AN3028

Guidelines for feedback loop calculation

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8

Guidelines for feedback loop calculation

8.1

Transfer function

The set PWM modulator + power stage is referred to as the “power plant” and is indicated by

G1(f), while C(f) is the “controller”, i.e. the network which is in charge of ensuring the stability

of the system.

Figure 28.

Control loop block diagram

The mathematical expression of the power plant G1(f) is the following:

Equation 2

where fp is the pole due to the output load and fz the zero due to the ESR of the output

capacitor:

Equation 3

Equation 4

)

fp

f

j

(1

)

Vdc

,

fsw

(

Ipkp

)

fz

f

j

(1

Vo

)

p

f

2

j

(1

)

Vdc

,

fsw

(

Ipkp

)

z

f

2

j

(1

Vo

=

I

V

(f)

pk

O

1

⋅

+

⋅

⋅

+

⋅

=

⋅

π

⋅

⋅

+

⋅

⋅

π

⋅

⋅

+

⋅

Δ

Δ

=

G

2ESR)

+

·(R

C

1

fp

OUT

OUT

⋅

π

=

·ESR

C

2

1

fz

OUT

⋅

π

⋅

=