fz= 1

2π⋅C0⋅ RES+N⋅Rd;fLC≅ 1

2π LC0 N⋅Rd

N⋅Rd+RSNS

(16)

Q≅ LC0⋅ RSNS+N⋅Rd⋅ N⋅Rd

L+C0⋅RSNS⋅N⋅Rd

(17)

with the assumption that the inductor parasitic resistance, RDC, and the output capacitor parasitic resistance, RES,

are negligible compared to LED dynamic resistance, Rd.

The closed loop gain is then given by:

GLOOPs =GLCs ⋅GPWOs ⋅GCOMPs

(18)

As shown in Eq. (16) , fz depends on the output capacitor parasitic resistance and on the LEDs dynamic

resistance. Following the considerations summarized in Section 6.2 Output capacitor and inductor selection , in

the typical application the programmed control loop bandwidth (BW) might be higher than fz, so this zero helps

stabilize the loop. If this assumption is verified, a type II compensation network is required for loop stabilization.

In Figure 17. Type II compensation network the type II compensation network is shown.

Figure 17. Type II compensation network

EA

COMP

V REF

FB

V SNS

RSNS

RU

CF

RF

CP

ZF

The type II compensation network transfer function, from VSNS to COMP, is computed in Eq. (19) .

GCOMPIIs =−ZFsRU =− 1RU⋅ 1+sCFRF

s⋅ CF+CP ⋅ 1+sCF//CPRF =−1

⋅ 1+ s2π⋅fZ1

s2π⋅fPO⋅ 1+ s2π⋅fP1

(19)

fZ1= 12π⋅CFRF;fP0= 1

2π⋅ CF+CP ⋅RU;fP1= 1

2π⋅CF//CPRF

(20)

The following suggestions can be followed for a quite common compensation strategy, assuming that CP<<CF.

•

Starting from Eq. (18) , the control loop gain module at s=2π*FBW allows the RF/RU ratio to be fixed :

GLOOP,IIs=2π⋅fBW =GLC0kFF⋅ fLC2fz⋅fBW⋅fP0fZ1≅GLC0kFF⋅ fLC2fz⋅fBW⋅RFRU=1

(21)

After choosing the regulator bandwidth (typically FBW<0.2*FSW ) and a value for RU, usually between 1 kΩ and 50

kΩ, in order to achieve CF and CP not comparable with parasitic capacitance of the board, the RF required value

is computed by Eq. (21) .

ALED6000

Compensation strategy

DS13018 - Rev 4

page 22/45