L6917B datasheet(18/33 Pages) STMICROELECTRONICS

18 / 33 page

L6917B

18/33

–ZF(s) is the compensation network impedance;

–ZL(s) is the parallel of the two inductor impedance;

– A(s) is the error amplifier gain;

–

· is the ACM PWM transfer function where DVosc is the oscillator ramp amplitude

and has a typical value of 2V

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 consid-

ered for the ZF(s) implementation. A zero at ωF=1/RFCF is then introduced together with an integrator. This in-

tegrator 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 (See Figure 12). In fact, considering the usual value for the output filter,

the LC resonance results to be at frequency lower than the above reported zero.

Figure 12. ACM Control Loop Gain Block Diagram (left) and Bode Diagram (right)

Compensation network can be simply designed placing

ωZ = ωLC and imposing the cross-over frequency ωT as

desired obtaining:

PWM

---

∆

OSC

∆

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

⋅

LOOP s

()

---

OS C

∆

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

F s

()

P s

() Z

L s

()

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

--------

P s

()

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







⋅⋅

⋅

–

LOO P s

()

---

OSC

∆

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

F s

()

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

DROOP

-------

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

1s Co

DROOP//Ro

ESR

()

⋅

---

2R o

⋅

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

Co ESR

-------

⋅

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

⋅⋅

⋅

–

LOO P s

()

---

OSC

∆

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

F s

()

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

1s Co

DROOP

ESR

()

⋅

---

2Ro

⋅

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

Co ESR

-------

⋅

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

⋅⋅

⋅

–

Rout

Cout

ESR

L/2

RFB

REF

PWM

IFB

VCOMP

VOUT

•VIN

GLOOP

ZF(s)

---

osc

∆

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

----------

⋅⋅

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