L6711 datasheet(42/50 Pages) STMICROELECTRONICS

42 / 50 page

System control loop compensation

L6711

42/50

●

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 resistance.

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 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.

Compensation network can be simply designed placing

ωZ=ωLC and imposing the cross-

over frequency

ωT as desired obtaining:

PWM

---

osc

∆

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

⋅

L OOP s

()

---

OSC

∆

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

F s

()

P s

() Z

L s

()

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

--------

P s

()

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

⎝⎠

⎛⎞

⋅⋅

⋅

–

L OOP s

()

---

OSC

∆

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

F s

()

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

DROOP

-------

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

1s Co

DROOP//Ro

ESR

()

⋅⋅

---

3Ro

⋅

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

Co ESR

-------

⋅⋅

⋅

⋅⋅

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

⋅⋅

⋅

–

L OOP s

()

---

OSC

∆

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

F s

()

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

1s Co

D ROOP

ESR

()

⋅⋅

---

3Ro

⋅

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

Co ESR

-------

⋅⋅

⋅

⋅⋅

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

⋅⋅

⋅

–

OSC

∆

⋅

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

---

DROOP

ESR

()

⋅

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

⋅⋅

⋅

---

⋅

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

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