50 Pages) Texas Instruments – LM3429Q1 N-Channel Controller for Constant Current LED Drivers

LM3429
SNVS616F – APRIL 2009 – REVISED JANUARY 2010
Boost 3
2
Z_P1= _{rD x CO}
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(49)
Buck-boo₃st
1+D
Z_P1= _{rD x CO}
(50)
And the RHP zero (ω_Z1) is approximated:
Boost ₃
Z_Z1
=
r_D
x Dc²
L1
(51)
Buck-boo₃st
Z_Z1
=
r_D x Dc²
D xL1
(52)
And the uncompensated DC loop gain (T_U0) is approximated:
Buck
T_U0 =
500V x R_CSH x R_SNS
R_HSP x R_LIM
620V
=
I_LED x R_LIM
(53)
Boost _30094432
T_U0
=
Dc x
500V x R_CSH x R_SNS
2 x R_HSP x R _LIM
=
Dc x 310V
I_LED x R_LIM
(54)
Buck-boost
T_U0
=
Dcx 500V x R_CSH x R_SNS
(1+ D) x R_HSP x R_LIM
Dc x 620V
=
(1+ D) x I_LED x R_LIM
(55)
For all topologies, the primary method of compensation is to place a low frequency dominant pole (ω_P2) which
will ensure that there is ample phase margin at the crossover frequency. This is accomplished by placing a
capacitor (C_CMP) from the COMP pin to GND, which is calculated according to the lower value of the pole and the
RHP zero of the system (shown as a minimizing function):
300 ^ZP2
=
min(Z_P1, Z_Z1)
5 x T_U0
1
C_CMP = _{ZP2 x 5e6}
(56)
(57)
If analog dimming is used, C_CMP should be approximately 4x larger to maintain stability as the LEDs are dimmed
to zero.
A high frequency compensation pole (ω_P3) can be used to attenuate switching noise and provide better gain
margin. Assuming R_FS = 10Ω, C_FS is calculated according to the higher value of the pole and the RHP zero of
the system (shown as a maximizing function):
300 ^{ZP3 = max(ZP1,ZZ1) x10}
C_FS
=
10
1
x Z_P3
(58)
(59)
The total system loop gain (T) can then be written as:
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