L6714 datasheet(58/70 Pages) STMICROELECTRONICS

58 / 70 page

System control loop compensation

L6714

58/70

Where:

●

RSENSE is the MOSFET RdsON or the Inductor DCR depending on the sensing element

selected;

●

is the equivalent output resistance determined by the droop

function;

●

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 parallel of the N inductor impedance;

●

A(s) is the error amplifier gain;

●

is the PWM transfer function where

∆VOSC is the oscillator ramp

amplitude and has a typical value of 4V.

Removing the dependence from the Error Amplifier gain, so assuming this gain high

enough, and with further simplifications, the control loop gain results:

The system Control Loop gain (See Figure 23) is designed in order to obtain a high DC gain

to minimize static error and to cross the 0dB axes with a constant -20dB/dec slope with the

desired crossover frequency

ωT. 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

ωLC) and the zero (ωESR) is fixed by ESR and the Droop resistance.

Figure 23. Equivalent control loop block diagram (left) and bode diagram (right).

To obtain the desired shape an RF - CF series network is considered for the ZF(s)

implementation. A zero at

ωF = 1/RFCF is then introduced together with an integrator. This

integrator minimizes the static error while placing the zero

ωF in correspondence with the L-

C resonance assures a simple -20dB/dec shape of the gain.

In fact, considering the usual value for the output filter, the LC resonance results to be at

frequency lower than the above reported zero.

DROOP

SENSE

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

⋅

PWM

---

∆V

OSC

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

⋅

LOOP

()

---

∆V

OSC

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

()

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

DROOP

-------

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

DROOP

//R

ESR

()

⋅⋅

-----

⋅⋅

⋅

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

ESR

⋅

-------

⋅

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

⋅⋅

⋅

–

VID

COMP

VSEN

FBR

FBG

64k

RFB

DROOP

PWM

L / N

ESR

d VOUT

VOUT

ZF(s)

ZFB(s)

REMOTE BUFFER

ZF(s)

GLOOP(s)

LC = ωF

ESR

RF[dB]

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