LED5000 Datasheet, PDF (44/52 Pages) STMicroelectronics – 3 A monolithic step-down current source with dimming capability

Application notes - alternative topologies
LED5000
6.4
Compensation network design for alternative topologies
The small signal analysis for the alternative topologies can be written as:
Equation 74
G_CO(s) =
R_{-----L---O----A----D-}
R_CS
⋅
-⁽--¹-----–----^D-----⁾
K_Dx
⋅
⎝⎛_---¹_{-----–------ω------Z------_---}^s-_{R--------H------P----}⎠⎞_-----^â‹_-----⎝⎛_---¹_{-----+-----ω}^---s_----z--⎠⎞_--
⎝⎛^{1 +} _ω^--s--_p^-⎠⎞
⋅
F_H(s)
that shares similar terms with Equation 1 which is valid for the buck (see Equation 1). In
addition K_DX depends on the topology (different for boost and buck-boost) and ω_{Z_RHP}
(Equation 75) is a zero in the right half plane:
Equation 75
ω_{Z_RHP}
=
R_{-----O----U----T----}⋅_------(_--1_{-----–-----}D_-----)_--²_-
L
The RHP (right half plane) zero has the same 20 dB/dec rising gain magnitude as a
conventional zero, but with 90 degree phase drop instead of lead. This characteristic cannot
be compensated with the error amplifier network so the loop gain is designed to roll off at
lower frequency in order to keep its contribution outside the small signal analysis.
ω_{Z_RHP} (see Equation 75) depends on the equivalent output resistance, inductor value and
the duty cycle. As a consequence the minimum ω_{Z_RHP} over the input voltage range
determines the maximum system bandwidth:
Equation 76
BW ≤BW_MAX
=
-¹--
K
⋅
-^ω---^Z---^_-₂-^R---^H-_â‹---^P---^__π--^M----^I--^N--
«
-^f-^S----^W--
6
the system phase margin depends on K.
This paragraph provides the equations to calculate the components of the compensation
network once selected the power components and given the BW specification.
Table 10: BB and boost parameters summarizes the K_D, K_m, K parameters useful for the
next calculations of the compensation network.
The DC gain of the total small loop is:
Equation 77
A₀ = G_m ⋅
R_EA ⋅
(1 – D) ⋅
--^R-----^S---
R_CS
⋅
---¹---
K_D
where G_m is the error amplifier transconductance, R_EA the equivalent output resistance of
the error amplifier, R_CS the internal current sense gain (for these parameters refer to
Table 5: Electrical characteristics), R_S the sensing resistor value, and K_D can be calculated
from Table 10
The calculation of the components composing the compensation network depends on the
relative position of the pole f_p (see Equation 3) and the designed bandwidth BW.
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