L6722 datasheet(28/34 Pages) STMICROELECTRONICS

28 / 34 page

11 System control loop compensation

L6722

28/34

●

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 17) 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 17. 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.

Compensation network can be simply designed placing

ωF=ωLC and imposing the cross-over

frequency

ωT as desired obtaining (always considering that ωT might be not higher than 1/10th

of the switching frequency FSW):

11.1

Compensation network guidelines

The Compensation Network design assures to having system response according to the cross-

over frequency selected and to the output filter considered: it is anyway possible to further fine-

tune the compensation network modifying the bandwidth in order to get the best response of

the system as follow:

●

Increase RF to increase the system bandwidth accordingly;

●

Decrease RF to decrease the system bandwidth accordingly;

PWM

---

∆V

OSC

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

⋅

OOP

()

---

∆V

OSC

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

()

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

DROOP

-------

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

DROOP

//R

ESR

()

⋅⋅

----

⋅⋅

3 R

⋅

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

ESR

⋅

-------

⋅

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

⋅⋅

⋅

–

Reference

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]

∆V

OSC

⋅

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

---

DROOP

ESR

(

⋅

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

⋅⋅

⋅

---

⋅

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

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