L6756D datasheet(30/36 Pages) STMICROELECTRONICS

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System control loop compensation

L6756D

30/36

System control loop compensation

The control system can be modeled with an equivalent single-phase converter which only

difference is the equivalent inductor L/N (where each phase has an L inductor and N is the

number of the configured phases). See Figure 14.

Figure 14.

Equivalent control loop

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

Where:

●

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

positioning);

●

ZP(s) is the impedance resulting by 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 0 dB axes with a constant -20 dB/dec slope with the desired crossover

frequency

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

poles; both the poles are fixed once the output filter is designed (LC filter resonance

LC)

and the zero (

ESR) is fixed by ESR and the droop resistance.

LOOP s

()

PWM Z

F s

() R

P s

()

⋅⋅

P s

() Z

L s

()

[]

F s

()

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

()

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

⎝⎠

⎛⎞

⋅

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

–

PWM

------

ΔV

OSC

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

⋅

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