L6718 datasheet(62/71 Pages) STMICROELECTRONICS

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System control loop compensation

L6718

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DocID023399 Rev 3

System control loop compensation

The multi-phase rail control system can be modeled with an equivalent single-phase rail

converter with the only difference being the equivalent inductor L/N (where each phase has

an L inductor and N is the number of the configured phases), see Figure 15.

Figure 15. Equivalent control loop

The control loop gain results (obtained opening the loop after the COMP pin):

Equation 14

where:

•

RLL is the equivalent output resistance determined by the droop function (voltage

positioning)

•

ZP(s) is the impedance resulting from the parallel of the output capacitor (and its ESR)

and the applied load RO

•

ZF(s) is the compensation network impedance

•

ZL(s) is the equivalent inductor impedance

•

A(s) is the error amplifier gain

•

is the PWM transfer function.

The control loop gain is designed in order to obtain a high DC gain to minimize static error

and to cross the 0dB axes with a constant -20 dB/dec slope with the desired crossover

frequency

ω T. Neglecting the effect of ZF(s), the transfer function has one zero and two

Ref

COMP

RFB

PWM

L/N

ESR

d VCOMP

VOUT

ZF(s)

ZFB(s)

VID

AM12889v1

LOOP s

()

PWM

F s

()

P s

()

⋅⋅

P s

() Z

L s

()

[]

F s

()

--------------

()

------------

⎝⎠

⎛⎞

⋅

-------------------------------------------------------------------------------------------------------------------------

–

PWM

------

ΔV

OSC

-------------------

⋅

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