(

)

(

)

CO

ESR

O

CO

O

O

PL =

tan 2

F

R

C

tan 2

F

R

C

a

a

p

p

´

´

´

´

-

´

´

´

´

(19)

(

)

90 deg

PB = PM

PL

-

-

(20)

÷

ø

ö

ç

è

æ

+

=

deg

45

2

tan

PB

k

(21)

k

F

F

CO

Z

=

1

(22)

k

F

F

CO

P

´

=

1

(23)

CO

O

O

OA

Z

ICOMP

ggm

REF

2 ×

× F

× V

× C

× R

R

=

GM

× V

× V

p

(24)

z

Z

Z

R

F

C

´

´

´

=

1

2

1

p

(25)

z

P

P

R

F

C

´

´

´

=

1

2

1

p

(26)

TPS54331

Where:

The measured overall loop response for the circuit is given in Figure 20. Note that the actual closed loop

crossover frequency is higher than intended at about 25 kHz. This is primarily due to variation in the actual

values of the output filter components and tolerance variation of the internal feed-forward gain circuitry. Overall

the design has greater than 60 degrees of phase margin and will be completely stable over all combinations of

line and load variability.

Now that the phase loss is known the required amount of phase boost to meet the phase margin requirement

can be determined. The required phase boost is given by Equation 20:

Where PM = the desired phase margin.

A zero / pole pair of the compensation network will be placed symmetrically around the intended closed loop

frequency to provide maximum phase boost at the crossover point. The amount of separation can be determined

by Equation 21 and the resultant zero and pole frequencies are given by Equation 22 and Equation 23

The low-frequency pole is set so that the gain at the crossover frequency is equal to the inverse of the gain of the

modulator and output filter. Due to the relationships established by the pole and zero relationships, the value of

Where:

For this design, the two 47-

µF output capacitors are used. For ceramic capacitors, the actual output capacitance

is less than the rated value when the capacitors have a dc bias voltage applied. This is the case in a dc/dc

converter. The actual output capacitance may be as low as 54

µF. The combined ESR is approximately .001 Ω.

14

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