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L6758A

System control loop compensation

42

11

System control loop compensation

The control system can be modeled with an equivalent single-phase converter whose only

difference is the equivalent inductor L/N (where each phase has an L inductor and N is the

number of the configured phases), see

Figure 11.

Figure 11. Equivalent control loop.

The control loop gain results (obtained opening the loop after the COMP pin):

Equation 13

where:

•

R

LL

is the equivalent output resistance determined by the droop function (voltage

positioning)

•

Z

P

(s) is the impedance resulting from the parallel of the output capacitor (and its ESR)

and the applied load R

O

•

Z

F

(s) is the compensation network impedance

•

Z

L

(s) is the equivalent inductor impedance

•

A(s) is the error amplifier gain

•

is the PWM transfer function.

The control loop gain is designed in order to obtain a high DC gain to minimize static error

and to cross the 0 dB axes with a constant -20 dB/dec slope with the desired crossover

frequency

ω

T

. Neglecting the effect of Z

F

(s), the transfer function has one zero and two

poles; both poles are fixed once the output filter is designed (LC filter resonance

ω

LC

) and

the zero (

ω

ESR

) is fixed by ESR and the droop resistance.

AM11144v1

Ref

COMP

PWM

L/N

ESR

VID

G

LOOP

s

()

PW M

Z

F

s

() R

LL

Z

P

s

()

+

()

⋅⋅

Z

P

s

() Z

L

s

()

+

[]

Z

F

s

()

As

()

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

1

1

As

()

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

+





R

FB

⋅

+

⋅

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

–

=

PWM

9

10

------

V

IN

ΔV

OS C

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

⋅

=