L6711 datasheet(30/38 Pages) STMICROELECTRONICS

30 / 38 page

L6711

30/38

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 three 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 3V

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

loop gain results:

With further simplifications, it results:

Considering now that in the application of interest it can be assumed that Ro>>RL; ESR<<Ro and

RDROOP<<Ro, it results:

The ACM control loop gain is designed to obtain a high DC gain to minimize static error and 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 and the zero is fixed by ESR and the Droop re-

sistance.

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

ωF =1/RFCF is then introduced together with an integrator. This integrator minimizes the static error

while placing the zero in correspondence with the L-C resonance a simple -20dB/dec shape of the gain is

assured).

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

than the above reported zero.

LO OP s

()

PWM Z

F s

() R

DROOP

P s

()

⋅

P s

() Z

L s

()

F s

()

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

()

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

⎝⎠

⎛⎞

⋅

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

–

DROO P

SENSE

---------------------- R

⋅

PWM

---

osc

∆

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

⋅

LO OP s

()

---

OSC

∆

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

F s

()

P s

() Z

L s

()

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

--------

P s

()

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

⎝⎠

⎜⎟

⎛⎞

⋅⋅

⋅

–

LO OP s

()

---

OSC

∆

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

F s

()

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

DRO OP

-------

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

1s Co

DROOP //Ro

ESR

()

⋅⋅

---

3Ro

⋅

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

Co ESR

-------

⋅⋅

⋅

⋅⋅

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

⋅⋅

⋅

–

LO OP s

()

---

OSC

∆

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

F s

()

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

1s Co

DROOP

ESR

()

⋅⋅

---

3Ro

⋅

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

Co ESR

-------

⋅⋅

⋅

⋅⋅

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

⋅⋅

⋅

–

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